searching the database
Your data matches 17 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
(click to perform a complete search on your data)
Matching statistic: St000529
(load all 4 compositions to match this statistic)
(load all 4 compositions to match this statistic)
Mp00224: Binary words —runsort⟶ Binary words
St000529: Binary words ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
St000529: Binary words ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
0 => 0 => 1
1 => 1 => 1
00 => 00 => 1
01 => 01 => 2
10 => 01 => 2
11 => 11 => 1
000 => 000 => 1
001 => 001 => 3
010 => 001 => 3
011 => 011 => 3
100 => 001 => 3
101 => 011 => 3
110 => 011 => 3
111 => 111 => 1
0000 => 0000 => 1
0001 => 0001 => 4
0010 => 0001 => 4
0011 => 0011 => 6
0100 => 0001 => 4
0101 => 0101 => 16
0110 => 0011 => 6
0111 => 0111 => 4
1000 => 0001 => 4
1001 => 0011 => 6
1010 => 0011 => 6
1011 => 0111 => 4
1100 => 0011 => 6
1101 => 0111 => 4
1110 => 0111 => 4
1111 => 1111 => 1
00000 => 00000 => 1
00001 => 00001 => 5
00010 => 00001 => 5
00011 => 00011 => 10
00100 => 00001 => 5
00101 => 00101 => 35
00110 => 00011 => 10
00111 => 00111 => 10
01000 => 00001 => 5
01001 => 00101 => 35
01010 => 00101 => 35
01011 => 01011 => 35
01100 => 00011 => 10
01101 => 01011 => 35
01110 => 00111 => 10
01111 => 01111 => 5
10000 => 00001 => 5
10001 => 00011 => 10
10010 => 00011 => 10
10011 => 00111 => 10
Description
The number of permutations whose descent word is the given binary word.
This is the sizes of the preimages of the map [[Mp00109]].
Matching statistic: St000277
(load all 4 compositions to match this statistic)
(load all 4 compositions to match this statistic)
Mp00224: Binary words —runsort⟶ Binary words
Mp00178: Binary words —to composition⟶ Integer compositions
St000277: Integer compositions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00178: Binary words —to composition⟶ Integer compositions
St000277: Integer compositions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
0 => 0 => [2] => 1
1 => 1 => [1,1] => 1
00 => 00 => [3] => 1
01 => 01 => [2,1] => 2
10 => 01 => [2,1] => 2
11 => 11 => [1,1,1] => 1
000 => 000 => [4] => 1
001 => 001 => [3,1] => 3
010 => 001 => [3,1] => 3
011 => 011 => [2,1,1] => 3
100 => 001 => [3,1] => 3
101 => 011 => [2,1,1] => 3
110 => 011 => [2,1,1] => 3
111 => 111 => [1,1,1,1] => 1
0000 => 0000 => [5] => 1
0001 => 0001 => [4,1] => 4
0010 => 0001 => [4,1] => 4
0011 => 0011 => [3,1,1] => 6
0100 => 0001 => [4,1] => 4
0101 => 0101 => [2,2,1] => 16
0110 => 0011 => [3,1,1] => 6
0111 => 0111 => [2,1,1,1] => 4
1000 => 0001 => [4,1] => 4
1001 => 0011 => [3,1,1] => 6
1010 => 0011 => [3,1,1] => 6
1011 => 0111 => [2,1,1,1] => 4
1100 => 0011 => [3,1,1] => 6
1101 => 0111 => [2,1,1,1] => 4
1110 => 0111 => [2,1,1,1] => 4
1111 => 1111 => [1,1,1,1,1] => 1
00000 => 00000 => [6] => 1
00001 => 00001 => [5,1] => 5
00010 => 00001 => [5,1] => 5
00011 => 00011 => [4,1,1] => 10
00100 => 00001 => [5,1] => 5
00101 => 00101 => [3,2,1] => 35
00110 => 00011 => [4,1,1] => 10
00111 => 00111 => [3,1,1,1] => 10
01000 => 00001 => [5,1] => 5
01001 => 00101 => [3,2,1] => 35
01010 => 00101 => [3,2,1] => 35
01011 => 01011 => [2,2,1,1] => 35
01100 => 00011 => [4,1,1] => 10
01101 => 01011 => [2,2,1,1] => 35
01110 => 00111 => [3,1,1,1] => 10
01111 => 01111 => [2,1,1,1,1] => 5
10000 => 00001 => [5,1] => 5
10001 => 00011 => [4,1,1] => 10
10010 => 00011 => [4,1,1] => 10
10011 => 00111 => [3,1,1,1] => 10
Description
The number of ribbon shaped standard tableaux.
A ribbon is a connected skew shape which does not contain a $2\times 2$ square. The set of ribbon shapes are therefore in bijection with integer compositons, the parts of the composition specify the row lengths. This statistic records the number of standard tableaux of the given shape.
This is also the size of the preimage of the map 'descent composition' [[Mp00071]] from permutations to integer compositions: reading a tableau from bottom to top we obtain a permutation whose descent set is as prescribed.
For a composition $c=c_1,\dots,c_k$ of $n$, the number of ribbon shaped standard tableaux equals
$$
\sum_d (-1)^{k-\ell} \binom{n}{d_1, d_2, \dots, d_\ell},
$$
where the sum is over all coarsenings of $c$ obtained by replacing consecutive summands by their sum, see [sec 14.4, 1]
Matching statistic: St001595
Mp00224: Binary words —runsort⟶ Binary words
Mp00178: Binary words —to composition⟶ Integer compositions
Mp00180: Integer compositions —to ribbon⟶ Skew partitions
St001595: Skew partitions ⟶ ℤResult quality: 50% ●values known / values provided: 50%●distinct values known / distinct values provided: 64%
Mp00178: Binary words —to composition⟶ Integer compositions
Mp00180: Integer compositions —to ribbon⟶ Skew partitions
St001595: Skew partitions ⟶ ℤResult quality: 50% ●values known / values provided: 50%●distinct values known / distinct values provided: 64%
Values
0 => 0 => [2] => [[2],[]]
=> 1
1 => 1 => [1,1] => [[1,1],[]]
=> 1
00 => 00 => [3] => [[3],[]]
=> 1
01 => 01 => [2,1] => [[2,2],[1]]
=> 2
10 => 01 => [2,1] => [[2,2],[1]]
=> 2
11 => 11 => [1,1,1] => [[1,1,1],[]]
=> 1
000 => 000 => [4] => [[4],[]]
=> 1
001 => 001 => [3,1] => [[3,3],[2]]
=> 3
010 => 001 => [3,1] => [[3,3],[2]]
=> 3
011 => 011 => [2,1,1] => [[2,2,2],[1,1]]
=> 3
100 => 001 => [3,1] => [[3,3],[2]]
=> 3
101 => 011 => [2,1,1] => [[2,2,2],[1,1]]
=> 3
110 => 011 => [2,1,1] => [[2,2,2],[1,1]]
=> 3
111 => 111 => [1,1,1,1] => [[1,1,1,1],[]]
=> 1
0000 => 0000 => [5] => [[5],[]]
=> 1
0001 => 0001 => [4,1] => [[4,4],[3]]
=> 4
0010 => 0001 => [4,1] => [[4,4],[3]]
=> 4
0011 => 0011 => [3,1,1] => [[3,3,3],[2,2]]
=> 6
0100 => 0001 => [4,1] => [[4,4],[3]]
=> 4
0101 => 0101 => [2,2,1] => [[3,3,2],[2,1]]
=> 16
0110 => 0011 => [3,1,1] => [[3,3,3],[2,2]]
=> 6
0111 => 0111 => [2,1,1,1] => [[2,2,2,2],[1,1,1]]
=> 4
1000 => 0001 => [4,1] => [[4,4],[3]]
=> 4
1001 => 0011 => [3,1,1] => [[3,3,3],[2,2]]
=> 6
1010 => 0011 => [3,1,1] => [[3,3,3],[2,2]]
=> 6
1011 => 0111 => [2,1,1,1] => [[2,2,2,2],[1,1,1]]
=> 4
1100 => 0011 => [3,1,1] => [[3,3,3],[2,2]]
=> 6
1101 => 0111 => [2,1,1,1] => [[2,2,2,2],[1,1,1]]
=> 4
1110 => 0111 => [2,1,1,1] => [[2,2,2,2],[1,1,1]]
=> 4
1111 => 1111 => [1,1,1,1,1] => [[1,1,1,1,1],[]]
=> 1
00000 => 00000 => [6] => [[6],[]]
=> 1
00001 => 00001 => [5,1] => [[5,5],[4]]
=> 5
00010 => 00001 => [5,1] => [[5,5],[4]]
=> 5
00011 => 00011 => [4,1,1] => [[4,4,4],[3,3]]
=> 10
00100 => 00001 => [5,1] => [[5,5],[4]]
=> 5
00101 => 00101 => [3,2,1] => [[4,4,3],[3,2]]
=> 35
00110 => 00011 => [4,1,1] => [[4,4,4],[3,3]]
=> 10
00111 => 00111 => [3,1,1,1] => [[3,3,3,3],[2,2,2]]
=> 10
01000 => 00001 => [5,1] => [[5,5],[4]]
=> 5
01001 => 00101 => [3,2,1] => [[4,4,3],[3,2]]
=> 35
01010 => 00101 => [3,2,1] => [[4,4,3],[3,2]]
=> 35
01011 => 01011 => [2,2,1,1] => [[3,3,3,2],[2,2,1]]
=> 35
01100 => 00011 => [4,1,1] => [[4,4,4],[3,3]]
=> 10
01101 => 01011 => [2,2,1,1] => [[3,3,3,2],[2,2,1]]
=> 35
01110 => 00111 => [3,1,1,1] => [[3,3,3,3],[2,2,2]]
=> 10
01111 => 01111 => [2,1,1,1,1] => [[2,2,2,2,2],[1,1,1,1]]
=> 5
10000 => 00001 => [5,1] => [[5,5],[4]]
=> 5
10001 => 00011 => [4,1,1] => [[4,4,4],[3,3]]
=> 10
10010 => 00011 => [4,1,1] => [[4,4,4],[3,3]]
=> 10
10011 => 00111 => [3,1,1,1] => [[3,3,3,3],[2,2,2]]
=> 10
0000000 => 0000000 => [8] => [[8],[]]
=> ? ∊ {1,1,7,7,7,7,7,7,7,7,7,7,7,7,7,7,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,105,105,105,105,105,105,105,105,105,105,105,105,105,105,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,203,203,203,203,203,203,245,245,245,245,259,259,315,315,315,315,315,315,315,315,791,791,791,791,791,791,791,791}
0000001 => 0000001 => [7,1] => [[7,7],[6]]
=> ? ∊ {1,1,7,7,7,7,7,7,7,7,7,7,7,7,7,7,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,105,105,105,105,105,105,105,105,105,105,105,105,105,105,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,203,203,203,203,203,203,245,245,245,245,259,259,315,315,315,315,315,315,315,315,791,791,791,791,791,791,791,791}
0000010 => 0000001 => [7,1] => [[7,7],[6]]
=> ? ∊ {1,1,7,7,7,7,7,7,7,7,7,7,7,7,7,7,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,105,105,105,105,105,105,105,105,105,105,105,105,105,105,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,203,203,203,203,203,203,245,245,245,245,259,259,315,315,315,315,315,315,315,315,791,791,791,791,791,791,791,791}
0000011 => 0000011 => [6,1,1] => [[6,6,6],[5,5]]
=> ? ∊ {1,1,7,7,7,7,7,7,7,7,7,7,7,7,7,7,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,105,105,105,105,105,105,105,105,105,105,105,105,105,105,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,203,203,203,203,203,203,245,245,245,245,259,259,315,315,315,315,315,315,315,315,791,791,791,791,791,791,791,791}
0000100 => 0000001 => [7,1] => [[7,7],[6]]
=> ? ∊ {1,1,7,7,7,7,7,7,7,7,7,7,7,7,7,7,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,105,105,105,105,105,105,105,105,105,105,105,105,105,105,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,203,203,203,203,203,203,245,245,245,245,259,259,315,315,315,315,315,315,315,315,791,791,791,791,791,791,791,791}
0000101 => 0000101 => [5,2,1] => [[6,6,5],[5,4]]
=> ? ∊ {1,1,7,7,7,7,7,7,7,7,7,7,7,7,7,7,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,105,105,105,105,105,105,105,105,105,105,105,105,105,105,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,203,203,203,203,203,203,245,245,245,245,259,259,315,315,315,315,315,315,315,315,791,791,791,791,791,791,791,791}
0000110 => 0000011 => [6,1,1] => [[6,6,6],[5,5]]
=> ? ∊ {1,1,7,7,7,7,7,7,7,7,7,7,7,7,7,7,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,105,105,105,105,105,105,105,105,105,105,105,105,105,105,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,203,203,203,203,203,203,245,245,245,245,259,259,315,315,315,315,315,315,315,315,791,791,791,791,791,791,791,791}
0000111 => 0000111 => [5,1,1,1] => [[5,5,5,5],[4,4,4]]
=> ? ∊ {1,1,7,7,7,7,7,7,7,7,7,7,7,7,7,7,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,105,105,105,105,105,105,105,105,105,105,105,105,105,105,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,203,203,203,203,203,203,245,245,245,245,259,259,315,315,315,315,315,315,315,315,791,791,791,791,791,791,791,791}
0001000 => 0000001 => [7,1] => [[7,7],[6]]
=> ? ∊ {1,1,7,7,7,7,7,7,7,7,7,7,7,7,7,7,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,105,105,105,105,105,105,105,105,105,105,105,105,105,105,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,203,203,203,203,203,203,245,245,245,245,259,259,315,315,315,315,315,315,315,315,791,791,791,791,791,791,791,791}
0001001 => 0001001 => [4,3,1] => [[6,6,4],[5,3]]
=> ? ∊ {1,1,7,7,7,7,7,7,7,7,7,7,7,7,7,7,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,105,105,105,105,105,105,105,105,105,105,105,105,105,105,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,203,203,203,203,203,203,245,245,245,245,259,259,315,315,315,315,315,315,315,315,791,791,791,791,791,791,791,791}
0001010 => 0000101 => [5,2,1] => [[6,6,5],[5,4]]
=> ? ∊ {1,1,7,7,7,7,7,7,7,7,7,7,7,7,7,7,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,105,105,105,105,105,105,105,105,105,105,105,105,105,105,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,203,203,203,203,203,203,245,245,245,245,259,259,315,315,315,315,315,315,315,315,791,791,791,791,791,791,791,791}
0001011 => 0001011 => [4,2,1,1] => [[5,5,5,4],[4,4,3]]
=> ? ∊ {1,1,7,7,7,7,7,7,7,7,7,7,7,7,7,7,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,105,105,105,105,105,105,105,105,105,105,105,105,105,105,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,203,203,203,203,203,203,245,245,245,245,259,259,315,315,315,315,315,315,315,315,791,791,791,791,791,791,791,791}
0001100 => 0000011 => [6,1,1] => [[6,6,6],[5,5]]
=> ? ∊ {1,1,7,7,7,7,7,7,7,7,7,7,7,7,7,7,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,105,105,105,105,105,105,105,105,105,105,105,105,105,105,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,203,203,203,203,203,203,245,245,245,245,259,259,315,315,315,315,315,315,315,315,791,791,791,791,791,791,791,791}
0001101 => 0001101 => [4,1,2,1] => [[5,5,4,4],[4,3,3]]
=> ? ∊ {1,1,7,7,7,7,7,7,7,7,7,7,7,7,7,7,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,105,105,105,105,105,105,105,105,105,105,105,105,105,105,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,203,203,203,203,203,203,245,245,245,245,259,259,315,315,315,315,315,315,315,315,791,791,791,791,791,791,791,791}
0001110 => 0000111 => [5,1,1,1] => [[5,5,5,5],[4,4,4]]
=> ? ∊ {1,1,7,7,7,7,7,7,7,7,7,7,7,7,7,7,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,105,105,105,105,105,105,105,105,105,105,105,105,105,105,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,203,203,203,203,203,203,245,245,245,245,259,259,315,315,315,315,315,315,315,315,791,791,791,791,791,791,791,791}
0001111 => 0001111 => [4,1,1,1,1] => [[4,4,4,4,4],[3,3,3,3]]
=> ? ∊ {1,1,7,7,7,7,7,7,7,7,7,7,7,7,7,7,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,105,105,105,105,105,105,105,105,105,105,105,105,105,105,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,203,203,203,203,203,203,245,245,245,245,259,259,315,315,315,315,315,315,315,315,791,791,791,791,791,791,791,791}
0010000 => 0000001 => [7,1] => [[7,7],[6]]
=> ? ∊ {1,1,7,7,7,7,7,7,7,7,7,7,7,7,7,7,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,105,105,105,105,105,105,105,105,105,105,105,105,105,105,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,203,203,203,203,203,203,245,245,245,245,259,259,315,315,315,315,315,315,315,315,791,791,791,791,791,791,791,791}
0010001 => 0001001 => [4,3,1] => [[6,6,4],[5,3]]
=> ? ∊ {1,1,7,7,7,7,7,7,7,7,7,7,7,7,7,7,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,105,105,105,105,105,105,105,105,105,105,105,105,105,105,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,203,203,203,203,203,203,245,245,245,245,259,259,315,315,315,315,315,315,315,315,791,791,791,791,791,791,791,791}
0010010 => 0001001 => [4,3,1] => [[6,6,4],[5,3]]
=> ? ∊ {1,1,7,7,7,7,7,7,7,7,7,7,7,7,7,7,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,105,105,105,105,105,105,105,105,105,105,105,105,105,105,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,203,203,203,203,203,203,245,245,245,245,259,259,315,315,315,315,315,315,315,315,791,791,791,791,791,791,791,791}
0010011 => 0010011 => [3,3,1,1] => [[5,5,5,3],[4,4,2]]
=> ? ∊ {1,1,7,7,7,7,7,7,7,7,7,7,7,7,7,7,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,105,105,105,105,105,105,105,105,105,105,105,105,105,105,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,203,203,203,203,203,203,245,245,245,245,259,259,315,315,315,315,315,315,315,315,791,791,791,791,791,791,791,791}
0010100 => 0000101 => [5,2,1] => [[6,6,5],[5,4]]
=> ? ∊ {1,1,7,7,7,7,7,7,7,7,7,7,7,7,7,7,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,105,105,105,105,105,105,105,105,105,105,105,105,105,105,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,203,203,203,203,203,203,245,245,245,245,259,259,315,315,315,315,315,315,315,315,791,791,791,791,791,791,791,791}
0010101 => 0010101 => [3,2,2,1] => [[5,5,4,3],[4,3,2]]
=> ? ∊ {1,1,7,7,7,7,7,7,7,7,7,7,7,7,7,7,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,105,105,105,105,105,105,105,105,105,105,105,105,105,105,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,203,203,203,203,203,203,245,245,245,245,259,259,315,315,315,315,315,315,315,315,791,791,791,791,791,791,791,791}
0010110 => 0001011 => [4,2,1,1] => [[5,5,5,4],[4,4,3]]
=> ? ∊ {1,1,7,7,7,7,7,7,7,7,7,7,7,7,7,7,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,105,105,105,105,105,105,105,105,105,105,105,105,105,105,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,203,203,203,203,203,203,245,245,245,245,259,259,315,315,315,315,315,315,315,315,791,791,791,791,791,791,791,791}
0010111 => 0010111 => [3,2,1,1,1] => [[4,4,4,4,3],[3,3,3,2]]
=> ? ∊ {1,1,7,7,7,7,7,7,7,7,7,7,7,7,7,7,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,105,105,105,105,105,105,105,105,105,105,105,105,105,105,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,203,203,203,203,203,203,245,245,245,245,259,259,315,315,315,315,315,315,315,315,791,791,791,791,791,791,791,791}
0011000 => 0000011 => [6,1,1] => [[6,6,6],[5,5]]
=> ? ∊ {1,1,7,7,7,7,7,7,7,7,7,7,7,7,7,7,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,105,105,105,105,105,105,105,105,105,105,105,105,105,105,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,203,203,203,203,203,203,245,245,245,245,259,259,315,315,315,315,315,315,315,315,791,791,791,791,791,791,791,791}
0011001 => 0010011 => [3,3,1,1] => [[5,5,5,3],[4,4,2]]
=> ? ∊ {1,1,7,7,7,7,7,7,7,7,7,7,7,7,7,7,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,105,105,105,105,105,105,105,105,105,105,105,105,105,105,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,203,203,203,203,203,203,245,245,245,245,259,259,315,315,315,315,315,315,315,315,791,791,791,791,791,791,791,791}
0011010 => 0001101 => [4,1,2,1] => [[5,5,4,4],[4,3,3]]
=> ? ∊ {1,1,7,7,7,7,7,7,7,7,7,7,7,7,7,7,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,105,105,105,105,105,105,105,105,105,105,105,105,105,105,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,203,203,203,203,203,203,245,245,245,245,259,259,315,315,315,315,315,315,315,315,791,791,791,791,791,791,791,791}
0011011 => 0011011 => [3,1,2,1,1] => [[4,4,4,3,3],[3,3,2,2]]
=> ? ∊ {1,1,7,7,7,7,7,7,7,7,7,7,7,7,7,7,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,105,105,105,105,105,105,105,105,105,105,105,105,105,105,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,203,203,203,203,203,203,245,245,245,245,259,259,315,315,315,315,315,315,315,315,791,791,791,791,791,791,791,791}
0011100 => 0000111 => [5,1,1,1] => [[5,5,5,5],[4,4,4]]
=> ? ∊ {1,1,7,7,7,7,7,7,7,7,7,7,7,7,7,7,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,105,105,105,105,105,105,105,105,105,105,105,105,105,105,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,203,203,203,203,203,203,245,245,245,245,259,259,315,315,315,315,315,315,315,315,791,791,791,791,791,791,791,791}
0011101 => 0011101 => [3,1,1,2,1] => [[4,4,3,3,3],[3,2,2,2]]
=> ? ∊ {1,1,7,7,7,7,7,7,7,7,7,7,7,7,7,7,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,105,105,105,105,105,105,105,105,105,105,105,105,105,105,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,203,203,203,203,203,203,245,245,245,245,259,259,315,315,315,315,315,315,315,315,791,791,791,791,791,791,791,791}
0011110 => 0001111 => [4,1,1,1,1] => [[4,4,4,4,4],[3,3,3,3]]
=> ? ∊ {1,1,7,7,7,7,7,7,7,7,7,7,7,7,7,7,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,105,105,105,105,105,105,105,105,105,105,105,105,105,105,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,203,203,203,203,203,203,245,245,245,245,259,259,315,315,315,315,315,315,315,315,791,791,791,791,791,791,791,791}
0011111 => 0011111 => [3,1,1,1,1,1] => [[3,3,3,3,3,3],[2,2,2,2,2]]
=> ? ∊ {1,1,7,7,7,7,7,7,7,7,7,7,7,7,7,7,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,105,105,105,105,105,105,105,105,105,105,105,105,105,105,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,203,203,203,203,203,203,245,245,245,245,259,259,315,315,315,315,315,315,315,315,791,791,791,791,791,791,791,791}
0100000 => 0000001 => [7,1] => [[7,7],[6]]
=> ? ∊ {1,1,7,7,7,7,7,7,7,7,7,7,7,7,7,7,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,105,105,105,105,105,105,105,105,105,105,105,105,105,105,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,203,203,203,203,203,203,245,245,245,245,259,259,315,315,315,315,315,315,315,315,791,791,791,791,791,791,791,791}
0100001 => 0000101 => [5,2,1] => [[6,6,5],[5,4]]
=> ? ∊ {1,1,7,7,7,7,7,7,7,7,7,7,7,7,7,7,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,105,105,105,105,105,105,105,105,105,105,105,105,105,105,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,203,203,203,203,203,203,245,245,245,245,259,259,315,315,315,315,315,315,315,315,791,791,791,791,791,791,791,791}
0100010 => 0000101 => [5,2,1] => [[6,6,5],[5,4]]
=> ? ∊ {1,1,7,7,7,7,7,7,7,7,7,7,7,7,7,7,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,105,105,105,105,105,105,105,105,105,105,105,105,105,105,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,203,203,203,203,203,203,245,245,245,245,259,259,315,315,315,315,315,315,315,315,791,791,791,791,791,791,791,791}
0100011 => 0001101 => [4,1,2,1] => [[5,5,4,4],[4,3,3]]
=> ? ∊ {1,1,7,7,7,7,7,7,7,7,7,7,7,7,7,7,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,105,105,105,105,105,105,105,105,105,105,105,105,105,105,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,203,203,203,203,203,203,245,245,245,245,259,259,315,315,315,315,315,315,315,315,791,791,791,791,791,791,791,791}
0100100 => 0000101 => [5,2,1] => [[6,6,5],[5,4]]
=> ? ∊ {1,1,7,7,7,7,7,7,7,7,7,7,7,7,7,7,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,105,105,105,105,105,105,105,105,105,105,105,105,105,105,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,203,203,203,203,203,203,245,245,245,245,259,259,315,315,315,315,315,315,315,315,791,791,791,791,791,791,791,791}
0100101 => 0010101 => [3,2,2,1] => [[5,5,4,3],[4,3,2]]
=> ? ∊ {1,1,7,7,7,7,7,7,7,7,7,7,7,7,7,7,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,105,105,105,105,105,105,105,105,105,105,105,105,105,105,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,203,203,203,203,203,203,245,245,245,245,259,259,315,315,315,315,315,315,315,315,791,791,791,791,791,791,791,791}
0100110 => 0001101 => [4,1,2,1] => [[5,5,4,4],[4,3,3]]
=> ? ∊ {1,1,7,7,7,7,7,7,7,7,7,7,7,7,7,7,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,105,105,105,105,105,105,105,105,105,105,105,105,105,105,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,203,203,203,203,203,203,245,245,245,245,259,259,315,315,315,315,315,315,315,315,791,791,791,791,791,791,791,791}
0100111 => 0011101 => [3,1,1,2,1] => [[4,4,3,3,3],[3,2,2,2]]
=> ? ∊ {1,1,7,7,7,7,7,7,7,7,7,7,7,7,7,7,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,105,105,105,105,105,105,105,105,105,105,105,105,105,105,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,203,203,203,203,203,203,245,245,245,245,259,259,315,315,315,315,315,315,315,315,791,791,791,791,791,791,791,791}
0101000 => 0000101 => [5,2,1] => [[6,6,5],[5,4]]
=> ? ∊ {1,1,7,7,7,7,7,7,7,7,7,7,7,7,7,7,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,105,105,105,105,105,105,105,105,105,105,105,105,105,105,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,203,203,203,203,203,203,245,245,245,245,259,259,315,315,315,315,315,315,315,315,791,791,791,791,791,791,791,791}
0101001 => 0010101 => [3,2,2,1] => [[5,5,4,3],[4,3,2]]
=> ? ∊ {1,1,7,7,7,7,7,7,7,7,7,7,7,7,7,7,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,105,105,105,105,105,105,105,105,105,105,105,105,105,105,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,203,203,203,203,203,203,245,245,245,245,259,259,315,315,315,315,315,315,315,315,791,791,791,791,791,791,791,791}
0101010 => 0010101 => [3,2,2,1] => [[5,5,4,3],[4,3,2]]
=> ? ∊ {1,1,7,7,7,7,7,7,7,7,7,7,7,7,7,7,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,105,105,105,105,105,105,105,105,105,105,105,105,105,105,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,203,203,203,203,203,203,245,245,245,245,259,259,315,315,315,315,315,315,315,315,791,791,791,791,791,791,791,791}
0101011 => 0101011 => [2,2,2,1,1] => [[4,4,4,3,2],[3,3,2,1]]
=> ? ∊ {1,1,7,7,7,7,7,7,7,7,7,7,7,7,7,7,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,105,105,105,105,105,105,105,105,105,105,105,105,105,105,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,203,203,203,203,203,203,245,245,245,245,259,259,315,315,315,315,315,315,315,315,791,791,791,791,791,791,791,791}
0101100 => 0001011 => [4,2,1,1] => [[5,5,5,4],[4,4,3]]
=> ? ∊ {1,1,7,7,7,7,7,7,7,7,7,7,7,7,7,7,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,105,105,105,105,105,105,105,105,105,105,105,105,105,105,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,203,203,203,203,203,203,245,245,245,245,259,259,315,315,315,315,315,315,315,315,791,791,791,791,791,791,791,791}
0101101 => 0101011 => [2,2,2,1,1] => [[4,4,4,3,2],[3,3,2,1]]
=> ? ∊ {1,1,7,7,7,7,7,7,7,7,7,7,7,7,7,7,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,105,105,105,105,105,105,105,105,105,105,105,105,105,105,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,203,203,203,203,203,203,245,245,245,245,259,259,315,315,315,315,315,315,315,315,791,791,791,791,791,791,791,791}
0101110 => 0010111 => [3,2,1,1,1] => [[4,4,4,4,3],[3,3,3,2]]
=> ? ∊ {1,1,7,7,7,7,7,7,7,7,7,7,7,7,7,7,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,105,105,105,105,105,105,105,105,105,105,105,105,105,105,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,203,203,203,203,203,203,245,245,245,245,259,259,315,315,315,315,315,315,315,315,791,791,791,791,791,791,791,791}
0101111 => 0101111 => [2,2,1,1,1,1] => [[3,3,3,3,3,2],[2,2,2,2,1]]
=> ? ∊ {1,1,7,7,7,7,7,7,7,7,7,7,7,7,7,7,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,105,105,105,105,105,105,105,105,105,105,105,105,105,105,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,203,203,203,203,203,203,245,245,245,245,259,259,315,315,315,315,315,315,315,315,791,791,791,791,791,791,791,791}
0110000 => 0000011 => [6,1,1] => [[6,6,6],[5,5]]
=> ? ∊ {1,1,7,7,7,7,7,7,7,7,7,7,7,7,7,7,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,105,105,105,105,105,105,105,105,105,105,105,105,105,105,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,203,203,203,203,203,203,245,245,245,245,259,259,315,315,315,315,315,315,315,315,791,791,791,791,791,791,791,791}
0110001 => 0001011 => [4,2,1,1] => [[5,5,5,4],[4,4,3]]
=> ? ∊ {1,1,7,7,7,7,7,7,7,7,7,7,7,7,7,7,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,105,105,105,105,105,105,105,105,105,105,105,105,105,105,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,203,203,203,203,203,203,245,245,245,245,259,259,315,315,315,315,315,315,315,315,791,791,791,791,791,791,791,791}
Description
The number of standard Young tableaux of the skew partition.
Matching statistic: St000071
Mp00224: Binary words —runsort⟶ Binary words
Mp00262: Binary words —poset of factors⟶ Posets
St000071: Posets ⟶ ℤResult quality: 36% ●values known / values provided: 39%●distinct values known / distinct values provided: 36%
Mp00262: Binary words —poset of factors⟶ Posets
St000071: Posets ⟶ ℤResult quality: 36% ●values known / values provided: 39%●distinct values known / distinct values provided: 36%
Values
0 => 0 => ([(0,1)],2)
=> 1
1 => 1 => ([(0,1)],2)
=> 1
00 => 00 => ([(0,2),(2,1)],3)
=> 1
01 => 01 => ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
10 => 01 => ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
11 => 11 => ([(0,2),(2,1)],3)
=> 1
000 => 000 => ([(0,3),(2,1),(3,2)],4)
=> 1
001 => 001 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 3
010 => 001 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 3
011 => 011 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 3
100 => 001 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 3
101 => 011 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 3
110 => 011 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 3
111 => 111 => ([(0,3),(2,1),(3,2)],4)
=> 1
0000 => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
0001 => 0001 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> 4
0010 => 0001 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> 4
0011 => 0011 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> 6
0100 => 0001 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> 4
0101 => 0101 => ([(0,1),(0,2),(1,6),(1,7),(2,6),(2,7),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5)],8)
=> ? = 16
0110 => 0011 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> 6
0111 => 0111 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> 4
1000 => 0001 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> 4
1001 => 0011 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> 6
1010 => 0011 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> 6
1011 => 0111 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> 4
1100 => 0011 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> 6
1101 => 0111 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> 4
1110 => 0111 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> 4
1111 => 1111 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
00000 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1
00001 => 00001 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> 5
00010 => 00001 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> 5
00011 => 00011 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> 10
00100 => 00001 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> 5
00101 => 00101 => ([(0,2),(0,3),(1,8),(2,10),(2,11),(3,1),(3,10),(3,11),(5,6),(6,4),(7,4),(8,7),(9,6),(9,7),(10,5),(10,9),(11,5),(11,8),(11,9)],12)
=> ? ∊ {35,35,35,35,35,35}
00110 => 00011 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> 10
00111 => 00111 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> 10
01000 => 00001 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> 5
01001 => 00101 => ([(0,2),(0,3),(1,8),(2,10),(2,11),(3,1),(3,10),(3,11),(5,6),(6,4),(7,4),(8,7),(9,6),(9,7),(10,5),(10,9),(11,5),(11,8),(11,9)],12)
=> ? ∊ {35,35,35,35,35,35}
01010 => 00101 => ([(0,2),(0,3),(1,8),(2,10),(2,11),(3,1),(3,10),(3,11),(5,6),(6,4),(7,4),(8,7),(9,6),(9,7),(10,5),(10,9),(11,5),(11,8),(11,9)],12)
=> ? ∊ {35,35,35,35,35,35}
01011 => 01011 => ([(0,2),(0,3),(1,8),(2,10),(2,11),(3,1),(3,10),(3,11),(5,6),(6,4),(7,4),(8,7),(9,6),(9,7),(10,5),(10,9),(11,5),(11,8),(11,9)],12)
=> ? ∊ {35,35,35,35,35,35}
01100 => 00011 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> 10
01101 => 01011 => ([(0,2),(0,3),(1,8),(2,10),(2,11),(3,1),(3,10),(3,11),(5,6),(6,4),(7,4),(8,7),(9,6),(9,7),(10,5),(10,9),(11,5),(11,8),(11,9)],12)
=> ? ∊ {35,35,35,35,35,35}
01110 => 00111 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> 10
01111 => 01111 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> 5
10000 => 00001 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> 5
10001 => 00011 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> 10
10010 => 00011 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> 10
10011 => 00111 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> 10
10100 => 00011 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> 10
10101 => 01011 => ([(0,2),(0,3),(1,8),(2,10),(2,11),(3,1),(3,10),(3,11),(5,6),(6,4),(7,4),(8,7),(9,6),(9,7),(10,5),(10,9),(11,5),(11,8),(11,9)],12)
=> ? ∊ {35,35,35,35,35,35}
10110 => 00111 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> 10
10111 => 01111 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> 5
11000 => 00011 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> 10
11001 => 00111 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> 10
11010 => 00111 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> 10
000101 => 000101 => ([(0,3),(0,4),(1,2),(1,14),(2,6),(3,13),(3,15),(4,1),(4,13),(4,15),(6,9),(7,8),(8,10),(9,5),(10,5),(11,8),(11,12),(12,9),(12,10),(13,7),(13,11),(14,6),(14,12),(15,7),(15,11),(15,14)],16)
=> ? ∊ {64,64,64,64,64,64,64,64,64,64,90,90,90,90,90,90,90,99,99,111,111,272}
001001 => 001001 => ([(0,2),(0,3),(1,11),(1,12),(2,13),(2,14),(3,1),(3,13),(3,14),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,9),(11,6),(11,9),(12,5),(12,6),(13,10),(13,11),(14,10),(14,12)],15)
=> ? ∊ {64,64,64,64,64,64,64,64,64,64,90,90,90,90,90,90,90,99,99,111,111,272}
001010 => 000101 => ([(0,3),(0,4),(1,2),(1,14),(2,6),(3,13),(3,15),(4,1),(4,13),(4,15),(6,9),(7,8),(8,10),(9,5),(10,5),(11,8),(11,12),(12,9),(12,10),(13,7),(13,11),(14,6),(14,12),(15,7),(15,11),(15,14)],16)
=> ? ∊ {64,64,64,64,64,64,64,64,64,64,90,90,90,90,90,90,90,99,99,111,111,272}
001011 => 001011 => ([(0,3),(0,4),(1,11),(2,10),(3,2),(3,15),(3,16),(4,1),(4,15),(4,16),(6,8),(7,9),(8,5),(9,5),(10,6),(11,7),(12,6),(12,14),(13,7),(13,14),(14,8),(14,9),(15,12),(15,13),(16,10),(16,11),(16,12),(16,13)],17)
=> ? ∊ {64,64,64,64,64,64,64,64,64,64,90,90,90,90,90,90,90,99,99,111,111,272}
001101 => 001101 => ([(0,3),(0,4),(1,11),(2,12),(2,13),(3,2),(3,15),(3,16),(4,1),(4,15),(4,16),(6,7),(7,9),(8,10),(9,5),(10,5),(11,8),(12,7),(12,14),(13,8),(13,14),(14,9),(14,10),(15,6),(15,12),(16,6),(16,11),(16,13)],17)
=> ? ∊ {64,64,64,64,64,64,64,64,64,64,90,90,90,90,90,90,90,99,99,111,111,272}
010001 => 000101 => ([(0,3),(0,4),(1,2),(1,14),(2,6),(3,13),(3,15),(4,1),(4,13),(4,15),(6,9),(7,8),(8,10),(9,5),(10,5),(11,8),(11,12),(12,9),(12,10),(13,7),(13,11),(14,6),(14,12),(15,7),(15,11),(15,14)],16)
=> ? ∊ {64,64,64,64,64,64,64,64,64,64,90,90,90,90,90,90,90,99,99,111,111,272}
010010 => 000101 => ([(0,3),(0,4),(1,2),(1,14),(2,6),(3,13),(3,15),(4,1),(4,13),(4,15),(6,9),(7,8),(8,10),(9,5),(10,5),(11,8),(11,12),(12,9),(12,10),(13,7),(13,11),(14,6),(14,12),(15,7),(15,11),(15,14)],16)
=> ? ∊ {64,64,64,64,64,64,64,64,64,64,90,90,90,90,90,90,90,99,99,111,111,272}
010011 => 001101 => ([(0,3),(0,4),(1,11),(2,12),(2,13),(3,2),(3,15),(3,16),(4,1),(4,15),(4,16),(6,7),(7,9),(8,10),(9,5),(10,5),(11,8),(12,7),(12,14),(13,8),(13,14),(14,9),(14,10),(15,6),(15,12),(16,6),(16,11),(16,13)],17)
=> ? ∊ {64,64,64,64,64,64,64,64,64,64,90,90,90,90,90,90,90,99,99,111,111,272}
010100 => 000101 => ([(0,3),(0,4),(1,2),(1,14),(2,6),(3,13),(3,15),(4,1),(4,13),(4,15),(6,9),(7,8),(8,10),(9,5),(10,5),(11,8),(11,12),(12,9),(12,10),(13,7),(13,11),(14,6),(14,12),(15,7),(15,11),(15,14)],16)
=> ? ∊ {64,64,64,64,64,64,64,64,64,64,90,90,90,90,90,90,90,99,99,111,111,272}
010101 => 010101 => ([(0,1),(0,2),(1,10),(1,11),(2,10),(2,11),(4,3),(5,3),(6,8),(6,9),(7,8),(7,9),(8,4),(8,5),(9,4),(9,5),(10,6),(10,7),(11,6),(11,7)],12)
=> ? ∊ {64,64,64,64,64,64,64,64,64,64,90,90,90,90,90,90,90,99,99,111,111,272}
010110 => 001011 => ([(0,3),(0,4),(1,11),(2,10),(3,2),(3,15),(3,16),(4,1),(4,15),(4,16),(6,8),(7,9),(8,5),(9,5),(10,6),(11,7),(12,6),(12,14),(13,7),(13,14),(14,8),(14,9),(15,12),(15,13),(16,10),(16,11),(16,12),(16,13)],17)
=> ? ∊ {64,64,64,64,64,64,64,64,64,64,90,90,90,90,90,90,90,99,99,111,111,272}
010111 => 010111 => ([(0,3),(0,4),(1,2),(1,14),(2,6),(3,13),(3,15),(4,1),(4,13),(4,15),(6,9),(7,8),(8,10),(9,5),(10,5),(11,8),(11,12),(12,9),(12,10),(13,7),(13,11),(14,6),(14,12),(15,7),(15,11),(15,14)],16)
=> ? ∊ {64,64,64,64,64,64,64,64,64,64,90,90,90,90,90,90,90,99,99,111,111,272}
011001 => 001011 => ([(0,3),(0,4),(1,11),(2,10),(3,2),(3,15),(3,16),(4,1),(4,15),(4,16),(6,8),(7,9),(8,5),(9,5),(10,6),(11,7),(12,6),(12,14),(13,7),(13,14),(14,8),(14,9),(15,12),(15,13),(16,10),(16,11),(16,12),(16,13)],17)
=> ? ∊ {64,64,64,64,64,64,64,64,64,64,90,90,90,90,90,90,90,99,99,111,111,272}
011010 => 001011 => ([(0,3),(0,4),(1,11),(2,10),(3,2),(3,15),(3,16),(4,1),(4,15),(4,16),(6,8),(7,9),(8,5),(9,5),(10,6),(11,7),(12,6),(12,14),(13,7),(13,14),(14,8),(14,9),(15,12),(15,13),(16,10),(16,11),(16,12),(16,13)],17)
=> ? ∊ {64,64,64,64,64,64,64,64,64,64,90,90,90,90,90,90,90,99,99,111,111,272}
011011 => 011011 => ([(0,2),(0,3),(1,11),(1,12),(2,13),(2,14),(3,1),(3,13),(3,14),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,9),(11,6),(11,9),(12,5),(12,6),(13,10),(13,11),(14,10),(14,12)],15)
=> ? ∊ {64,64,64,64,64,64,64,64,64,64,90,90,90,90,90,90,90,99,99,111,111,272}
011101 => 010111 => ([(0,3),(0,4),(1,2),(1,14),(2,6),(3,13),(3,15),(4,1),(4,13),(4,15),(6,9),(7,8),(8,10),(9,5),(10,5),(11,8),(11,12),(12,9),(12,10),(13,7),(13,11),(14,6),(14,12),(15,7),(15,11),(15,14)],16)
=> ? ∊ {64,64,64,64,64,64,64,64,64,64,90,90,90,90,90,90,90,99,99,111,111,272}
100101 => 001011 => ([(0,3),(0,4),(1,11),(2,10),(3,2),(3,15),(3,16),(4,1),(4,15),(4,16),(6,8),(7,9),(8,5),(9,5),(10,6),(11,7),(12,6),(12,14),(13,7),(13,14),(14,8),(14,9),(15,12),(15,13),(16,10),(16,11),(16,12),(16,13)],17)
=> ? ∊ {64,64,64,64,64,64,64,64,64,64,90,90,90,90,90,90,90,99,99,111,111,272}
101001 => 001011 => ([(0,3),(0,4),(1,11),(2,10),(3,2),(3,15),(3,16),(4,1),(4,15),(4,16),(6,8),(7,9),(8,5),(9,5),(10,6),(11,7),(12,6),(12,14),(13,7),(13,14),(14,8),(14,9),(15,12),(15,13),(16,10),(16,11),(16,12),(16,13)],17)
=> ? ∊ {64,64,64,64,64,64,64,64,64,64,90,90,90,90,90,90,90,99,99,111,111,272}
101010 => 001011 => ([(0,3),(0,4),(1,11),(2,10),(3,2),(3,15),(3,16),(4,1),(4,15),(4,16),(6,8),(7,9),(8,5),(9,5),(10,6),(11,7),(12,6),(12,14),(13,7),(13,14),(14,8),(14,9),(15,12),(15,13),(16,10),(16,11),(16,12),(16,13)],17)
=> ? ∊ {64,64,64,64,64,64,64,64,64,64,90,90,90,90,90,90,90,99,99,111,111,272}
101011 => 010111 => ([(0,3),(0,4),(1,2),(1,14),(2,6),(3,13),(3,15),(4,1),(4,13),(4,15),(6,9),(7,8),(8,10),(9,5),(10,5),(11,8),(11,12),(12,9),(12,10),(13,7),(13,11),(14,6),(14,12),(15,7),(15,11),(15,14)],16)
=> ? ∊ {64,64,64,64,64,64,64,64,64,64,90,90,90,90,90,90,90,99,99,111,111,272}
101101 => 010111 => ([(0,3),(0,4),(1,2),(1,14),(2,6),(3,13),(3,15),(4,1),(4,13),(4,15),(6,9),(7,8),(8,10),(9,5),(10,5),(11,8),(11,12),(12,9),(12,10),(13,7),(13,11),(14,6),(14,12),(15,7),(15,11),(15,14)],16)
=> ? ∊ {64,64,64,64,64,64,64,64,64,64,90,90,90,90,90,90,90,99,99,111,111,272}
110101 => 010111 => ([(0,3),(0,4),(1,2),(1,14),(2,6),(3,13),(3,15),(4,1),(4,13),(4,15),(6,9),(7,8),(8,10),(9,5),(10,5),(11,8),(11,12),(12,9),(12,10),(13,7),(13,11),(14,6),(14,12),(15,7),(15,11),(15,14)],16)
=> ? ∊ {64,64,64,64,64,64,64,64,64,64,90,90,90,90,90,90,90,99,99,111,111,272}
0000001 => 0000001 => ([(0,2),(0,7),(1,9),(2,8),(3,4),(3,11),(4,6),(4,10),(5,3),(5,13),(6,1),(6,12),(7,5),(7,8),(8,13),(10,12),(11,10),(12,9),(13,11)],14)
=> ? ∊ {7,7,7,7,7,7,7,7,7,7,7,7,7,7,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,105,105,105,105,105,105,105,105,105,105,105,105,105,105,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,203,203,203,203,203,203,245,245,245,245,259,259,315,315,315,315,315,315,315,315,791,791,791,791,791,791,791,791}
0000010 => 0000001 => ([(0,2),(0,7),(1,9),(2,8),(3,4),(3,11),(4,6),(4,10),(5,3),(5,13),(6,1),(6,12),(7,5),(7,8),(8,13),(10,12),(11,10),(12,9),(13,11)],14)
=> ? ∊ {7,7,7,7,7,7,7,7,7,7,7,7,7,7,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,105,105,105,105,105,105,105,105,105,105,105,105,105,105,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,203,203,203,203,203,203,245,245,245,245,259,259,315,315,315,315,315,315,315,315,791,791,791,791,791,791,791,791}
0000011 => 0000011 => ([(0,6),(0,7),(1,11),(2,5),(2,15),(3,13),(4,3),(4,17),(5,4),(5,16),(6,2),(6,14),(7,1),(7,14),(9,12),(10,9),(11,10),(12,8),(13,8),(14,11),(14,15),(15,10),(15,16),(16,9),(16,17),(17,12),(17,13)],18)
=> ? ∊ {7,7,7,7,7,7,7,7,7,7,7,7,7,7,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,105,105,105,105,105,105,105,105,105,105,105,105,105,105,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,203,203,203,203,203,203,245,245,245,245,259,259,315,315,315,315,315,315,315,315,791,791,791,791,791,791,791,791}
0000100 => 0000001 => ([(0,2),(0,7),(1,9),(2,8),(3,4),(3,11),(4,6),(4,10),(5,3),(5,13),(6,1),(6,12),(7,5),(7,8),(8,13),(10,12),(11,10),(12,9),(13,11)],14)
=> ? ∊ {7,7,7,7,7,7,7,7,7,7,7,7,7,7,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,105,105,105,105,105,105,105,105,105,105,105,105,105,105,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,203,203,203,203,203,203,245,245,245,245,259,259,315,315,315,315,315,315,315,315,791,791,791,791,791,791,791,791}
0000101 => 0000101 => ([(0,4),(0,5),(1,3),(1,14),(2,12),(3,2),(3,18),(4,17),(4,19),(5,1),(5,17),(5,19),(7,8),(8,9),(9,10),(10,6),(11,6),(12,11),(13,8),(13,16),(14,16),(14,18),(15,10),(15,11),(16,9),(16,15),(17,7),(17,13),(18,12),(18,15),(19,7),(19,13),(19,14)],20)
=> ? ∊ {7,7,7,7,7,7,7,7,7,7,7,7,7,7,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,105,105,105,105,105,105,105,105,105,105,105,105,105,105,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,203,203,203,203,203,203,245,245,245,245,259,259,315,315,315,315,315,315,315,315,791,791,791,791,791,791,791,791}
0000110 => 0000011 => ([(0,6),(0,7),(1,11),(2,5),(2,15),(3,13),(4,3),(4,17),(5,4),(5,16),(6,2),(6,14),(7,1),(7,14),(9,12),(10,9),(11,10),(12,8),(13,8),(14,11),(14,15),(15,10),(15,16),(16,9),(16,17),(17,12),(17,13)],18)
=> ? ∊ {7,7,7,7,7,7,7,7,7,7,7,7,7,7,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,105,105,105,105,105,105,105,105,105,105,105,105,105,105,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,203,203,203,203,203,203,245,245,245,245,259,259,315,315,315,315,315,315,315,315,791,791,791,791,791,791,791,791}
0000111 => 0000111 => ([(0,6),(0,7),(1,4),(1,16),(2,5),(2,15),(3,13),(4,12),(5,3),(5,19),(6,1),(6,17),(7,2),(7,17),(9,11),(10,8),(11,8),(12,9),(13,10),(14,9),(14,18),(15,14),(15,19),(16,12),(16,14),(17,15),(17,16),(18,10),(18,11),(19,13),(19,18)],20)
=> ? ∊ {7,7,7,7,7,7,7,7,7,7,7,7,7,7,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,105,105,105,105,105,105,105,105,105,105,105,105,105,105,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,203,203,203,203,203,203,245,245,245,245,259,259,315,315,315,315,315,315,315,315,791,791,791,791,791,791,791,791}
0001000 => 0000001 => ([(0,2),(0,7),(1,9),(2,8),(3,4),(3,11),(4,6),(4,10),(5,3),(5,13),(6,1),(6,12),(7,5),(7,8),(8,13),(10,12),(11,10),(12,9),(13,11)],14)
=> ? ∊ {7,7,7,7,7,7,7,7,7,7,7,7,7,7,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,105,105,105,105,105,105,105,105,105,105,105,105,105,105,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,203,203,203,203,203,203,245,245,245,245,259,259,315,315,315,315,315,315,315,315,791,791,791,791,791,791,791,791}
0001001 => 0001001 => ([(0,3),(0,4),(1,11),(2,1),(2,15),(2,19),(3,17),(3,18),(4,2),(4,17),(4,18),(6,10),(7,8),(8,9),(9,5),(10,5),(11,6),(12,8),(12,13),(13,9),(13,10),(14,12),(14,16),(15,7),(15,12),(16,6),(16,13),(17,14),(17,15),(18,14),(18,19),(19,7),(19,11),(19,16)],20)
=> ? ∊ {7,7,7,7,7,7,7,7,7,7,7,7,7,7,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,105,105,105,105,105,105,105,105,105,105,105,105,105,105,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,203,203,203,203,203,203,245,245,245,245,259,259,315,315,315,315,315,315,315,315,791,791,791,791,791,791,791,791}
0001010 => 0000101 => ([(0,4),(0,5),(1,3),(1,14),(2,12),(3,2),(3,18),(4,17),(4,19),(5,1),(5,17),(5,19),(7,8),(8,9),(9,10),(10,6),(11,6),(12,11),(13,8),(13,16),(14,16),(14,18),(15,10),(15,11),(16,9),(16,15),(17,7),(17,13),(18,12),(18,15),(19,7),(19,13),(19,14)],20)
=> ? ∊ {7,7,7,7,7,7,7,7,7,7,7,7,7,7,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,105,105,105,105,105,105,105,105,105,105,105,105,105,105,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,203,203,203,203,203,203,245,245,245,245,259,259,315,315,315,315,315,315,315,315,791,791,791,791,791,791,791,791}
0001011 => 0001011 => ([(0,4),(0,5),(1,13),(2,3),(2,20),(3,7),(4,1),(4,19),(4,21),(5,2),(5,19),(5,21),(7,9),(8,11),(9,12),(10,8),(11,6),(12,6),(13,10),(14,10),(14,17),(15,16),(15,17),(16,9),(16,18),(17,8),(17,18),(18,11),(18,12),(19,14),(19,15),(20,7),(20,16),(21,13),(21,14),(21,15),(21,20)],22)
=> ? ∊ {7,7,7,7,7,7,7,7,7,7,7,7,7,7,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,105,105,105,105,105,105,105,105,105,105,105,105,105,105,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,203,203,203,203,203,203,245,245,245,245,259,259,315,315,315,315,315,315,315,315,791,791,791,791,791,791,791,791}
0001100 => 0000011 => ([(0,6),(0,7),(1,11),(2,5),(2,15),(3,13),(4,3),(4,17),(5,4),(5,16),(6,2),(6,14),(7,1),(7,14),(9,12),(10,9),(11,10),(12,8),(13,8),(14,11),(14,15),(15,10),(15,16),(16,9),(16,17),(17,12),(17,13)],18)
=> ? ∊ {7,7,7,7,7,7,7,7,7,7,7,7,7,7,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,105,105,105,105,105,105,105,105,105,105,105,105,105,105,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,203,203,203,203,203,203,245,245,245,245,259,259,315,315,315,315,315,315,315,315,791,791,791,791,791,791,791,791}
0001101 => 0001101 => ([(0,4),(0,5),(1,13),(2,1),(2,15),(3,14),(3,16),(4,2),(4,20),(4,21),(5,3),(5,20),(5,21),(7,8),(8,9),(9,11),(10,12),(11,6),(12,6),(13,10),(14,8),(14,18),(15,13),(15,17),(16,17),(16,18),(17,10),(17,19),(18,9),(18,19),(19,11),(19,12),(20,7),(20,14),(21,7),(21,15),(21,16)],22)
=> ? ∊ {7,7,7,7,7,7,7,7,7,7,7,7,7,7,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,105,105,105,105,105,105,105,105,105,105,105,105,105,105,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,203,203,203,203,203,203,245,245,245,245,259,259,315,315,315,315,315,315,315,315,791,791,791,791,791,791,791,791}
0001110 => 0000111 => ([(0,6),(0,7),(1,4),(1,16),(2,5),(2,15),(3,13),(4,12),(5,3),(5,19),(6,1),(6,17),(7,2),(7,17),(9,11),(10,8),(11,8),(12,9),(13,10),(14,9),(14,18),(15,14),(15,19),(16,12),(16,14),(17,15),(17,16),(18,10),(18,11),(19,13),(19,18)],20)
=> ? ∊ {7,7,7,7,7,7,7,7,7,7,7,7,7,7,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,105,105,105,105,105,105,105,105,105,105,105,105,105,105,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,203,203,203,203,203,203,245,245,245,245,259,259,315,315,315,315,315,315,315,315,791,791,791,791,791,791,791,791}
0001111 => 0001111 => ([(0,6),(0,7),(1,4),(1,16),(2,5),(2,15),(3,13),(4,12),(5,3),(5,19),(6,1),(6,17),(7,2),(7,17),(9,11),(10,8),(11,8),(12,9),(13,10),(14,9),(14,18),(15,14),(15,19),(16,12),(16,14),(17,15),(17,16),(18,10),(18,11),(19,13),(19,18)],20)
=> ? ∊ {7,7,7,7,7,7,7,7,7,7,7,7,7,7,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,105,105,105,105,105,105,105,105,105,105,105,105,105,105,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,203,203,203,203,203,203,245,245,245,245,259,259,315,315,315,315,315,315,315,315,791,791,791,791,791,791,791,791}
0010000 => 0000001 => ([(0,2),(0,7),(1,9),(2,8),(3,4),(3,11),(4,6),(4,10),(5,3),(5,13),(6,1),(6,12),(7,5),(7,8),(8,13),(10,12),(11,10),(12,9),(13,11)],14)
=> ? ∊ {7,7,7,7,7,7,7,7,7,7,7,7,7,7,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,105,105,105,105,105,105,105,105,105,105,105,105,105,105,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,203,203,203,203,203,203,245,245,245,245,259,259,315,315,315,315,315,315,315,315,791,791,791,791,791,791,791,791}
0010001 => 0001001 => ([(0,3),(0,4),(1,11),(2,1),(2,15),(2,19),(3,17),(3,18),(4,2),(4,17),(4,18),(6,10),(7,8),(8,9),(9,5),(10,5),(11,6),(12,8),(12,13),(13,9),(13,10),(14,12),(14,16),(15,7),(15,12),(16,6),(16,13),(17,14),(17,15),(18,14),(18,19),(19,7),(19,11),(19,16)],20)
=> ? ∊ {7,7,7,7,7,7,7,7,7,7,7,7,7,7,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,105,105,105,105,105,105,105,105,105,105,105,105,105,105,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,203,203,203,203,203,203,245,245,245,245,259,259,315,315,315,315,315,315,315,315,791,791,791,791,791,791,791,791}
0010010 => 0001001 => ([(0,3),(0,4),(1,11),(2,1),(2,15),(2,19),(3,17),(3,18),(4,2),(4,17),(4,18),(6,10),(7,8),(8,9),(9,5),(10,5),(11,6),(12,8),(12,13),(13,9),(13,10),(14,12),(14,16),(15,7),(15,12),(16,6),(16,13),(17,14),(17,15),(18,14),(18,19),(19,7),(19,11),(19,16)],20)
=> ? ∊ {7,7,7,7,7,7,7,7,7,7,7,7,7,7,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,105,105,105,105,105,105,105,105,105,105,105,105,105,105,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,203,203,203,203,203,203,245,245,245,245,259,259,315,315,315,315,315,315,315,315,791,791,791,791,791,791,791,791}
0010011 => 0010011 => ([(0,3),(0,4),(1,12),(2,14),(2,19),(3,2),(3,18),(3,20),(4,1),(4,18),(4,20),(6,8),(7,10),(8,11),(9,7),(10,5),(11,5),(12,6),(13,9),(13,16),(14,15),(14,16),(15,8),(15,17),(16,7),(16,17),(17,10),(17,11),(18,13),(18,14),(19,6),(19,9),(19,15),(20,12),(20,13),(20,19)],21)
=> ? ∊ {7,7,7,7,7,7,7,7,7,7,7,7,7,7,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,105,105,105,105,105,105,105,105,105,105,105,105,105,105,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,203,203,203,203,203,203,245,245,245,245,259,259,315,315,315,315,315,315,315,315,791,791,791,791,791,791,791,791}
0010100 => 0000101 => ([(0,4),(0,5),(1,3),(1,14),(2,12),(3,2),(3,18),(4,17),(4,19),(5,1),(5,17),(5,19),(7,8),(8,9),(9,10),(10,6),(11,6),(12,11),(13,8),(13,16),(14,16),(14,18),(15,10),(15,11),(16,9),(16,15),(17,7),(17,13),(18,12),(18,15),(19,7),(19,13),(19,14)],20)
=> ? ∊ {7,7,7,7,7,7,7,7,7,7,7,7,7,7,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,105,105,105,105,105,105,105,105,105,105,105,105,105,105,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,203,203,203,203,203,203,245,245,245,245,259,259,315,315,315,315,315,315,315,315,791,791,791,791,791,791,791,791}
0010101 => 0010101 => ([(0,2),(0,3),(1,10),(2,14),(2,17),(3,1),(3,14),(3,17),(5,8),(6,5),(7,9),(8,4),(9,4),(10,6),(11,13),(11,16),(12,8),(12,9),(13,7),(13,12),(14,11),(14,15),(15,6),(15,13),(15,16),(16,5),(16,7),(16,12),(17,10),(17,11),(17,15)],18)
=> ? ∊ {7,7,7,7,7,7,7,7,7,7,7,7,7,7,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,35,105,105,105,105,105,105,105,105,105,105,105,105,105,105,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,189,203,203,203,203,203,203,245,245,245,245,259,259,315,315,315,315,315,315,315,315,791,791,791,791,791,791,791,791}
Description
The number of maximal chains in a poset.
Matching statistic: St000909
Mp00224: Binary words —runsort⟶ Binary words
Mp00262: Binary words —poset of factors⟶ Posets
St000909: Posets ⟶ ℤResult quality: 14% ●values known / values provided: 14%●distinct values known / distinct values provided: 20%
Mp00262: Binary words —poset of factors⟶ Posets
St000909: Posets ⟶ ℤResult quality: 14% ●values known / values provided: 14%●distinct values known / distinct values provided: 20%
Values
0 => 0 => ([(0,1)],2)
=> 1
1 => 1 => ([(0,1)],2)
=> 1
00 => 00 => ([(0,2),(2,1)],3)
=> 1
01 => 01 => ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
10 => 01 => ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
11 => 11 => ([(0,2),(2,1)],3)
=> 1
000 => 000 => ([(0,3),(2,1),(3,2)],4)
=> 1
001 => 001 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 3
010 => 001 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 3
011 => 011 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 3
100 => 001 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 3
101 => 011 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 3
110 => 011 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 3
111 => 111 => ([(0,3),(2,1),(3,2)],4)
=> 1
0000 => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
0001 => 0001 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> 4
0010 => 0001 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> 4
0011 => 0011 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> 6
0100 => 0001 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> 4
0101 => 0101 => ([(0,1),(0,2),(1,6),(1,7),(2,6),(2,7),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5)],8)
=> ? = 16
0110 => 0011 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> 6
0111 => 0111 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> 4
1000 => 0001 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> 4
1001 => 0011 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> 6
1010 => 0011 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> 6
1011 => 0111 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> 4
1100 => 0011 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> 6
1101 => 0111 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> 4
1110 => 0111 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> 4
1111 => 1111 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
00000 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1
00001 => 00001 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35}
00010 => 00001 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35}
00011 => 00011 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35}
00100 => 00001 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35}
00101 => 00101 => ([(0,2),(0,3),(1,8),(2,10),(2,11),(3,1),(3,10),(3,11),(5,6),(6,4),(7,4),(8,7),(9,6),(9,7),(10,5),(10,9),(11,5),(11,8),(11,9)],12)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35}
00110 => 00011 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35}
00111 => 00111 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35}
01000 => 00001 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35}
01001 => 00101 => ([(0,2),(0,3),(1,8),(2,10),(2,11),(3,1),(3,10),(3,11),(5,6),(6,4),(7,4),(8,7),(9,6),(9,7),(10,5),(10,9),(11,5),(11,8),(11,9)],12)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35}
01010 => 00101 => ([(0,2),(0,3),(1,8),(2,10),(2,11),(3,1),(3,10),(3,11),(5,6),(6,4),(7,4),(8,7),(9,6),(9,7),(10,5),(10,9),(11,5),(11,8),(11,9)],12)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35}
01011 => 01011 => ([(0,2),(0,3),(1,8),(2,10),(2,11),(3,1),(3,10),(3,11),(5,6),(6,4),(7,4),(8,7),(9,6),(9,7),(10,5),(10,9),(11,5),(11,8),(11,9)],12)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35}
01100 => 00011 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35}
01101 => 01011 => ([(0,2),(0,3),(1,8),(2,10),(2,11),(3,1),(3,10),(3,11),(5,6),(6,4),(7,4),(8,7),(9,6),(9,7),(10,5),(10,9),(11,5),(11,8),(11,9)],12)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35}
01110 => 00111 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35}
01111 => 01111 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35}
10000 => 00001 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35}
10001 => 00011 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35}
10010 => 00011 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35}
10011 => 00111 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35}
10100 => 00011 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35}
10101 => 01011 => ([(0,2),(0,3),(1,8),(2,10),(2,11),(3,1),(3,10),(3,11),(5,6),(6,4),(7,4),(8,7),(9,6),(9,7),(10,5),(10,9),(11,5),(11,8),(11,9)],12)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35}
10110 => 00111 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35}
10111 => 01111 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35}
11000 => 00011 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35}
11001 => 00111 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35}
11010 => 00111 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35}
11011 => 01111 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35}
11100 => 00111 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35}
11101 => 01111 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35}
11110 => 01111 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35}
11111 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1
000000 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 1
000001 => 000001 => ([(0,2),(0,6),(1,8),(2,7),(3,5),(3,9),(4,3),(4,11),(5,1),(5,10),(6,4),(6,7),(7,11),(9,10),(10,8),(11,9)],12)
=> ? ∊ {6,6,6,6,6,6,6,6,6,6,6,6,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,20,20,20,20,20,20,20,20,20,20,64,64,64,64,64,64,64,64,64,64,90,90,90,90,90,90,90,99,99,111,111,272}
000010 => 000001 => ([(0,2),(0,6),(1,8),(2,7),(3,5),(3,9),(4,3),(4,11),(5,1),(5,10),(6,4),(6,7),(7,11),(9,10),(10,8),(11,9)],12)
=> ? ∊ {6,6,6,6,6,6,6,6,6,6,6,6,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,20,20,20,20,20,20,20,20,20,20,64,64,64,64,64,64,64,64,64,64,90,90,90,90,90,90,90,99,99,111,111,272}
000011 => 000011 => ([(0,5),(0,6),(1,4),(1,14),(2,11),(3,10),(4,3),(4,12),(5,1),(5,13),(6,2),(6,13),(8,9),(9,7),(10,7),(11,8),(12,9),(12,10),(13,11),(13,14),(14,8),(14,12)],15)
=> ? ∊ {6,6,6,6,6,6,6,6,6,6,6,6,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,20,20,20,20,20,20,20,20,20,20,64,64,64,64,64,64,64,64,64,64,90,90,90,90,90,90,90,99,99,111,111,272}
000100 => 000001 => ([(0,2),(0,6),(1,8),(2,7),(3,5),(3,9),(4,3),(4,11),(5,1),(5,10),(6,4),(6,7),(7,11),(9,10),(10,8),(11,9)],12)
=> ? ∊ {6,6,6,6,6,6,6,6,6,6,6,6,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,20,20,20,20,20,20,20,20,20,20,64,64,64,64,64,64,64,64,64,64,90,90,90,90,90,90,90,99,99,111,111,272}
000101 => 000101 => ([(0,3),(0,4),(1,2),(1,14),(2,6),(3,13),(3,15),(4,1),(4,13),(4,15),(6,9),(7,8),(8,10),(9,5),(10,5),(11,8),(11,12),(12,9),(12,10),(13,7),(13,11),(14,6),(14,12),(15,7),(15,11),(15,14)],16)
=> ? ∊ {6,6,6,6,6,6,6,6,6,6,6,6,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,20,20,20,20,20,20,20,20,20,20,64,64,64,64,64,64,64,64,64,64,90,90,90,90,90,90,90,99,99,111,111,272}
000110 => 000011 => ([(0,5),(0,6),(1,4),(1,14),(2,11),(3,10),(4,3),(4,12),(5,1),(5,13),(6,2),(6,13),(8,9),(9,7),(10,7),(11,8),(12,9),(12,10),(13,11),(13,14),(14,8),(14,12)],15)
=> ? ∊ {6,6,6,6,6,6,6,6,6,6,6,6,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,20,20,20,20,20,20,20,20,20,20,64,64,64,64,64,64,64,64,64,64,90,90,90,90,90,90,90,99,99,111,111,272}
000111 => 000111 => ([(0,5),(0,6),(1,4),(1,15),(2,3),(2,14),(3,8),(4,9),(5,2),(5,13),(6,1),(6,13),(8,10),(9,11),(10,7),(11,7),(12,10),(12,11),(13,14),(13,15),(14,8),(14,12),(15,9),(15,12)],16)
=> ? ∊ {6,6,6,6,6,6,6,6,6,6,6,6,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,20,20,20,20,20,20,20,20,20,20,64,64,64,64,64,64,64,64,64,64,90,90,90,90,90,90,90,99,99,111,111,272}
001000 => 000001 => ([(0,2),(0,6),(1,8),(2,7),(3,5),(3,9),(4,3),(4,11),(5,1),(5,10),(6,4),(6,7),(7,11),(9,10),(10,8),(11,9)],12)
=> ? ∊ {6,6,6,6,6,6,6,6,6,6,6,6,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,20,20,20,20,20,20,20,20,20,20,64,64,64,64,64,64,64,64,64,64,90,90,90,90,90,90,90,99,99,111,111,272}
001001 => 001001 => ([(0,2),(0,3),(1,11),(1,12),(2,13),(2,14),(3,1),(3,13),(3,14),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,9),(11,6),(11,9),(12,5),(12,6),(13,10),(13,11),(14,10),(14,12)],15)
=> ? ∊ {6,6,6,6,6,6,6,6,6,6,6,6,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,20,20,20,20,20,20,20,20,20,20,64,64,64,64,64,64,64,64,64,64,90,90,90,90,90,90,90,99,99,111,111,272}
001010 => 000101 => ([(0,3),(0,4),(1,2),(1,14),(2,6),(3,13),(3,15),(4,1),(4,13),(4,15),(6,9),(7,8),(8,10),(9,5),(10,5),(11,8),(11,12),(12,9),(12,10),(13,7),(13,11),(14,6),(14,12),(15,7),(15,11),(15,14)],16)
=> ? ∊ {6,6,6,6,6,6,6,6,6,6,6,6,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,20,20,20,20,20,20,20,20,20,20,64,64,64,64,64,64,64,64,64,64,90,90,90,90,90,90,90,99,99,111,111,272}
001011 => 001011 => ([(0,3),(0,4),(1,11),(2,10),(3,2),(3,15),(3,16),(4,1),(4,15),(4,16),(6,8),(7,9),(8,5),(9,5),(10,6),(11,7),(12,6),(12,14),(13,7),(13,14),(14,8),(14,9),(15,12),(15,13),(16,10),(16,11),(16,12),(16,13)],17)
=> ? ∊ {6,6,6,6,6,6,6,6,6,6,6,6,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,20,20,20,20,20,20,20,20,20,20,64,64,64,64,64,64,64,64,64,64,90,90,90,90,90,90,90,99,99,111,111,272}
001100 => 000011 => ([(0,5),(0,6),(1,4),(1,14),(2,11),(3,10),(4,3),(4,12),(5,1),(5,13),(6,2),(6,13),(8,9),(9,7),(10,7),(11,8),(12,9),(12,10),(13,11),(13,14),(14,8),(14,12)],15)
=> ? ∊ {6,6,6,6,6,6,6,6,6,6,6,6,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,20,20,20,20,20,20,20,20,20,20,64,64,64,64,64,64,64,64,64,64,90,90,90,90,90,90,90,99,99,111,111,272}
001101 => 001101 => ([(0,3),(0,4),(1,11),(2,12),(2,13),(3,2),(3,15),(3,16),(4,1),(4,15),(4,16),(6,7),(7,9),(8,10),(9,5),(10,5),(11,8),(12,7),(12,14),(13,8),(13,14),(14,9),(14,10),(15,6),(15,12),(16,6),(16,11),(16,13)],17)
=> ? ∊ {6,6,6,6,6,6,6,6,6,6,6,6,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,20,20,20,20,20,20,20,20,20,20,64,64,64,64,64,64,64,64,64,64,90,90,90,90,90,90,90,99,99,111,111,272}
001110 => 000111 => ([(0,5),(0,6),(1,4),(1,15),(2,3),(2,14),(3,8),(4,9),(5,2),(5,13),(6,1),(6,13),(8,10),(9,11),(10,7),(11,7),(12,10),(12,11),(13,14),(13,15),(14,8),(14,12),(15,9),(15,12)],16)
=> ? ∊ {6,6,6,6,6,6,6,6,6,6,6,6,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,20,20,20,20,20,20,20,20,20,20,64,64,64,64,64,64,64,64,64,64,90,90,90,90,90,90,90,99,99,111,111,272}
001111 => 001111 => ([(0,5),(0,6),(1,4),(1,14),(2,11),(3,10),(4,3),(4,12),(5,1),(5,13),(6,2),(6,13),(8,9),(9,7),(10,7),(11,8),(12,9),(12,10),(13,11),(13,14),(14,8),(14,12)],15)
=> ? ∊ {6,6,6,6,6,6,6,6,6,6,6,6,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,20,20,20,20,20,20,20,20,20,20,64,64,64,64,64,64,64,64,64,64,90,90,90,90,90,90,90,99,99,111,111,272}
010000 => 000001 => ([(0,2),(0,6),(1,8),(2,7),(3,5),(3,9),(4,3),(4,11),(5,1),(5,10),(6,4),(6,7),(7,11),(9,10),(10,8),(11,9)],12)
=> ? ∊ {6,6,6,6,6,6,6,6,6,6,6,6,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,20,20,20,20,20,20,20,20,20,20,64,64,64,64,64,64,64,64,64,64,90,90,90,90,90,90,90,99,99,111,111,272}
010001 => 000101 => ([(0,3),(0,4),(1,2),(1,14),(2,6),(3,13),(3,15),(4,1),(4,13),(4,15),(6,9),(7,8),(8,10),(9,5),(10,5),(11,8),(11,12),(12,9),(12,10),(13,7),(13,11),(14,6),(14,12),(15,7),(15,11),(15,14)],16)
=> ? ∊ {6,6,6,6,6,6,6,6,6,6,6,6,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,20,20,20,20,20,20,20,20,20,20,64,64,64,64,64,64,64,64,64,64,90,90,90,90,90,90,90,99,99,111,111,272}
010010 => 000101 => ([(0,3),(0,4),(1,2),(1,14),(2,6),(3,13),(3,15),(4,1),(4,13),(4,15),(6,9),(7,8),(8,10),(9,5),(10,5),(11,8),(11,12),(12,9),(12,10),(13,7),(13,11),(14,6),(14,12),(15,7),(15,11),(15,14)],16)
=> ? ∊ {6,6,6,6,6,6,6,6,6,6,6,6,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,20,20,20,20,20,20,20,20,20,20,64,64,64,64,64,64,64,64,64,64,90,90,90,90,90,90,90,99,99,111,111,272}
010011 => 001101 => ([(0,3),(0,4),(1,11),(2,12),(2,13),(3,2),(3,15),(3,16),(4,1),(4,15),(4,16),(6,7),(7,9),(8,10),(9,5),(10,5),(11,8),(12,7),(12,14),(13,8),(13,14),(14,9),(14,10),(15,6),(15,12),(16,6),(16,11),(16,13)],17)
=> ? ∊ {6,6,6,6,6,6,6,6,6,6,6,6,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,20,20,20,20,20,20,20,20,20,20,64,64,64,64,64,64,64,64,64,64,90,90,90,90,90,90,90,99,99,111,111,272}
111111 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 1
0000000 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
=> 1
1111111 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
=> 1
Description
The number of maximal chains of maximal size in a poset.
Matching statistic: St001330
Mp00097: Binary words —delta morphism⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
Mp00203: Graphs —cone⟶ Graphs
St001330: Graphs ⟶ ℤResult quality: 10% ●values known / values provided: 10%●distinct values known / distinct values provided: 28%
Mp00184: Integer compositions —to threshold graph⟶ Graphs
Mp00203: Graphs —cone⟶ Graphs
St001330: Graphs ⟶ ℤResult quality: 10% ●values known / values provided: 10%●distinct values known / distinct values provided: 28%
Values
0 => [1] => ([],1)
=> ([(0,1)],2)
=> 2 = 1 + 1
1 => [1] => ([],1)
=> ([(0,1)],2)
=> 2 = 1 + 1
00 => [2] => ([],2)
=> ([(0,2),(1,2)],3)
=> 2 = 1 + 1
01 => [1,1] => ([(0,1)],2)
=> ([(0,1),(0,2),(1,2)],3)
=> 3 = 2 + 1
10 => [1,1] => ([(0,1)],2)
=> ([(0,1),(0,2),(1,2)],3)
=> 3 = 2 + 1
11 => [2] => ([],2)
=> ([(0,2),(1,2)],3)
=> 2 = 1 + 1
000 => [3] => ([],3)
=> ([(0,3),(1,3),(2,3)],4)
=> 2 = 1 + 1
001 => [2,1] => ([(0,2),(1,2)],3)
=> ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ? ∊ {3,3,3,3} + 1
010 => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 4 = 3 + 1
011 => [1,2] => ([(1,2)],3)
=> ([(0,3),(1,2),(1,3),(2,3)],4)
=> ? ∊ {3,3,3,3} + 1
100 => [1,2] => ([(1,2)],3)
=> ([(0,3),(1,2),(1,3),(2,3)],4)
=> ? ∊ {3,3,3,3} + 1
101 => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 4 = 3 + 1
110 => [2,1] => ([(0,2),(1,2)],3)
=> ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ? ∊ {3,3,3,3} + 1
111 => [3] => ([],3)
=> ([(0,3),(1,3),(2,3)],4)
=> 2 = 1 + 1
0000 => [4] => ([],4)
=> ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 1 + 1
0001 => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {4,4,4,4,4,4,6,6,6,6,6,16} + 1
0010 => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {4,4,4,4,4,4,6,6,6,6,6,16} + 1
0011 => [2,2] => ([(1,3),(2,3)],4)
=> ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {4,4,4,4,4,4,6,6,6,6,6,16} + 1
0100 => [1,1,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {4,4,4,4,4,4,6,6,6,6,6,16} + 1
0101 => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 5 = 4 + 1
0110 => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {4,4,4,4,4,4,6,6,6,6,6,16} + 1
0111 => [1,3] => ([(2,3)],4)
=> ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {4,4,4,4,4,4,6,6,6,6,6,16} + 1
1000 => [1,3] => ([(2,3)],4)
=> ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {4,4,4,4,4,4,6,6,6,6,6,16} + 1
1001 => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {4,4,4,4,4,4,6,6,6,6,6,16} + 1
1010 => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 5 = 4 + 1
1011 => [1,1,2] => ([(1,2),(1,3),(2,3)],4)
=> ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {4,4,4,4,4,4,6,6,6,6,6,16} + 1
1100 => [2,2] => ([(1,3),(2,3)],4)
=> ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {4,4,4,4,4,4,6,6,6,6,6,16} + 1
1101 => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {4,4,4,4,4,4,6,6,6,6,6,16} + 1
1110 => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? ∊ {4,4,4,4,4,4,6,6,6,6,6,16} + 1
1111 => [4] => ([],4)
=> ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 1 + 1
00000 => [5] => ([],5)
=> ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 2 = 1 + 1
00001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} + 1
00010 => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} + 1
00011 => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} + 1
00100 => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} + 1
00101 => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} + 1
00110 => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} + 1
00111 => [2,3] => ([(2,4),(3,4)],5)
=> ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} + 1
01000 => [1,1,3] => ([(2,3),(2,4),(3,4)],5)
=> ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} + 1
01001 => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} + 1
01010 => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6 = 5 + 1
01011 => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} + 1
01100 => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} + 1
01101 => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} + 1
01110 => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} + 1
01111 => [1,4] => ([(3,4)],5)
=> ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} + 1
10000 => [1,4] => ([(3,4)],5)
=> ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} + 1
10001 => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} + 1
10010 => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} + 1
10011 => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} + 1
10100 => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} + 1
10101 => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 6 = 5 + 1
10110 => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} + 1
10111 => [1,1,3] => ([(2,3),(2,4),(3,4)],5)
=> ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} + 1
11000 => [2,3] => ([(2,4),(3,4)],5)
=> ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} + 1
11001 => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} + 1
11010 => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} + 1
11011 => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} + 1
11100 => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} + 1
11101 => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} + 1
11110 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? ∊ {5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} + 1
11111 => [5] => ([],5)
=> ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 2 = 1 + 1
000000 => [6] => ([],6)
=> ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2 = 1 + 1
000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {6,6,6,6,6,6,6,6,6,6,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,20,20,20,20,20,20,20,20,20,20,64,64,64,64,64,64,64,64,64,64,90,90,90,90,90,90,90,99,99,111,111,272} + 1
000010 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {6,6,6,6,6,6,6,6,6,6,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,20,20,20,20,20,20,20,20,20,20,64,64,64,64,64,64,64,64,64,64,90,90,90,90,90,90,90,99,99,111,111,272} + 1
000011 => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {6,6,6,6,6,6,6,6,6,6,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,20,20,20,20,20,20,20,20,20,20,64,64,64,64,64,64,64,64,64,64,90,90,90,90,90,90,90,99,99,111,111,272} + 1
000100 => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {6,6,6,6,6,6,6,6,6,6,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,20,20,20,20,20,20,20,20,20,20,64,64,64,64,64,64,64,64,64,64,90,90,90,90,90,90,90,99,99,111,111,272} + 1
000101 => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {6,6,6,6,6,6,6,6,6,6,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,20,20,20,20,20,20,20,20,20,20,64,64,64,64,64,64,64,64,64,64,90,90,90,90,90,90,90,99,99,111,111,272} + 1
000110 => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? ∊ {6,6,6,6,6,6,6,6,6,6,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,20,20,20,20,20,20,20,20,20,20,64,64,64,64,64,64,64,64,64,64,90,90,90,90,90,90,90,99,99,111,111,272} + 1
010101 => [1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 6 + 1
101010 => [1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 6 + 1
111111 => [6] => ([],6)
=> ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2 = 1 + 1
0000000 => [7] => ([],7)
=> ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
=> 2 = 1 + 1
0101010 => [1,1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> 8 = 7 + 1
1010101 => [1,1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
=> 8 = 7 + 1
1111111 => [7] => ([],7)
=> ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
=> 2 = 1 + 1
Description
The hat guessing number of a graph.
Suppose that each vertex of a graph corresponds to a player, wearing a hat whose color is arbitrarily chosen from a set of $q$ possible colors. Each player can see the hat colors of his neighbors, but not his own hat color. All of the players are asked to guess their own hat colors simultaneously, according to a predetermined guessing strategy and the hat colors they see, where no communication between them is allowed. The hat guessing number $HG(G)$ of a graph $G$ is the largest integer $q$ such that there exists a guessing strategy guaranteeing at least one correct guess for any hat assignment of $q$ possible colors.
Because it suffices that a single player guesses correctly, the hat guessing number of a graph is the maximum of the hat guessing numbers of its connected components.
Matching statistic: St001633
(load all 4 compositions to match this statistic)
(load all 4 compositions to match this statistic)
Mp00262: Binary words —poset of factors⟶ Posets
St001633: Posets ⟶ ℤResult quality: 8% ●values known / values provided: 8%●distinct values known / distinct values provided: 12%
St001633: Posets ⟶ ℤResult quality: 8% ●values known / values provided: 8%●distinct values known / distinct values provided: 12%
Values
0 => ([(0,1)],2)
=> 0 = 1 - 1
1 => ([(0,1)],2)
=> 0 = 1 - 1
00 => ([(0,2),(2,1)],3)
=> 0 = 1 - 1
01 => ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1 = 2 - 1
10 => ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1 = 2 - 1
11 => ([(0,2),(2,1)],3)
=> 0 = 1 - 1
000 => ([(0,3),(2,1),(3,2)],4)
=> 0 = 1 - 1
001 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 2 = 3 - 1
010 => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> 2 = 3 - 1
011 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 2 = 3 - 1
100 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 2 = 3 - 1
101 => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> 2 = 3 - 1
110 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 2 = 3 - 1
111 => ([(0,3),(2,1),(3,2)],4)
=> 0 = 1 - 1
0000 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 0 = 1 - 1
0001 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,6,16} - 1
0010 => ([(0,2),(0,3),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,5),(8,5),(8,6)],9)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,6,16} - 1
0011 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,6,16} - 1
0100 => ([(0,2),(0,3),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,5),(8,5),(8,6)],9)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,6,16} - 1
0101 => ([(0,1),(0,2),(1,6),(1,7),(2,6),(2,7),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5)],8)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,6,16} - 1
0110 => ([(0,2),(0,3),(1,5),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,6),(8,5)],9)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,6,16} - 1
0111 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,6,16} - 1
1000 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,6,16} - 1
1001 => ([(0,2),(0,3),(1,5),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,6),(8,5)],9)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,6,16} - 1
1010 => ([(0,1),(0,2),(1,6),(1,7),(2,6),(2,7),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5)],8)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,6,16} - 1
1011 => ([(0,2),(0,3),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,5),(8,5),(8,6)],9)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,6,16} - 1
1100 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,6,16} - 1
1101 => ([(0,2),(0,3),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,5),(8,5),(8,6)],9)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,6,16} - 1
1110 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,6,16} - 1
1111 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 0 = 1 - 1
00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0 = 1 - 1
00001 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} - 1
00010 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} - 1
00011 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} - 1
00100 => ([(0,2),(0,3),(1,5),(1,6),(2,10),(2,11),(3,1),(3,10),(3,11),(5,8),(6,7),(7,4),(8,4),(9,7),(9,8),(10,6),(10,9),(11,5),(11,9)],12)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} - 1
00101 => ([(0,2),(0,3),(1,8),(2,10),(2,11),(3,1),(3,10),(3,11),(5,6),(6,4),(7,4),(8,7),(9,6),(9,7),(10,5),(10,9),(11,5),(11,8),(11,9)],12)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} - 1
00110 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} - 1
00111 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} - 1
01000 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} - 1
01001 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} - 1
01010 => ([(0,1),(0,2),(1,8),(1,9),(2,8),(2,9),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5),(8,6),(8,7),(9,6),(9,7)],10)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} - 1
01011 => ([(0,2),(0,3),(1,8),(2,10),(2,11),(3,1),(3,10),(3,11),(5,6),(6,4),(7,4),(8,7),(9,6),(9,7),(10,5),(10,9),(11,5),(11,8),(11,9)],12)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} - 1
01100 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} - 1
01101 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} - 1
01110 => ([(0,3),(0,4),(1,2),(1,10),(1,11),(2,8),(2,9),(3,6),(3,7),(4,1),(4,6),(4,7),(6,11),(7,10),(8,5),(9,5),(10,8),(11,9)],12)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} - 1
01111 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} - 1
10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} - 1
10001 => ([(0,3),(0,4),(1,2),(1,10),(1,11),(2,8),(2,9),(3,6),(3,7),(4,1),(4,6),(4,7),(6,11),(7,10),(8,5),(9,5),(10,8),(11,9)],12)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} - 1
10010 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} - 1
10011 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} - 1
10100 => ([(0,2),(0,3),(1,8),(2,10),(2,11),(3,1),(3,10),(3,11),(5,6),(6,4),(7,4),(8,7),(9,6),(9,7),(10,5),(10,9),(11,5),(11,8),(11,9)],12)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} - 1
10101 => ([(0,1),(0,2),(1,8),(1,9),(2,8),(2,9),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5),(8,6),(8,7),(9,6),(9,7)],10)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} - 1
10110 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} - 1
10111 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} - 1
11000 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} - 1
11001 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} - 1
11010 => ([(0,2),(0,3),(1,8),(2,10),(2,11),(3,1),(3,10),(3,11),(5,6),(6,4),(7,4),(8,7),(9,6),(9,7),(10,5),(10,9),(11,5),(11,8),(11,9)],12)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} - 1
11011 => ([(0,2),(0,3),(1,5),(1,6),(2,10),(2,11),(3,1),(3,10),(3,11),(5,8),(6,7),(7,4),(8,4),(9,7),(9,8),(10,6),(10,9),(11,5),(11,9)],12)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} - 1
11100 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} - 1
11101 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} - 1
11110 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} - 1
11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0 = 1 - 1
000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 0 = 1 - 1
000001 => ([(0,2),(0,6),(1,8),(2,7),(3,5),(3,9),(4,3),(4,11),(5,1),(5,10),(6,4),(6,7),(7,11),(9,10),(10,8),(11,9)],12)
=> ? ∊ {6,6,6,6,6,6,6,6,6,6,6,6,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,20,20,20,20,20,20,20,20,20,20,64,64,64,64,64,64,64,64,64,64,90,90,90,90,90,90,90,99,99,111,111,272} - 1
000010 => ([(0,4),(0,5),(1,3),(1,12),(2,11),(3,2),(3,14),(4,10),(4,13),(5,1),(5,10),(5,13),(7,8),(8,9),(9,6),(10,7),(11,6),(12,8),(12,14),(13,7),(13,12),(14,9),(14,11)],15)
=> ? ∊ {6,6,6,6,6,6,6,6,6,6,6,6,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,20,20,20,20,20,20,20,20,20,20,64,64,64,64,64,64,64,64,64,64,90,90,90,90,90,90,90,99,99,111,111,272} - 1
000011 => ([(0,5),(0,6),(1,4),(1,14),(2,11),(3,10),(4,3),(4,12),(5,1),(5,13),(6,2),(6,13),(8,9),(9,7),(10,7),(11,8),(12,9),(12,10),(13,11),(13,14),(14,8),(14,12)],15)
=> ? ∊ {6,6,6,6,6,6,6,6,6,6,6,6,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,20,20,20,20,20,20,20,20,20,20,64,64,64,64,64,64,64,64,64,64,90,90,90,90,90,90,90,99,99,111,111,272} - 1
000100 => ([(0,3),(0,4),(1,10),(2,1),(2,6),(2,12),(3,14),(3,15),(4,2),(4,14),(4,15),(6,7),(7,8),(8,5),(9,5),(10,9),(11,7),(11,13),(12,10),(12,13),(13,8),(13,9),(14,6),(14,11),(15,11),(15,12)],16)
=> ? ∊ {6,6,6,6,6,6,6,6,6,6,6,6,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,20,20,20,20,20,20,20,20,20,20,64,64,64,64,64,64,64,64,64,64,90,90,90,90,90,90,90,99,99,111,111,272} - 1
000101 => ([(0,3),(0,4),(1,2),(1,14),(2,6),(3,13),(3,15),(4,1),(4,13),(4,15),(6,9),(7,8),(8,10),(9,5),(10,5),(11,8),(11,12),(12,9),(12,10),(13,7),(13,11),(14,6),(14,12),(15,7),(15,11),(15,14)],16)
=> ? ∊ {6,6,6,6,6,6,6,6,6,6,6,6,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,20,20,20,20,20,20,20,20,20,20,64,64,64,64,64,64,64,64,64,64,90,90,90,90,90,90,90,99,99,111,111,272} - 1
000110 => ([(0,4),(0,5),(1,11),(2,1),(2,13),(3,7),(3,14),(4,2),(4,12),(4,16),(5,3),(5,12),(5,16),(7,8),(8,9),(9,6),(10,6),(11,10),(12,7),(13,11),(13,15),(14,8),(14,15),(15,9),(15,10),(16,13),(16,14)],17)
=> ? ∊ {6,6,6,6,6,6,6,6,6,6,6,6,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,20,20,20,20,20,20,20,20,20,20,64,64,64,64,64,64,64,64,64,64,90,90,90,90,90,90,90,99,99,111,111,272} - 1
111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 0 = 1 - 1
Description
The number of simple modules with projective dimension two in the incidence algebra of the poset.
Matching statistic: St001725
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Values
0 => ([(0,1)],2)
=> ([],2)
=> 1
1 => ([(0,1)],2)
=> ([],2)
=> 1
00 => ([(0,2),(2,1)],3)
=> ([],3)
=> 1
01 => ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(2,3)],4)
=> 2
10 => ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(2,3)],4)
=> 2
11 => ([(0,2),(2,1)],3)
=> ([],3)
=> 1
000 => ([(0,3),(2,1),(3,2)],4)
=> ([],4)
=> 1
001 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(2,5),(3,4),(4,5)],6)
=> 3
010 => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> ([(2,5),(3,4)],6)
=> 3
011 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(2,5),(3,4),(4,5)],6)
=> 3
100 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(2,5),(3,4),(4,5)],6)
=> 3
101 => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> ([(2,5),(3,4)],6)
=> 3
110 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(2,5),(3,4),(4,5)],6)
=> 3
111 => ([(0,3),(2,1),(3,2)],4)
=> ([],4)
=> 1
0000 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([],5)
=> 1
0001 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,6,16}
0010 => ([(0,2),(0,3),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,5),(8,5),(8,6)],9)
=> ([(2,6),(3,4),(3,8),(4,7),(5,7),(5,8),(6,8),(7,8)],9)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,6,16}
0011 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(2,5),(2,8),(3,4),(3,8),(4,7),(5,7),(6,7),(6,8),(7,8)],9)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,6,16}
0100 => ([(0,2),(0,3),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,5),(8,5),(8,6)],9)
=> ([(2,6),(3,4),(3,8),(4,7),(5,7),(5,8),(6,8),(7,8)],9)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,6,16}
0101 => ([(0,1),(0,2),(1,6),(1,7),(2,6),(2,7),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5)],8)
=> ([(2,7),(3,6),(4,5)],8)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,6,16}
0110 => ([(0,2),(0,3),(1,5),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,6),(8,5)],9)
=> ([(2,5),(3,4),(3,7),(4,6),(5,8),(6,7),(6,8),(7,8)],9)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,6,16}
0111 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,6,16}
1000 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,6,16}
1001 => ([(0,2),(0,3),(1,5),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,6),(8,5)],9)
=> ([(2,5),(3,4),(3,7),(4,6),(5,8),(6,7),(6,8),(7,8)],9)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,6,16}
1010 => ([(0,1),(0,2),(1,6),(1,7),(2,6),(2,7),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5)],8)
=> ([(2,7),(3,6),(4,5)],8)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,6,16}
1011 => ([(0,2),(0,3),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,5),(8,5),(8,6)],9)
=> ([(2,6),(3,4),(3,8),(4,7),(5,7),(5,8),(6,8),(7,8)],9)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,6,16}
1100 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(2,5),(2,8),(3,4),(3,8),(4,7),(5,7),(6,7),(6,8),(7,8)],9)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,6,16}
1101 => ([(0,2),(0,3),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,5),(8,5),(8,6)],9)
=> ([(2,6),(3,4),(3,8),(4,7),(5,7),(5,8),(6,8),(7,8)],9)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,6,16}
1110 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,6,16}
1111 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([],5)
=> 1
00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([],6)
=> 1
00001 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ([(2,9),(3,8),(4,7),(4,8),(5,6),(5,9),(6,7),(6,8),(7,9),(8,9)],10)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35}
00010 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12)
=> ([(2,7),(3,6),(3,11),(4,8),(4,10),(4,11),(5,9),(5,10),(5,11),(6,8),(6,10),(7,9),(7,11),(8,9),(8,11),(9,10),(10,11)],12)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35}
00011 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ([(2,7),(2,11),(3,6),(3,10),(4,8),(4,10),(4,11),(5,9),(5,10),(5,11),(6,8),(6,11),(7,9),(7,10),(8,9),(8,10),(9,11),(10,11)],12)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35}
00100 => ([(0,2),(0,3),(1,5),(1,6),(2,10),(2,11),(3,1),(3,10),(3,11),(5,8),(6,7),(7,4),(8,4),(9,7),(9,8),(10,6),(10,9),(11,5),(11,9)],12)
=> ([(2,5),(3,4),(3,10),(4,9),(5,11),(6,9),(6,10),(6,11),(7,8),(7,9),(7,11),(8,10),(8,11),(9,10)],12)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35}
00101 => ([(0,2),(0,3),(1,8),(2,10),(2,11),(3,1),(3,10),(3,11),(5,6),(6,4),(7,4),(8,7),(9,6),(9,7),(10,5),(10,9),(11,5),(11,8),(11,9)],12)
=> ([(2,5),(3,6),(3,11),(4,7),(4,9),(5,11),(6,10),(6,11),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11)],12)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35}
00110 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ([(2,3),(2,10),(3,12),(4,5),(4,8),(4,12),(5,9),(5,11),(6,8),(6,9),(6,11),(6,12),(7,9),(7,10),(7,11),(7,12),(8,9),(8,10),(8,11),(9,12),(10,11),(10,12),(11,12)],13)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35}
00111 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ([(2,7),(2,11),(3,6),(3,10),(4,8),(4,10),(4,11),(5,9),(5,10),(5,11),(6,8),(6,11),(7,9),(7,10),(8,9),(8,10),(9,11),(10,11)],12)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35}
01000 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12)
=> ([(2,7),(3,6),(3,11),(4,8),(4,10),(4,11),(5,9),(5,10),(5,11),(6,8),(6,10),(7,9),(7,11),(8,9),(8,11),(9,10),(10,11)],12)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35}
01001 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ([(2,5),(3,4),(3,11),(4,9),(5,10),(6,8),(6,9),(6,11),(7,8),(7,10),(7,11),(8,10),(9,10),(9,11)],12)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35}
01010 => ([(0,1),(0,2),(1,8),(1,9),(2,8),(2,9),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5),(8,6),(8,7),(9,6),(9,7)],10)
=> ([(2,9),(3,8),(4,7),(5,6)],10)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35}
01011 => ([(0,2),(0,3),(1,8),(2,10),(2,11),(3,1),(3,10),(3,11),(5,6),(6,4),(7,4),(8,7),(9,6),(9,7),(10,5),(10,9),(11,5),(11,8),(11,9)],12)
=> ([(2,5),(3,6),(3,11),(4,7),(4,9),(5,11),(6,10),(6,11),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11)],12)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35}
01100 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ([(2,3),(2,10),(3,12),(4,5),(4,8),(4,12),(5,9),(5,11),(6,8),(6,9),(6,11),(6,12),(7,9),(7,10),(7,11),(7,12),(8,9),(8,10),(8,11),(9,12),(10,11),(10,12),(11,12)],13)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35}
01101 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ([(2,5),(3,4),(3,11),(4,9),(5,10),(6,8),(6,9),(6,11),(7,8),(7,10),(7,11),(8,10),(9,10),(9,11)],12)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35}
01110 => ([(0,3),(0,4),(1,2),(1,10),(1,11),(2,8),(2,9),(3,6),(3,7),(4,1),(4,6),(4,7),(6,11),(7,10),(8,5),(9,5),(10,8),(11,9)],12)
=> ([(2,6),(3,6),(3,9),(3,10),(4,5),(4,8),(4,10),(5,7),(5,9),(6,11),(7,8),(7,10),(7,11),(8,9),(8,11),(9,10),(9,11),(10,11)],12)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35}
01111 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ([(2,9),(3,8),(4,7),(4,8),(5,6),(5,9),(6,7),(6,8),(7,9),(8,9)],10)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35}
10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ([(2,9),(3,8),(4,7),(4,8),(5,6),(5,9),(6,7),(6,8),(7,9),(8,9)],10)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35}
10001 => ([(0,3),(0,4),(1,2),(1,10),(1,11),(2,8),(2,9),(3,6),(3,7),(4,1),(4,6),(4,7),(6,11),(7,10),(8,5),(9,5),(10,8),(11,9)],12)
=> ([(2,6),(3,6),(3,9),(3,10),(4,5),(4,8),(4,10),(5,7),(5,9),(6,11),(7,8),(7,10),(7,11),(8,9),(8,11),(9,10),(9,11),(10,11)],12)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35}
10010 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ([(2,5),(3,4),(3,11),(4,9),(5,10),(6,8),(6,9),(6,11),(7,8),(7,10),(7,11),(8,10),(9,10),(9,11)],12)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35}
10011 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ([(2,3),(2,10),(3,12),(4,5),(4,8),(4,12),(5,9),(5,11),(6,8),(6,9),(6,11),(6,12),(7,9),(7,10),(7,11),(7,12),(8,9),(8,10),(8,11),(9,12),(10,11),(10,12),(11,12)],13)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35}
10100 => ([(0,2),(0,3),(1,8),(2,10),(2,11),(3,1),(3,10),(3,11),(5,6),(6,4),(7,4),(8,7),(9,6),(9,7),(10,5),(10,9),(11,5),(11,8),(11,9)],12)
=> ([(2,5),(3,6),(3,11),(4,7),(4,9),(5,11),(6,10),(6,11),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11)],12)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35}
10101 => ([(0,1),(0,2),(1,8),(1,9),(2,8),(2,9),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5),(8,6),(8,7),(9,6),(9,7)],10)
=> ([(2,9),(3,8),(4,7),(5,6)],10)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35}
10110 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ([(2,5),(3,4),(3,11),(4,9),(5,10),(6,8),(6,9),(6,11),(7,8),(7,10),(7,11),(8,10),(9,10),(9,11)],12)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35}
10111 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12)
=> ([(2,7),(3,6),(3,11),(4,8),(4,10),(4,11),(5,9),(5,10),(5,11),(6,8),(6,10),(7,9),(7,11),(8,9),(8,11),(9,10),(10,11)],12)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35}
11000 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ([(2,7),(2,11),(3,6),(3,10),(4,8),(4,10),(4,11),(5,9),(5,10),(5,11),(6,8),(6,11),(7,9),(7,10),(8,9),(8,10),(9,11),(10,11)],12)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35}
11001 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ([(2,3),(2,10),(3,12),(4,5),(4,8),(4,12),(5,9),(5,11),(6,8),(6,9),(6,11),(6,12),(7,9),(7,10),(7,11),(7,12),(8,9),(8,10),(8,11),(9,12),(10,11),(10,12),(11,12)],13)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35}
11010 => ([(0,2),(0,3),(1,8),(2,10),(2,11),(3,1),(3,10),(3,11),(5,6),(6,4),(7,4),(8,7),(9,6),(9,7),(10,5),(10,9),(11,5),(11,8),(11,9)],12)
=> ([(2,5),(3,6),(3,11),(4,7),(4,9),(5,11),(6,10),(6,11),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11)],12)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35}
11011 => ([(0,2),(0,3),(1,5),(1,6),(2,10),(2,11),(3,1),(3,10),(3,11),(5,8),(6,7),(7,4),(8,4),(9,7),(9,8),(10,6),(10,9),(11,5),(11,9)],12)
=> ([(2,5),(3,4),(3,10),(4,9),(5,11),(6,9),(6,10),(6,11),(7,8),(7,9),(7,11),(8,10),(8,11),(9,10)],12)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35}
11100 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ([(2,7),(2,11),(3,6),(3,10),(4,8),(4,10),(4,11),(5,9),(5,10),(5,11),(6,8),(6,11),(7,9),(7,10),(8,9),(8,10),(9,11),(10,11)],12)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35}
11101 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12)
=> ([(2,7),(3,6),(3,11),(4,8),(4,10),(4,11),(5,9),(5,10),(5,11),(6,8),(6,10),(7,9),(7,11),(8,9),(8,11),(9,10),(10,11)],12)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35}
11110 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ([(2,9),(3,8),(4,7),(4,8),(5,6),(5,9),(6,7),(6,8),(7,9),(8,9)],10)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35}
11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([],6)
=> 1
000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ([],7)
=> 1
000001 => ([(0,2),(0,6),(1,8),(2,7),(3,5),(3,9),(4,3),(4,11),(5,1),(5,10),(6,4),(6,7),(7,11),(9,10),(10,8),(11,9)],12)
=> ([(2,11),(3,10),(4,9),(4,10),(5,8),(5,11),(6,7),(6,9),(6,10),(7,8),(7,11),(8,9),(8,10),(9,11),(10,11)],12)
=> ? ∊ {6,6,6,6,6,6,6,6,6,6,6,6,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,20,20,20,20,20,20,20,20,20,20,64,64,64,64,64,64,64,64,64,64,90,90,90,90,90,90,90,99,99,111,111,272}
000010 => ([(0,4),(0,5),(1,3),(1,12),(2,11),(3,2),(3,14),(4,10),(4,13),(5,1),(5,10),(5,13),(7,8),(8,9),(9,6),(10,7),(11,6),(12,8),(12,14),(13,7),(13,12),(14,9),(14,11)],15)
=> ([(2,10),(3,9),(3,14),(4,7),(4,9),(4,12),(4,14),(5,6),(5,10),(5,11),(5,13),(6,12),(6,13),(6,14),(7,11),(7,13),(7,14),(8,11),(8,12),(8,13),(8,14),(9,11),(9,13),(10,12),(10,14),(11,12),(11,14),(12,13),(13,14)],15)
=> ? ∊ {6,6,6,6,6,6,6,6,6,6,6,6,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,20,20,20,20,20,20,20,20,20,20,64,64,64,64,64,64,64,64,64,64,90,90,90,90,90,90,90,99,99,111,111,272}
000011 => ([(0,5),(0,6),(1,4),(1,14),(2,11),(3,10),(4,3),(4,12),(5,1),(5,13),(6,2),(6,13),(8,9),(9,7),(10,7),(11,8),(12,9),(12,10),(13,11),(13,14),(14,8),(14,12)],15)
=> ([(2,10),(2,14),(3,9),(3,13),(4,6),(4,9),(4,12),(4,13),(5,7),(5,10),(5,11),(5,14),(6,11),(6,13),(6,14),(7,12),(7,13),(7,14),(8,11),(8,12),(8,13),(8,14),(9,11),(9,14),(10,12),(10,13),(11,12),(11,13),(12,14),(13,14)],15)
=> ? ∊ {6,6,6,6,6,6,6,6,6,6,6,6,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,20,20,20,20,20,20,20,20,20,20,64,64,64,64,64,64,64,64,64,64,90,90,90,90,90,90,90,99,99,111,111,272}
000100 => ([(0,3),(0,4),(1,10),(2,1),(2,6),(2,12),(3,14),(3,15),(4,2),(4,14),(4,15),(6,7),(7,8),(8,5),(9,5),(10,9),(11,7),(11,13),(12,10),(12,13),(13,8),(13,9),(14,6),(14,11),(15,11),(15,12)],16)
=> ([(2,5),(3,4),(3,12),(3,14),(4,13),(4,15),(5,7),(5,15),(6,12),(6,13),(6,14),(6,15),(7,8),(7,10),(7,11),(8,11),(8,14),(8,15),(9,10),(9,11),(9,12),(9,14),(9,15),(10,13),(10,14),(10,15),(11,13),(11,15),(12,13),(12,15),(13,14),(14,15)],16)
=> ? ∊ {6,6,6,6,6,6,6,6,6,6,6,6,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,20,20,20,20,20,20,20,20,20,20,64,64,64,64,64,64,64,64,64,64,90,90,90,90,90,90,90,99,99,111,111,272}
000101 => ([(0,3),(0,4),(1,2),(1,14),(2,6),(3,13),(3,15),(4,1),(4,13),(4,15),(6,9),(7,8),(8,10),(9,5),(10,5),(11,8),(11,12),(12,9),(12,10),(13,7),(13,11),(14,6),(14,12),(15,7),(15,11),(15,14)],16)
=> ([(2,6),(3,4),(3,13),(3,15),(4,12),(4,14),(5,8),(5,11),(5,15),(6,11),(6,15),(7,12),(7,13),(7,14),(7,15),(8,10),(8,11),(8,13),(8,15),(9,10),(9,11),(9,13),(9,14),(9,15),(10,12),(10,14),(10,15),(11,12),(11,14),(12,13),(12,15),(13,14),(14,15)],16)
=> ? ∊ {6,6,6,6,6,6,6,6,6,6,6,6,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,20,20,20,20,20,20,20,20,20,20,64,64,64,64,64,64,64,64,64,64,90,90,90,90,90,90,90,99,99,111,111,272}
000110 => ([(0,4),(0,5),(1,11),(2,1),(2,13),(3,7),(3,14),(4,2),(4,12),(4,16),(5,3),(5,12),(5,16),(7,8),(8,9),(9,6),(10,6),(11,10),(12,7),(13,11),(13,15),(14,8),(14,15),(15,9),(15,10),(16,13),(16,14)],17)
=> ([(2,4),(2,13),(3,5),(3,12),(3,16),(4,11),(4,16),(5,10),(5,14),(5,15),(6,10),(6,12),(6,14),(6,15),(6,16),(7,11),(7,13),(7,14),(7,15),(7,16),(8,9),(8,10),(8,13),(8,14),(8,15),(8,16),(9,11),(9,12),(9,14),(9,15),(9,16),(10,11),(10,12),(10,16),(11,13),(11,14),(11,15),(12,13),(12,14),(12,15),(13,15),(13,16),(14,16),(15,16)],17)
=> ? ∊ {6,6,6,6,6,6,6,6,6,6,6,6,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,20,20,20,20,20,20,20,20,20,20,64,64,64,64,64,64,64,64,64,64,90,90,90,90,90,90,90,99,99,111,111,272}
111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ([],7)
=> 1
Description
The harmonious chromatic number of a graph.
A harmonious colouring is a proper vertex colouring such that any pair of colours appears at most once on adjacent vertices.
Matching statistic: St000362
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Values
0 => ([(0,1)],2)
=> ([],2)
=> 0 = 1 - 1
1 => ([(0,1)],2)
=> ([],2)
=> 0 = 1 - 1
00 => ([(0,2),(2,1)],3)
=> ([],3)
=> 0 = 1 - 1
01 => ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(2,3)],4)
=> 1 = 2 - 1
10 => ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(2,3)],4)
=> 1 = 2 - 1
11 => ([(0,2),(2,1)],3)
=> ([],3)
=> 0 = 1 - 1
000 => ([(0,3),(2,1),(3,2)],4)
=> ([],4)
=> 0 = 1 - 1
001 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(2,5),(3,4),(4,5)],6)
=> 2 = 3 - 1
010 => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> ([(2,5),(3,4)],6)
=> 2 = 3 - 1
011 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(2,5),(3,4),(4,5)],6)
=> 2 = 3 - 1
100 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(2,5),(3,4),(4,5)],6)
=> 2 = 3 - 1
101 => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> ([(2,5),(3,4)],6)
=> 2 = 3 - 1
110 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(2,5),(3,4),(4,5)],6)
=> 2 = 3 - 1
111 => ([(0,3),(2,1),(3,2)],4)
=> ([],4)
=> 0 = 1 - 1
0000 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([],5)
=> 0 = 1 - 1
0001 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,6,16} - 1
0010 => ([(0,2),(0,3),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,5),(8,5),(8,6)],9)
=> ([(2,6),(3,4),(3,8),(4,7),(5,7),(5,8),(6,8),(7,8)],9)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,6,16} - 1
0011 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(2,5),(2,8),(3,4),(3,8),(4,7),(5,7),(6,7),(6,8),(7,8)],9)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,6,16} - 1
0100 => ([(0,2),(0,3),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,5),(8,5),(8,6)],9)
=> ([(2,6),(3,4),(3,8),(4,7),(5,7),(5,8),(6,8),(7,8)],9)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,6,16} - 1
0101 => ([(0,1),(0,2),(1,6),(1,7),(2,6),(2,7),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5)],8)
=> ([(2,7),(3,6),(4,5)],8)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,6,16} - 1
0110 => ([(0,2),(0,3),(1,5),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,6),(8,5)],9)
=> ([(2,5),(3,4),(3,7),(4,6),(5,8),(6,7),(6,8),(7,8)],9)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,6,16} - 1
0111 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,6,16} - 1
1000 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,6,16} - 1
1001 => ([(0,2),(0,3),(1,5),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,6),(8,5)],9)
=> ([(2,5),(3,4),(3,7),(4,6),(5,8),(6,7),(6,8),(7,8)],9)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,6,16} - 1
1010 => ([(0,1),(0,2),(1,6),(1,7),(2,6),(2,7),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5)],8)
=> ([(2,7),(3,6),(4,5)],8)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,6,16} - 1
1011 => ([(0,2),(0,3),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,5),(8,5),(8,6)],9)
=> ([(2,6),(3,4),(3,8),(4,7),(5,7),(5,8),(6,8),(7,8)],9)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,6,16} - 1
1100 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(2,5),(2,8),(3,4),(3,8),(4,7),(5,7),(6,7),(6,8),(7,8)],9)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,6,16} - 1
1101 => ([(0,2),(0,3),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,5),(8,5),(8,6)],9)
=> ([(2,6),(3,4),(3,8),(4,7),(5,7),(5,8),(6,8),(7,8)],9)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,6,16} - 1
1110 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,6,16} - 1
1111 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([],5)
=> 0 = 1 - 1
00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([],6)
=> 0 = 1 - 1
00001 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ([(2,9),(3,8),(4,7),(4,8),(5,6),(5,9),(6,7),(6,8),(7,9),(8,9)],10)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} - 1
00010 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12)
=> ([(2,7),(3,6),(3,11),(4,8),(4,10),(4,11),(5,9),(5,10),(5,11),(6,8),(6,10),(7,9),(7,11),(8,9),(8,11),(9,10),(10,11)],12)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} - 1
00011 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ([(2,7),(2,11),(3,6),(3,10),(4,8),(4,10),(4,11),(5,9),(5,10),(5,11),(6,8),(6,11),(7,9),(7,10),(8,9),(8,10),(9,11),(10,11)],12)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} - 1
00100 => ([(0,2),(0,3),(1,5),(1,6),(2,10),(2,11),(3,1),(3,10),(3,11),(5,8),(6,7),(7,4),(8,4),(9,7),(9,8),(10,6),(10,9),(11,5),(11,9)],12)
=> ([(2,5),(3,4),(3,10),(4,9),(5,11),(6,9),(6,10),(6,11),(7,8),(7,9),(7,11),(8,10),(8,11),(9,10)],12)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} - 1
00101 => ([(0,2),(0,3),(1,8),(2,10),(2,11),(3,1),(3,10),(3,11),(5,6),(6,4),(7,4),(8,7),(9,6),(9,7),(10,5),(10,9),(11,5),(11,8),(11,9)],12)
=> ([(2,5),(3,6),(3,11),(4,7),(4,9),(5,11),(6,10),(6,11),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11)],12)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} - 1
00110 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ([(2,3),(2,10),(3,12),(4,5),(4,8),(4,12),(5,9),(5,11),(6,8),(6,9),(6,11),(6,12),(7,9),(7,10),(7,11),(7,12),(8,9),(8,10),(8,11),(9,12),(10,11),(10,12),(11,12)],13)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} - 1
00111 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ([(2,7),(2,11),(3,6),(3,10),(4,8),(4,10),(4,11),(5,9),(5,10),(5,11),(6,8),(6,11),(7,9),(7,10),(8,9),(8,10),(9,11),(10,11)],12)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} - 1
01000 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12)
=> ([(2,7),(3,6),(3,11),(4,8),(4,10),(4,11),(5,9),(5,10),(5,11),(6,8),(6,10),(7,9),(7,11),(8,9),(8,11),(9,10),(10,11)],12)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} - 1
01001 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ([(2,5),(3,4),(3,11),(4,9),(5,10),(6,8),(6,9),(6,11),(7,8),(7,10),(7,11),(8,10),(9,10),(9,11)],12)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} - 1
01010 => ([(0,1),(0,2),(1,8),(1,9),(2,8),(2,9),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5),(8,6),(8,7),(9,6),(9,7)],10)
=> ([(2,9),(3,8),(4,7),(5,6)],10)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} - 1
01011 => ([(0,2),(0,3),(1,8),(2,10),(2,11),(3,1),(3,10),(3,11),(5,6),(6,4),(7,4),(8,7),(9,6),(9,7),(10,5),(10,9),(11,5),(11,8),(11,9)],12)
=> ([(2,5),(3,6),(3,11),(4,7),(4,9),(5,11),(6,10),(6,11),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11)],12)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} - 1
01100 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ([(2,3),(2,10),(3,12),(4,5),(4,8),(4,12),(5,9),(5,11),(6,8),(6,9),(6,11),(6,12),(7,9),(7,10),(7,11),(7,12),(8,9),(8,10),(8,11),(9,12),(10,11),(10,12),(11,12)],13)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} - 1
01101 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ([(2,5),(3,4),(3,11),(4,9),(5,10),(6,8),(6,9),(6,11),(7,8),(7,10),(7,11),(8,10),(9,10),(9,11)],12)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} - 1
01110 => ([(0,3),(0,4),(1,2),(1,10),(1,11),(2,8),(2,9),(3,6),(3,7),(4,1),(4,6),(4,7),(6,11),(7,10),(8,5),(9,5),(10,8),(11,9)],12)
=> ([(2,6),(3,6),(3,9),(3,10),(4,5),(4,8),(4,10),(5,7),(5,9),(6,11),(7,8),(7,10),(7,11),(8,9),(8,11),(9,10),(9,11),(10,11)],12)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} - 1
01111 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ([(2,9),(3,8),(4,7),(4,8),(5,6),(5,9),(6,7),(6,8),(7,9),(8,9)],10)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} - 1
10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ([(2,9),(3,8),(4,7),(4,8),(5,6),(5,9),(6,7),(6,8),(7,9),(8,9)],10)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} - 1
10001 => ([(0,3),(0,4),(1,2),(1,10),(1,11),(2,8),(2,9),(3,6),(3,7),(4,1),(4,6),(4,7),(6,11),(7,10),(8,5),(9,5),(10,8),(11,9)],12)
=> ([(2,6),(3,6),(3,9),(3,10),(4,5),(4,8),(4,10),(5,7),(5,9),(6,11),(7,8),(7,10),(7,11),(8,9),(8,11),(9,10),(9,11),(10,11)],12)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} - 1
10010 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ([(2,5),(3,4),(3,11),(4,9),(5,10),(6,8),(6,9),(6,11),(7,8),(7,10),(7,11),(8,10),(9,10),(9,11)],12)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} - 1
10011 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ([(2,3),(2,10),(3,12),(4,5),(4,8),(4,12),(5,9),(5,11),(6,8),(6,9),(6,11),(6,12),(7,9),(7,10),(7,11),(7,12),(8,9),(8,10),(8,11),(9,12),(10,11),(10,12),(11,12)],13)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} - 1
10100 => ([(0,2),(0,3),(1,8),(2,10),(2,11),(3,1),(3,10),(3,11),(5,6),(6,4),(7,4),(8,7),(9,6),(9,7),(10,5),(10,9),(11,5),(11,8),(11,9)],12)
=> ([(2,5),(3,6),(3,11),(4,7),(4,9),(5,11),(6,10),(6,11),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11)],12)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} - 1
10101 => ([(0,1),(0,2),(1,8),(1,9),(2,8),(2,9),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5),(8,6),(8,7),(9,6),(9,7)],10)
=> ([(2,9),(3,8),(4,7),(5,6)],10)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} - 1
10110 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ([(2,5),(3,4),(3,11),(4,9),(5,10),(6,8),(6,9),(6,11),(7,8),(7,10),(7,11),(8,10),(9,10),(9,11)],12)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} - 1
10111 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12)
=> ([(2,7),(3,6),(3,11),(4,8),(4,10),(4,11),(5,9),(5,10),(5,11),(6,8),(6,10),(7,9),(7,11),(8,9),(8,11),(9,10),(10,11)],12)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} - 1
11000 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ([(2,7),(2,11),(3,6),(3,10),(4,8),(4,10),(4,11),(5,9),(5,10),(5,11),(6,8),(6,11),(7,9),(7,10),(8,9),(8,10),(9,11),(10,11)],12)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} - 1
11001 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ([(2,3),(2,10),(3,12),(4,5),(4,8),(4,12),(5,9),(5,11),(6,8),(6,9),(6,11),(6,12),(7,9),(7,10),(7,11),(7,12),(8,9),(8,10),(8,11),(9,12),(10,11),(10,12),(11,12)],13)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} - 1
11010 => ([(0,2),(0,3),(1,8),(2,10),(2,11),(3,1),(3,10),(3,11),(5,6),(6,4),(7,4),(8,7),(9,6),(9,7),(10,5),(10,9),(11,5),(11,8),(11,9)],12)
=> ([(2,5),(3,6),(3,11),(4,7),(4,9),(5,11),(6,10),(6,11),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11)],12)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} - 1
11011 => ([(0,2),(0,3),(1,5),(1,6),(2,10),(2,11),(3,1),(3,10),(3,11),(5,8),(6,7),(7,4),(8,4),(9,7),(9,8),(10,6),(10,9),(11,5),(11,9)],12)
=> ([(2,5),(3,4),(3,10),(4,9),(5,11),(6,9),(6,10),(6,11),(7,8),(7,9),(7,11),(8,10),(8,11),(9,10)],12)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} - 1
11100 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ([(2,7),(2,11),(3,6),(3,10),(4,8),(4,10),(4,11),(5,9),(5,10),(5,11),(6,8),(6,11),(7,9),(7,10),(8,9),(8,10),(9,11),(10,11)],12)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} - 1
11101 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12)
=> ([(2,7),(3,6),(3,11),(4,8),(4,10),(4,11),(5,9),(5,10),(5,11),(6,8),(6,10),(7,9),(7,11),(8,9),(8,11),(9,10),(10,11)],12)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} - 1
11110 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ([(2,9),(3,8),(4,7),(4,8),(5,6),(5,9),(6,7),(6,8),(7,9),(8,9)],10)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} - 1
11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([],6)
=> 0 = 1 - 1
000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ([],7)
=> 0 = 1 - 1
000001 => ([(0,2),(0,6),(1,8),(2,7),(3,5),(3,9),(4,3),(4,11),(5,1),(5,10),(6,4),(6,7),(7,11),(9,10),(10,8),(11,9)],12)
=> ([(2,11),(3,10),(4,9),(4,10),(5,8),(5,11),(6,7),(6,9),(6,10),(7,8),(7,11),(8,9),(8,10),(9,11),(10,11)],12)
=> ? ∊ {6,6,6,6,6,6,6,6,6,6,6,6,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,20,20,20,20,20,20,20,20,20,20,64,64,64,64,64,64,64,64,64,64,90,90,90,90,90,90,90,99,99,111,111,272} - 1
000010 => ([(0,4),(0,5),(1,3),(1,12),(2,11),(3,2),(3,14),(4,10),(4,13),(5,1),(5,10),(5,13),(7,8),(8,9),(9,6),(10,7),(11,6),(12,8),(12,14),(13,7),(13,12),(14,9),(14,11)],15)
=> ([(2,10),(3,9),(3,14),(4,7),(4,9),(4,12),(4,14),(5,6),(5,10),(5,11),(5,13),(6,12),(6,13),(6,14),(7,11),(7,13),(7,14),(8,11),(8,12),(8,13),(8,14),(9,11),(9,13),(10,12),(10,14),(11,12),(11,14),(12,13),(13,14)],15)
=> ? ∊ {6,6,6,6,6,6,6,6,6,6,6,6,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,20,20,20,20,20,20,20,20,20,20,64,64,64,64,64,64,64,64,64,64,90,90,90,90,90,90,90,99,99,111,111,272} - 1
000011 => ([(0,5),(0,6),(1,4),(1,14),(2,11),(3,10),(4,3),(4,12),(5,1),(5,13),(6,2),(6,13),(8,9),(9,7),(10,7),(11,8),(12,9),(12,10),(13,11),(13,14),(14,8),(14,12)],15)
=> ([(2,10),(2,14),(3,9),(3,13),(4,6),(4,9),(4,12),(4,13),(5,7),(5,10),(5,11),(5,14),(6,11),(6,13),(6,14),(7,12),(7,13),(7,14),(8,11),(8,12),(8,13),(8,14),(9,11),(9,14),(10,12),(10,13),(11,12),(11,13),(12,14),(13,14)],15)
=> ? ∊ {6,6,6,6,6,6,6,6,6,6,6,6,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,20,20,20,20,20,20,20,20,20,20,64,64,64,64,64,64,64,64,64,64,90,90,90,90,90,90,90,99,99,111,111,272} - 1
000100 => ([(0,3),(0,4),(1,10),(2,1),(2,6),(2,12),(3,14),(3,15),(4,2),(4,14),(4,15),(6,7),(7,8),(8,5),(9,5),(10,9),(11,7),(11,13),(12,10),(12,13),(13,8),(13,9),(14,6),(14,11),(15,11),(15,12)],16)
=> ([(2,5),(3,4),(3,12),(3,14),(4,13),(4,15),(5,7),(5,15),(6,12),(6,13),(6,14),(6,15),(7,8),(7,10),(7,11),(8,11),(8,14),(8,15),(9,10),(9,11),(9,12),(9,14),(9,15),(10,13),(10,14),(10,15),(11,13),(11,15),(12,13),(12,15),(13,14),(14,15)],16)
=> ? ∊ {6,6,6,6,6,6,6,6,6,6,6,6,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,20,20,20,20,20,20,20,20,20,20,64,64,64,64,64,64,64,64,64,64,90,90,90,90,90,90,90,99,99,111,111,272} - 1
000101 => ([(0,3),(0,4),(1,2),(1,14),(2,6),(3,13),(3,15),(4,1),(4,13),(4,15),(6,9),(7,8),(8,10),(9,5),(10,5),(11,8),(11,12),(12,9),(12,10),(13,7),(13,11),(14,6),(14,12),(15,7),(15,11),(15,14)],16)
=> ([(2,6),(3,4),(3,13),(3,15),(4,12),(4,14),(5,8),(5,11),(5,15),(6,11),(6,15),(7,12),(7,13),(7,14),(7,15),(8,10),(8,11),(8,13),(8,15),(9,10),(9,11),(9,13),(9,14),(9,15),(10,12),(10,14),(10,15),(11,12),(11,14),(12,13),(12,15),(13,14),(14,15)],16)
=> ? ∊ {6,6,6,6,6,6,6,6,6,6,6,6,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,20,20,20,20,20,20,20,20,20,20,64,64,64,64,64,64,64,64,64,64,90,90,90,90,90,90,90,99,99,111,111,272} - 1
000110 => ([(0,4),(0,5),(1,11),(2,1),(2,13),(3,7),(3,14),(4,2),(4,12),(4,16),(5,3),(5,12),(5,16),(7,8),(8,9),(9,6),(10,6),(11,10),(12,7),(13,11),(13,15),(14,8),(14,15),(15,9),(15,10),(16,13),(16,14)],17)
=> ([(2,4),(2,13),(3,5),(3,12),(3,16),(4,11),(4,16),(5,10),(5,14),(5,15),(6,10),(6,12),(6,14),(6,15),(6,16),(7,11),(7,13),(7,14),(7,15),(7,16),(8,9),(8,10),(8,13),(8,14),(8,15),(8,16),(9,11),(9,12),(9,14),(9,15),(9,16),(10,11),(10,12),(10,16),(11,13),(11,14),(11,15),(12,13),(12,14),(12,15),(13,15),(13,16),(14,16),(15,16)],17)
=> ? ∊ {6,6,6,6,6,6,6,6,6,6,6,6,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,20,20,20,20,20,20,20,20,20,20,64,64,64,64,64,64,64,64,64,64,90,90,90,90,90,90,90,99,99,111,111,272} - 1
111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ([],7)
=> 0 = 1 - 1
Description
The size of a minimal vertex cover of a graph.
A '''vertex cover''' of a graph $G$ is a subset $S$ of the vertices of $G$ such that each edge of $G$ contains at least one vertex of $S$. Finding a minimal vertex cover is an NP-hard optimization problem.
Matching statistic: St000387
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Values
0 => ([(0,1)],2)
=> ([],2)
=> 0 = 1 - 1
1 => ([(0,1)],2)
=> ([],2)
=> 0 = 1 - 1
00 => ([(0,2),(2,1)],3)
=> ([],3)
=> 0 = 1 - 1
01 => ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(2,3)],4)
=> 1 = 2 - 1
10 => ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(2,3)],4)
=> 1 = 2 - 1
11 => ([(0,2),(2,1)],3)
=> ([],3)
=> 0 = 1 - 1
000 => ([(0,3),(2,1),(3,2)],4)
=> ([],4)
=> 0 = 1 - 1
001 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(2,5),(3,4),(4,5)],6)
=> 2 = 3 - 1
010 => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> ([(2,5),(3,4)],6)
=> 2 = 3 - 1
011 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(2,5),(3,4),(4,5)],6)
=> 2 = 3 - 1
100 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(2,5),(3,4),(4,5)],6)
=> 2 = 3 - 1
101 => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> ([(2,5),(3,4)],6)
=> 2 = 3 - 1
110 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(2,5),(3,4),(4,5)],6)
=> 2 = 3 - 1
111 => ([(0,3),(2,1),(3,2)],4)
=> ([],4)
=> 0 = 1 - 1
0000 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([],5)
=> 0 = 1 - 1
0001 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,6,16} - 1
0010 => ([(0,2),(0,3),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,5),(8,5),(8,6)],9)
=> ([(2,6),(3,4),(3,8),(4,7),(5,7),(5,8),(6,8),(7,8)],9)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,6,16} - 1
0011 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(2,5),(2,8),(3,4),(3,8),(4,7),(5,7),(6,7),(6,8),(7,8)],9)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,6,16} - 1
0100 => ([(0,2),(0,3),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,5),(8,5),(8,6)],9)
=> ([(2,6),(3,4),(3,8),(4,7),(5,7),(5,8),(6,8),(7,8)],9)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,6,16} - 1
0101 => ([(0,1),(0,2),(1,6),(1,7),(2,6),(2,7),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5)],8)
=> ([(2,7),(3,6),(4,5)],8)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,6,16} - 1
0110 => ([(0,2),(0,3),(1,5),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,6),(8,5)],9)
=> ([(2,5),(3,4),(3,7),(4,6),(5,8),(6,7),(6,8),(7,8)],9)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,6,16} - 1
0111 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,6,16} - 1
1000 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,6,16} - 1
1001 => ([(0,2),(0,3),(1,5),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,6),(8,5)],9)
=> ([(2,5),(3,4),(3,7),(4,6),(5,8),(6,7),(6,8),(7,8)],9)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,6,16} - 1
1010 => ([(0,1),(0,2),(1,6),(1,7),(2,6),(2,7),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5)],8)
=> ([(2,7),(3,6),(4,5)],8)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,6,16} - 1
1011 => ([(0,2),(0,3),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,5),(8,5),(8,6)],9)
=> ([(2,6),(3,4),(3,8),(4,7),(5,7),(5,8),(6,8),(7,8)],9)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,6,16} - 1
1100 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(2,5),(2,8),(3,4),(3,8),(4,7),(5,7),(6,7),(6,8),(7,8)],9)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,6,16} - 1
1101 => ([(0,2),(0,3),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,5),(8,5),(8,6)],9)
=> ([(2,6),(3,4),(3,8),(4,7),(5,7),(5,8),(6,8),(7,8)],9)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,6,16} - 1
1110 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? ∊ {4,4,4,4,4,4,4,4,6,6,6,6,6,16} - 1
1111 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([],5)
=> 0 = 1 - 1
00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([],6)
=> 0 = 1 - 1
00001 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ([(2,9),(3,8),(4,7),(4,8),(5,6),(5,9),(6,7),(6,8),(7,9),(8,9)],10)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} - 1
00010 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12)
=> ([(2,7),(3,6),(3,11),(4,8),(4,10),(4,11),(5,9),(5,10),(5,11),(6,8),(6,10),(7,9),(7,11),(8,9),(8,11),(9,10),(10,11)],12)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} - 1
00011 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ([(2,7),(2,11),(3,6),(3,10),(4,8),(4,10),(4,11),(5,9),(5,10),(5,11),(6,8),(6,11),(7,9),(7,10),(8,9),(8,10),(9,11),(10,11)],12)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} - 1
00100 => ([(0,2),(0,3),(1,5),(1,6),(2,10),(2,11),(3,1),(3,10),(3,11),(5,8),(6,7),(7,4),(8,4),(9,7),(9,8),(10,6),(10,9),(11,5),(11,9)],12)
=> ([(2,5),(3,4),(3,10),(4,9),(5,11),(6,9),(6,10),(6,11),(7,8),(7,9),(7,11),(8,10),(8,11),(9,10)],12)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} - 1
00101 => ([(0,2),(0,3),(1,8),(2,10),(2,11),(3,1),(3,10),(3,11),(5,6),(6,4),(7,4),(8,7),(9,6),(9,7),(10,5),(10,9),(11,5),(11,8),(11,9)],12)
=> ([(2,5),(3,6),(3,11),(4,7),(4,9),(5,11),(6,10),(6,11),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11)],12)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} - 1
00110 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ([(2,3),(2,10),(3,12),(4,5),(4,8),(4,12),(5,9),(5,11),(6,8),(6,9),(6,11),(6,12),(7,9),(7,10),(7,11),(7,12),(8,9),(8,10),(8,11),(9,12),(10,11),(10,12),(11,12)],13)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} - 1
00111 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ([(2,7),(2,11),(3,6),(3,10),(4,8),(4,10),(4,11),(5,9),(5,10),(5,11),(6,8),(6,11),(7,9),(7,10),(8,9),(8,10),(9,11),(10,11)],12)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} - 1
01000 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12)
=> ([(2,7),(3,6),(3,11),(4,8),(4,10),(4,11),(5,9),(5,10),(5,11),(6,8),(6,10),(7,9),(7,11),(8,9),(8,11),(9,10),(10,11)],12)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} - 1
01001 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ([(2,5),(3,4),(3,11),(4,9),(5,10),(6,8),(6,9),(6,11),(7,8),(7,10),(7,11),(8,10),(9,10),(9,11)],12)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} - 1
01010 => ([(0,1),(0,2),(1,8),(1,9),(2,8),(2,9),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5),(8,6),(8,7),(9,6),(9,7)],10)
=> ([(2,9),(3,8),(4,7),(5,6)],10)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} - 1
01011 => ([(0,2),(0,3),(1,8),(2,10),(2,11),(3,1),(3,10),(3,11),(5,6),(6,4),(7,4),(8,7),(9,6),(9,7),(10,5),(10,9),(11,5),(11,8),(11,9)],12)
=> ([(2,5),(3,6),(3,11),(4,7),(4,9),(5,11),(6,10),(6,11),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11)],12)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} - 1
01100 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ([(2,3),(2,10),(3,12),(4,5),(4,8),(4,12),(5,9),(5,11),(6,8),(6,9),(6,11),(6,12),(7,9),(7,10),(7,11),(7,12),(8,9),(8,10),(8,11),(9,12),(10,11),(10,12),(11,12)],13)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} - 1
01101 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ([(2,5),(3,4),(3,11),(4,9),(5,10),(6,8),(6,9),(6,11),(7,8),(7,10),(7,11),(8,10),(9,10),(9,11)],12)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} - 1
01110 => ([(0,3),(0,4),(1,2),(1,10),(1,11),(2,8),(2,9),(3,6),(3,7),(4,1),(4,6),(4,7),(6,11),(7,10),(8,5),(9,5),(10,8),(11,9)],12)
=> ([(2,6),(3,6),(3,9),(3,10),(4,5),(4,8),(4,10),(5,7),(5,9),(6,11),(7,8),(7,10),(7,11),(8,9),(8,11),(9,10),(9,11),(10,11)],12)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} - 1
01111 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ([(2,9),(3,8),(4,7),(4,8),(5,6),(5,9),(6,7),(6,8),(7,9),(8,9)],10)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} - 1
10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ([(2,9),(3,8),(4,7),(4,8),(5,6),(5,9),(6,7),(6,8),(7,9),(8,9)],10)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} - 1
10001 => ([(0,3),(0,4),(1,2),(1,10),(1,11),(2,8),(2,9),(3,6),(3,7),(4,1),(4,6),(4,7),(6,11),(7,10),(8,5),(9,5),(10,8),(11,9)],12)
=> ([(2,6),(3,6),(3,9),(3,10),(4,5),(4,8),(4,10),(5,7),(5,9),(6,11),(7,8),(7,10),(7,11),(8,9),(8,11),(9,10),(9,11),(10,11)],12)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} - 1
10010 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ([(2,5),(3,4),(3,11),(4,9),(5,10),(6,8),(6,9),(6,11),(7,8),(7,10),(7,11),(8,10),(9,10),(9,11)],12)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} - 1
10011 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ([(2,3),(2,10),(3,12),(4,5),(4,8),(4,12),(5,9),(5,11),(6,8),(6,9),(6,11),(6,12),(7,9),(7,10),(7,11),(7,12),(8,9),(8,10),(8,11),(9,12),(10,11),(10,12),(11,12)],13)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} - 1
10100 => ([(0,2),(0,3),(1,8),(2,10),(2,11),(3,1),(3,10),(3,11),(5,6),(6,4),(7,4),(8,7),(9,6),(9,7),(10,5),(10,9),(11,5),(11,8),(11,9)],12)
=> ([(2,5),(3,6),(3,11),(4,7),(4,9),(5,11),(6,10),(6,11),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11)],12)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} - 1
10101 => ([(0,1),(0,2),(1,8),(1,9),(2,8),(2,9),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5),(8,6),(8,7),(9,6),(9,7)],10)
=> ([(2,9),(3,8),(4,7),(5,6)],10)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} - 1
10110 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ([(2,5),(3,4),(3,11),(4,9),(5,10),(6,8),(6,9),(6,11),(7,8),(7,10),(7,11),(8,10),(9,10),(9,11)],12)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} - 1
10111 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12)
=> ([(2,7),(3,6),(3,11),(4,8),(4,10),(4,11),(5,9),(5,10),(5,11),(6,8),(6,10),(7,9),(7,11),(8,9),(8,11),(9,10),(10,11)],12)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} - 1
11000 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ([(2,7),(2,11),(3,6),(3,10),(4,8),(4,10),(4,11),(5,9),(5,10),(5,11),(6,8),(6,11),(7,9),(7,10),(8,9),(8,10),(9,11),(10,11)],12)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} - 1
11001 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ([(2,3),(2,10),(3,12),(4,5),(4,8),(4,12),(5,9),(5,11),(6,8),(6,9),(6,11),(6,12),(7,9),(7,10),(7,11),(7,12),(8,9),(8,10),(8,11),(9,12),(10,11),(10,12),(11,12)],13)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} - 1
11010 => ([(0,2),(0,3),(1,8),(2,10),(2,11),(3,1),(3,10),(3,11),(5,6),(6,4),(7,4),(8,7),(9,6),(9,7),(10,5),(10,9),(11,5),(11,8),(11,9)],12)
=> ([(2,5),(3,6),(3,11),(4,7),(4,9),(5,11),(6,10),(6,11),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11)],12)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} - 1
11011 => ([(0,2),(0,3),(1,5),(1,6),(2,10),(2,11),(3,1),(3,10),(3,11),(5,8),(6,7),(7,4),(8,4),(9,7),(9,8),(10,6),(10,9),(11,5),(11,9)],12)
=> ([(2,5),(3,4),(3,10),(4,9),(5,11),(6,9),(6,10),(6,11),(7,8),(7,9),(7,11),(8,10),(8,11),(9,10)],12)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} - 1
11100 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ([(2,7),(2,11),(3,6),(3,10),(4,8),(4,10),(4,11),(5,9),(5,10),(5,11),(6,8),(6,11),(7,9),(7,10),(8,9),(8,10),(9,11),(10,11)],12)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} - 1
11101 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12)
=> ([(2,7),(3,6),(3,11),(4,8),(4,10),(4,11),(5,9),(5,10),(5,11),(6,8),(6,10),(7,9),(7,11),(8,9),(8,11),(9,10),(10,11)],12)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} - 1
11110 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ([(2,9),(3,8),(4,7),(4,8),(5,6),(5,9),(6,7),(6,8),(7,9),(8,9)],10)
=> ? ∊ {5,5,5,5,5,5,5,5,5,5,10,10,10,10,10,10,10,10,10,10,10,10,10,10,35,35,35,35,35,35} - 1
11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([],6)
=> 0 = 1 - 1
000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ([],7)
=> 0 = 1 - 1
000001 => ([(0,2),(0,6),(1,8),(2,7),(3,5),(3,9),(4,3),(4,11),(5,1),(5,10),(6,4),(6,7),(7,11),(9,10),(10,8),(11,9)],12)
=> ([(2,11),(3,10),(4,9),(4,10),(5,8),(5,11),(6,7),(6,9),(6,10),(7,8),(7,11),(8,9),(8,10),(9,11),(10,11)],12)
=> ? ∊ {6,6,6,6,6,6,6,6,6,6,6,6,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,20,20,20,20,20,20,20,20,20,20,64,64,64,64,64,64,64,64,64,64,90,90,90,90,90,90,90,99,99,111,111,272} - 1
000010 => ([(0,4),(0,5),(1,3),(1,12),(2,11),(3,2),(3,14),(4,10),(4,13),(5,1),(5,10),(5,13),(7,8),(8,9),(9,6),(10,7),(11,6),(12,8),(12,14),(13,7),(13,12),(14,9),(14,11)],15)
=> ([(2,10),(3,9),(3,14),(4,7),(4,9),(4,12),(4,14),(5,6),(5,10),(5,11),(5,13),(6,12),(6,13),(6,14),(7,11),(7,13),(7,14),(8,11),(8,12),(8,13),(8,14),(9,11),(9,13),(10,12),(10,14),(11,12),(11,14),(12,13),(13,14)],15)
=> ? ∊ {6,6,6,6,6,6,6,6,6,6,6,6,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,20,20,20,20,20,20,20,20,20,20,64,64,64,64,64,64,64,64,64,64,90,90,90,90,90,90,90,99,99,111,111,272} - 1
000011 => ([(0,5),(0,6),(1,4),(1,14),(2,11),(3,10),(4,3),(4,12),(5,1),(5,13),(6,2),(6,13),(8,9),(9,7),(10,7),(11,8),(12,9),(12,10),(13,11),(13,14),(14,8),(14,12)],15)
=> ([(2,10),(2,14),(3,9),(3,13),(4,6),(4,9),(4,12),(4,13),(5,7),(5,10),(5,11),(5,14),(6,11),(6,13),(6,14),(7,12),(7,13),(7,14),(8,11),(8,12),(8,13),(8,14),(9,11),(9,14),(10,12),(10,13),(11,12),(11,13),(12,14),(13,14)],15)
=> ? ∊ {6,6,6,6,6,6,6,6,6,6,6,6,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,20,20,20,20,20,20,20,20,20,20,64,64,64,64,64,64,64,64,64,64,90,90,90,90,90,90,90,99,99,111,111,272} - 1
000100 => ([(0,3),(0,4),(1,10),(2,1),(2,6),(2,12),(3,14),(3,15),(4,2),(4,14),(4,15),(6,7),(7,8),(8,5),(9,5),(10,9),(11,7),(11,13),(12,10),(12,13),(13,8),(13,9),(14,6),(14,11),(15,11),(15,12)],16)
=> ([(2,5),(3,4),(3,12),(3,14),(4,13),(4,15),(5,7),(5,15),(6,12),(6,13),(6,14),(6,15),(7,8),(7,10),(7,11),(8,11),(8,14),(8,15),(9,10),(9,11),(9,12),(9,14),(9,15),(10,13),(10,14),(10,15),(11,13),(11,15),(12,13),(12,15),(13,14),(14,15)],16)
=> ? ∊ {6,6,6,6,6,6,6,6,6,6,6,6,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,20,20,20,20,20,20,20,20,20,20,64,64,64,64,64,64,64,64,64,64,90,90,90,90,90,90,90,99,99,111,111,272} - 1
000101 => ([(0,3),(0,4),(1,2),(1,14),(2,6),(3,13),(3,15),(4,1),(4,13),(4,15),(6,9),(7,8),(8,10),(9,5),(10,5),(11,8),(11,12),(12,9),(12,10),(13,7),(13,11),(14,6),(14,12),(15,7),(15,11),(15,14)],16)
=> ([(2,6),(3,4),(3,13),(3,15),(4,12),(4,14),(5,8),(5,11),(5,15),(6,11),(6,15),(7,12),(7,13),(7,14),(7,15),(8,10),(8,11),(8,13),(8,15),(9,10),(9,11),(9,13),(9,14),(9,15),(10,12),(10,14),(10,15),(11,12),(11,14),(12,13),(12,15),(13,14),(14,15)],16)
=> ? ∊ {6,6,6,6,6,6,6,6,6,6,6,6,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,20,20,20,20,20,20,20,20,20,20,64,64,64,64,64,64,64,64,64,64,90,90,90,90,90,90,90,99,99,111,111,272} - 1
000110 => ([(0,4),(0,5),(1,11),(2,1),(2,13),(3,7),(3,14),(4,2),(4,12),(4,16),(5,3),(5,12),(5,16),(7,8),(8,9),(9,6),(10,6),(11,10),(12,7),(13,11),(13,15),(14,8),(14,15),(15,9),(15,10),(16,13),(16,14)],17)
=> ([(2,4),(2,13),(3,5),(3,12),(3,16),(4,11),(4,16),(5,10),(5,14),(5,15),(6,10),(6,12),(6,14),(6,15),(6,16),(7,11),(7,13),(7,14),(7,15),(7,16),(8,9),(8,10),(8,13),(8,14),(8,15),(8,16),(9,11),(9,12),(9,14),(9,15),(9,16),(10,11),(10,12),(10,16),(11,13),(11,14),(11,15),(12,13),(12,14),(12,15),(13,15),(13,16),(14,16),(15,16)],17)
=> ? ∊ {6,6,6,6,6,6,6,6,6,6,6,6,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,20,20,20,20,20,20,20,20,20,20,64,64,64,64,64,64,64,64,64,64,90,90,90,90,90,90,90,99,99,111,111,272} - 1
111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ([],7)
=> 0 = 1 - 1
Description
The matching number of a graph.
For a graph $G$, this is defined as the maximal size of a '''matching''' or '''independent edge set''' (a set of edges without common vertices) contained in $G$.
The following 7 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
St000985The number of positive eigenvalues of the adjacency matrix of the graph. St001176The size of a partition minus its first part. St001214The aft of an integer partition. St001704The size of the largest multi-subset-intersection of the deck of a graph with the deck of another graph. St001883The mutual visibility number of a graph. St001971The number of negative eigenvalues of the adjacency matrix of the graph. St001880The number of 2-Gorenstein indecomposable injective modules in the incidence algebra of the lattice.
Sorry, this statistic was not found in the database
or
add this statistic to the database – it's very simple and we need your support!