Your data matches 6 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St001657
Mapping
Mp00178: Binary words —to composition⟶ Integer compositions
Mp00180: Integer compositions —to ribbon⟶ Skew partitions
Mp00182: Skew partitions —outer shape⟶ Integer partitions
St001657: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
0 => [2] => [[2],[]]
 => [2]
 => 1
1 => [1,1] => [[1,1],[]]
 => [1,1]
 => 0
00 => [3] => [[3],[]]
 => [3]
 => 0
01 => [2,1] => [[2,2],[1]]
 => [2,2]
 => 2
10 => [1,2] => [[2,1],[]]
 => [2,1]
 => 1
11 => [1,1,1] => [[1,1,1],[]]
 => [1,1,1]
 => 0
000 => [4] => [[4],[]]
 => [4]
 => 0
001 => [3,1] => [[3,3],[2]]
 => [3,3]
 => 0
010 => [2,2] => [[3,2],[1]]
 => [3,2]
 => 1
011 => [2,1,1] => [[2,2,2],[1,1]]
 => [2,2,2]
 => 3
100 => [1,3] => [[3,1],[]]
 => [3,1]
 => 0
101 => [1,2,1] => [[2,2,1],[1]]
 => [2,2,1]
 => 2
110 => [1,1,2] => [[2,1,1],[]]
 => [2,1,1]
 => 1
111 => [1,1,1,1] => [[1,1,1,1],[]]
 => [1,1,1,1]
 => 0
0000 => [5] => [[5],[]]
 => [5]
 => 0
0001 => [4,1] => [[4,4],[3]]
 => [4,4]
 => 0
0010 => [3,2] => [[4,3],[2]]
 => [4,3]
 => 0
0011 => [3,1,1] => [[3,3,3],[2,2]]
 => [3,3,3]
 => 0
0100 => [2,3] => [[4,2],[1]]
 => [4,2]
 => 1
0101 => [2,2,1] => [[3,3,2],[2,1]]
 => [3,3,2]
 => 1
0110 => [2,1,2] => [[3,2,2],[1,1]]
 => [3,2,2]
 => 2
0111 => [2,1,1,1] => [[2,2,2,2],[1,1,1]]
 => [2,2,2,2]
 => 4
1000 => [1,4] => [[4,1],[]]
 => [4,1]
 => 0
1001 => [1,3,1] => [[3,3,1],[2]]
 => [3,3,1]
 => 0
1010 => [1,2,2] => [[3,2,1],[1]]
 => [3,2,1]
 => 1
1011 => [1,2,1,1] => [[2,2,2,1],[1,1]]
 => [2,2,2,1]
 => 3
1100 => [1,1,3] => [[3,1,1],[]]
 => [3,1,1]
 => 0
1101 => [1,1,2,1] => [[2,2,1,1],[1]]
 => [2,2,1,1]
 => 2
1110 => [1,1,1,2] => [[2,1,1,1],[]]
 => [2,1,1,1]
 => 1
1111 => [1,1,1,1,1] => [[1,1,1,1,1],[]]
 => [1,1,1,1,1]
 => 0
00000 => [6] => [[6],[]]
 => [6]
 => 0
00001 => [5,1] => [[5,5],[4]]
 => [5,5]
 => 0
00010 => [4,2] => [[5,4],[3]]
 => [5,4]
 => 0
00011 => [4,1,1] => [[4,4,4],[3,3]]
 => [4,4,4]
 => 0
00100 => [3,3] => [[5,3],[2]]
 => [5,3]
 => 0
00101 => [3,2,1] => [[4,4,3],[3,2]]
 => [4,4,3]
 => 0
00110 => [3,1,2] => [[4,3,3],[2,2]]
 => [4,3,3]
 => 0
00111 => [3,1,1,1] => [[3,3,3,3],[2,2,2]]
 => [3,3,3,3]
 => 0
01000 => [2,4] => [[5,2],[1]]
 => [5,2]
 => 1
01001 => [2,3,1] => [[4,4,2],[3,1]]
 => [4,4,2]
 => 1
01010 => [2,2,2] => [[4,3,2],[2,1]]
 => [4,3,2]
 => 1
01011 => [2,2,1,1] => [[3,3,3,2],[2,2,1]]
 => [3,3,3,2]
 => 1
01100 => [2,1,3] => [[4,2,2],[1,1]]
 => [4,2,2]
 => 2
01101 => [2,1,2,1] => [[3,3,2,2],[2,1,1]]
 => [3,3,2,2]
 => 2
01110 => [2,1,1,2] => [[3,2,2,2],[1,1,1]]
 => [3,2,2,2]
 => 3
01111 => [2,1,1,1,1] => [[2,2,2,2,2],[1,1,1,1]]
 => [2,2,2,2,2]
 => 5
10000 => [1,5] => [[5,1],[]]
 => [5,1]
 => 0
10001 => [1,4,1] => [[4,4,1],[3]]
 => [4,4,1]
 => 0
10010 => [1,3,2] => [[4,3,1],[2]]
 => [4,3,1]
 => 0
10011 => [1,3,1,1] => [[3,3,3,1],[2,2]]
 => [3,3,3,1]
 => 0
Description
The number of twos in an integer partition. The total number of twos in all partitions of $n$ is equal to the total number of singletons [[St001484]] in all partitions of $n-1$, see [1].
Matching statistic: St000326
(load all 2 compositions to match this statistic)
Mapping
Mp00268: Binary words —zeros to flag zeros⟶ Binary words
Mp00096: Binary words —Foata bijection⟶ Binary words
St000326: Binary words ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
0 => 0 => 0 => 2 = 1 + 1
1 => 1 => 1 => 1 = 0 + 1
00 => 10 => 10 => 1 = 0 + 1
01 => 00 => 00 => 3 = 2 + 1
10 => 01 => 01 => 2 = 1 + 1
11 => 11 => 11 => 1 = 0 + 1
000 => 010 => 100 => 1 = 0 + 1
001 => 110 => 110 => 1 = 0 + 1
010 => 100 => 010 => 2 = 1 + 1
011 => 000 => 000 => 4 = 3 + 1
100 => 101 => 101 => 1 = 0 + 1
101 => 001 => 001 => 3 = 2 + 1
110 => 011 => 011 => 2 = 1 + 1
111 => 111 => 111 => 1 = 0 + 1
0000 => 1010 => 1100 => 1 = 0 + 1
0001 => 0010 => 1000 => 1 = 0 + 1
0010 => 0110 => 1010 => 1 = 0 + 1
0011 => 1110 => 1110 => 1 = 0 + 1
0100 => 0100 => 0100 => 2 = 1 + 1
0101 => 1100 => 0110 => 2 = 1 + 1
0110 => 1000 => 0010 => 3 = 2 + 1
0111 => 0000 => 0000 => 5 = 4 + 1
1000 => 0101 => 1001 => 1 = 0 + 1
1001 => 1101 => 1101 => 1 = 0 + 1
1010 => 1001 => 0101 => 2 = 1 + 1
1011 => 0001 => 0001 => 4 = 3 + 1
1100 => 1011 => 1011 => 1 = 0 + 1
1101 => 0011 => 0011 => 3 = 2 + 1
1110 => 0111 => 0111 => 2 = 1 + 1
1111 => 1111 => 1111 => 1 = 0 + 1
00000 => 01010 => 11000 => 1 = 0 + 1
00001 => 11010 => 11100 => 1 = 0 + 1
00010 => 10010 => 10100 => 1 = 0 + 1
00011 => 00010 => 10000 => 1 = 0 + 1
00100 => 10110 => 11010 => 1 = 0 + 1
00101 => 00110 => 10010 => 1 = 0 + 1
00110 => 01110 => 10110 => 1 = 0 + 1
00111 => 11110 => 11110 => 1 = 0 + 1
01000 => 10100 => 01100 => 2 = 1 + 1
01001 => 00100 => 01000 => 2 = 1 + 1
01010 => 01100 => 01010 => 2 = 1 + 1
01011 => 11100 => 01110 => 2 = 1 + 1
01100 => 01000 => 00100 => 3 = 2 + 1
01101 => 11000 => 00110 => 3 = 2 + 1
01110 => 10000 => 00010 => 4 = 3 + 1
01111 => 00000 => 00000 => 6 = 5 + 1
10000 => 10101 => 11001 => 1 = 0 + 1
10001 => 00101 => 10001 => 1 = 0 + 1
10010 => 01101 => 10101 => 1 = 0 + 1
10011 => 11101 => 11101 => 1 = 0 + 1
=> => => ? = 0 + 1
Description
The position of the first one in a binary word after appending a 1 at the end. Regarding the binary word as a subset of $\{1,\dots,n,n+1\}$ that contains $n+1$, this is the minimal element of the set.
Matching statistic: St000297
Mapping
Mp00268: Binary words —zeros to flag zeros⟶ Binary words
Mp00096: Binary words —Foata bijection⟶ Binary words
Mp00105: Binary words —complement⟶ Binary words
St000297: Binary words ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
0 => 0 => 0 => 1 => 1
1 => 1 => 1 => 0 => 0
00 => 10 => 10 => 01 => 0
01 => 00 => 00 => 11 => 2
10 => 01 => 01 => 10 => 1
11 => 11 => 11 => 00 => 0
000 => 010 => 100 => 011 => 0
001 => 110 => 110 => 001 => 0
010 => 100 => 010 => 101 => 1
011 => 000 => 000 => 111 => 3
100 => 101 => 101 => 010 => 0
101 => 001 => 001 => 110 => 2
110 => 011 => 011 => 100 => 1
111 => 111 => 111 => 000 => 0
0000 => 1010 => 1100 => 0011 => 0
0001 => 0010 => 1000 => 0111 => 0
0010 => 0110 => 1010 => 0101 => 0
0011 => 1110 => 1110 => 0001 => 0
0100 => 0100 => 0100 => 1011 => 1
0101 => 1100 => 0110 => 1001 => 1
0110 => 1000 => 0010 => 1101 => 2
0111 => 0000 => 0000 => 1111 => 4
1000 => 0101 => 1001 => 0110 => 0
1001 => 1101 => 1101 => 0010 => 0
1010 => 1001 => 0101 => 1010 => 1
1011 => 0001 => 0001 => 1110 => 3
1100 => 1011 => 1011 => 0100 => 0
1101 => 0011 => 0011 => 1100 => 2
1110 => 0111 => 0111 => 1000 => 1
1111 => 1111 => 1111 => 0000 => 0
00000 => 01010 => 11000 => 00111 => 0
00001 => 11010 => 11100 => 00011 => 0
00010 => 10010 => 10100 => 01011 => 0
00011 => 00010 => 10000 => 01111 => 0
00100 => 10110 => 11010 => 00101 => 0
00101 => 00110 => 10010 => 01101 => 0
00110 => 01110 => 10110 => 01001 => 0
00111 => 11110 => 11110 => 00001 => 0
01000 => 10100 => 01100 => 10011 => 1
01001 => 00100 => 01000 => 10111 => 1
01010 => 01100 => 01010 => 10101 => 1
01011 => 11100 => 01110 => 10001 => 1
01100 => 01000 => 00100 => 11011 => 2
01101 => 11000 => 00110 => 11001 => 2
01110 => 10000 => 00010 => 11101 => 3
01111 => 00000 => 00000 => 11111 => 5
10000 => 10101 => 11001 => 00110 => 0
10001 => 00101 => 10001 => 01110 => 0
10010 => 01101 => 10101 => 01010 => 0
10011 => 11101 => 11101 => 00010 => 0
=> => => => ? = 0
Description
The number of leading ones in a binary word.
Matching statistic: St000382
Mapping
Mp00268: Binary words —zeros to flag zeros⟶ Binary words
Mp00096: Binary words —Foata bijection⟶ Binary words
Mp00178: Binary words —to composition⟶ Integer compositions
St000382: Integer compositions ⟶ ℤResult quality: 98% ●values known / values provided: 98%●distinct values known / distinct values provided: 100%
Values
0 => 0 => 0 => [2] => 2 = 1 + 1
1 => 1 => 1 => [1,1] => 1 = 0 + 1
00 => 10 => 10 => [1,2] => 1 = 0 + 1
01 => 00 => 00 => [3] => 3 = 2 + 1
10 => 01 => 01 => [2,1] => 2 = 1 + 1
11 => 11 => 11 => [1,1,1] => 1 = 0 + 1
000 => 010 => 100 => [1,3] => 1 = 0 + 1
001 => 110 => 110 => [1,1,2] => 1 = 0 + 1
010 => 100 => 010 => [2,2] => 2 = 1 + 1
011 => 000 => 000 => [4] => 4 = 3 + 1
100 => 101 => 101 => [1,2,1] => 1 = 0 + 1
101 => 001 => 001 => [3,1] => 3 = 2 + 1
110 => 011 => 011 => [2,1,1] => 2 = 1 + 1
111 => 111 => 111 => [1,1,1,1] => 1 = 0 + 1
0000 => 1010 => 1100 => [1,1,3] => 1 = 0 + 1
0001 => 0010 => 1000 => [1,4] => 1 = 0 + 1
0010 => 0110 => 1010 => [1,2,2] => 1 = 0 + 1
0011 => 1110 => 1110 => [1,1,1,2] => 1 = 0 + 1
0100 => 0100 => 0100 => [2,3] => 2 = 1 + 1
0101 => 1100 => 0110 => [2,1,2] => 2 = 1 + 1
0110 => 1000 => 0010 => [3,2] => 3 = 2 + 1
0111 => 0000 => 0000 => [5] => 5 = 4 + 1
1000 => 0101 => 1001 => [1,3,1] => 1 = 0 + 1
1001 => 1101 => 1101 => [1,1,2,1] => 1 = 0 + 1
1010 => 1001 => 0101 => [2,2,1] => 2 = 1 + 1
1011 => 0001 => 0001 => [4,1] => 4 = 3 + 1
1100 => 1011 => 1011 => [1,2,1,1] => 1 = 0 + 1
1101 => 0011 => 0011 => [3,1,1] => 3 = 2 + 1
1110 => 0111 => 0111 => [2,1,1,1] => 2 = 1 + 1
1111 => 1111 => 1111 => [1,1,1,1,1] => 1 = 0 + 1
00000 => 01010 => 11000 => [1,1,4] => 1 = 0 + 1
00001 => 11010 => 11100 => [1,1,1,3] => 1 = 0 + 1
00010 => 10010 => 10100 => [1,2,3] => 1 = 0 + 1
00011 => 00010 => 10000 => [1,5] => 1 = 0 + 1
00100 => 10110 => 11010 => [1,1,2,2] => 1 = 0 + 1
00101 => 00110 => 10010 => [1,3,2] => 1 = 0 + 1
00110 => 01110 => 10110 => [1,2,1,2] => 1 = 0 + 1
00111 => 11110 => 11110 => [1,1,1,1,2] => 1 = 0 + 1
01000 => 10100 => 01100 => [2,1,3] => 2 = 1 + 1
01001 => 00100 => 01000 => [2,4] => 2 = 1 + 1
01010 => 01100 => 01010 => [2,2,2] => 2 = 1 + 1
01011 => 11100 => 01110 => [2,1,1,2] => 2 = 1 + 1
01100 => 01000 => 00100 => [3,3] => 3 = 2 + 1
01101 => 11000 => 00110 => [3,1,2] => 3 = 2 + 1
01110 => 10000 => 00010 => [4,2] => 4 = 3 + 1
01111 => 00000 => 00000 => [6] => 6 = 5 + 1
10000 => 10101 => 11001 => [1,1,3,1] => 1 = 0 + 1
10001 => 00101 => 10001 => [1,4,1] => 1 = 0 + 1
10010 => 01101 => 10101 => [1,2,2,1] => 1 = 0 + 1
10011 => 11101 => 11101 => [1,1,1,2,1] => 1 = 0 + 1
110000000 => 010101011 => 111000011 => [1,1,1,5,1,1] => ? = 0 + 1
111000000 => 101010111 => 111000111 => [1,1,1,4,1,1,1] => ? = 0 + 1
111100000 => 010101111 => 110001111 => [1,1,4,1,1,1,1] => ? = 0 + 1
111110000 => 101011111 => 110011111 => [1,1,3,1,1,1,1,1] => ? = 0 + 1
111111000 => 010111111 => 100111111 => [1,3,1,1,1,1,1,1] => ? = 0 + 1
Description
The first part of an integer composition.
Matching statistic: St001826
Mapping
Mp00178: Binary words —to composition⟶ Integer compositions
Mp00041: Integer compositions —conjugate⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St001826: Graphs ⟶ ℤResult quality: 54% ●values known / values provided: 54%●distinct values known / distinct values provided: 78%
Values
0 => [2] => [1,1] => ([(0,1)],2)
 => 1
1 => [1,1] => [2] => ([],2)
 => 0
00 => [3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 0
01 => [2,1] => [2,1] => ([(0,2),(1,2)],3)
 => 2
10 => [1,2] => [1,2] => ([(1,2)],3)
 => 1
11 => [1,1,1] => [3] => ([],3)
 => 0
000 => [4] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 0
001 => [3,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 0
010 => [2,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 1
011 => [2,1,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
 => 3
100 => [1,3] => [1,1,2] => ([(1,2),(1,3),(2,3)],4)
 => 0
101 => [1,2,1] => [2,2] => ([(1,3),(2,3)],4)
 => 2
110 => [1,1,2] => [1,3] => ([(2,3)],4)
 => 1
111 => [1,1,1,1] => [4] => ([],4)
 => 0
0000 => [5] => [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
0001 => [4,1] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 0
0010 => [3,2] => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 0
0011 => [3,1,1] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 0
0100 => [2,3] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
0101 => [2,2,1] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
0110 => [2,1,2] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
0111 => [2,1,1,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 4
1000 => [1,4] => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 0
1001 => [1,3,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 0
1010 => [1,2,2] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
 => 1
1011 => [1,2,1,1] => [3,2] => ([(1,4),(2,4),(3,4)],5)
 => 3
1100 => [1,1,3] => [1,1,3] => ([(2,3),(2,4),(3,4)],5)
 => 0
1101 => [1,1,2,1] => [2,3] => ([(2,4),(3,4)],5)
 => 2
1110 => [1,1,1,2] => [1,4] => ([(3,4)],5)
 => 1
1111 => [1,1,1,1,1] => [5] => ([],5)
 => 0
00000 => [6] => [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
00001 => [5,1] => [2,1,1,1,1] => ([(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
00010 => [4,2] => [1,2,1,1,1] => ([(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
00011 => [4,1,1] => [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
00100 => [3,3] => [1,1,2,1,1] => ([(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
00101 => [3,2,1] => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 0
00110 => [3,1,2] => [1,3,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 0
00111 => [3,1,1,1] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 0
01000 => [2,4] => [1,1,1,2,1] => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1
01001 => [2,3,1] => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1
01010 => [2,2,2] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1
01011 => [2,2,1,1] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1
01100 => [2,1,3] => [1,1,3,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
01101 => [2,1,2,1] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
01110 => [2,1,1,2] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => 3
01111 => [2,1,1,1,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 5
10000 => [1,5] => [1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 0
10001 => [1,4,1] => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 0
10010 => [1,3,2] => [1,2,1,2] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 0
10011 => [1,3,1,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 0
001100 => [3,1,3] => [1,1,3,1,1] => ([(0,5),(0,6),(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
0000000 => [8] => [1,1,1,1,1,1,1,1] => ([(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)
 => ? = 0
0000001 => [7,1] => [2,1,1,1,1,1,1] => ([(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)
 => ? = 0
0001000 => [4,4] => [1,1,1,2,1,1,1] => ([(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)
 => ? = 0
0001001 => [4,3,1] => [2,1,2,1,1,1] => ([(0,5),(0,6),(0,7),(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)
 => ? = 0
0001010 => [4,2,2] => [1,2,2,1,1,1] => ([(0,5),(0,6),(0,7),(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)
 => ? = 0
0001100 => [4,1,3] => [1,1,3,1,1,1] => ([(0,5),(0,6),(0,7),(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)
 => ? = 0
0001110 => [4,1,1,2] => [1,4,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(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)
 => ? = 0
0010001 => [3,4,1] => [2,1,1,2,1,1] => ([(0,6),(0,7),(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)
 => ? = 0
0010010 => [3,3,2] => [1,2,1,2,1,1] => ([(0,6),(0,7),(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)
 => ? = 0
0010100 => [3,2,3] => [1,1,2,2,1,1] => ([(0,6),(0,7),(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)
 => ? = 0
0010101 => [3,2,2,1] => [2,2,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(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)
 => ? = 0
0010110 => [3,2,1,2] => [1,3,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(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)
 => ? = 0
0011001 => [3,1,3,1] => [2,1,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(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)
 => ? = 0
0011010 => [3,1,2,2] => [1,2,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(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)
 => ? = 0
0011100 => [3,1,1,3] => [1,1,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(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)
 => ? = 0
0011101 => [3,1,1,2,1] => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 0
0100010 => [2,4,2] => [1,2,1,1,2,1] => ([(0,7),(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)
 => ? = 1
0100011 => [2,4,1,1] => [3,1,1,2,1] => ([(0,7),(1,4),(1,5),(1,6),(1,7),(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)
 => ? = 1
0100100 => [2,3,3] => [1,1,2,1,2,1] => ([(0,7),(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)
 => ? = 1
0100101 => [2,3,2,1] => [2,2,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(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)
 => ? = 1
0100110 => [2,3,1,2] => [1,3,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(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)
 => ? = 1
0101001 => [2,2,3,1] => [2,1,2,2,1] => ([(0,7),(1,6),(1,7),(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)
 => ? = 1
0101010 => [2,2,2,2] => [1,2,2,2,1] => ([(0,7),(1,6),(1,7),(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)
 => ? = 1
0101011 => [2,2,2,1,1] => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 1
0101100 => [2,2,1,3] => [1,1,3,2,1] => ([(0,7),(1,6),(1,7),(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)
 => ? = 1
0101101 => [2,2,1,2,1] => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 1
0101110 => [2,2,1,1,2] => [1,4,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 1
0101111 => [2,2,1,1,1,1] => [5,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 1
0110010 => [2,1,3,2] => [1,2,1,3,1] => ([(0,7),(1,7),(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)
 => ? = 2
0110011 => [2,1,3,1,1] => [3,1,3,1] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 2
0110100 => [2,1,2,3] => [1,1,2,3,1] => ([(0,7),(1,7),(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)
 => ? = 2
0110101 => [2,1,2,2,1] => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 2
0110110 => [2,1,2,1,2] => [1,3,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 2
0110111 => [2,1,2,1,1,1] => [4,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 2
0111001 => [2,1,1,3,1] => [2,1,4,1] => ([(0,7),(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 3
0111010 => [2,1,1,2,2] => [1,2,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 3
0111011 => [2,1,1,2,1,1] => [3,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 3
0111101 => [2,1,1,1,2,1] => [2,5,1] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 4
0111110 => [2,1,1,1,1,2] => [1,6,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 5
0111111 => [2,1,1,1,1,1,1] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
 => ? = 7
1000000 => [1,7] => [1,1,1,1,1,1,2] => ([(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)
 => ? = 0
1000100 => [1,4,3] => [1,1,2,1,1,2] => ([(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)
 => ? = 0
1000101 => [1,4,2,1] => [2,2,1,1,2] => ([(1,5),(1,6),(1,7),(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)
 => ? = 0
1000110 => [1,4,1,2] => [1,3,1,1,2] => ([(1,5),(1,6),(1,7),(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)
 => ? = 0
1000111 => [1,4,1,1,1] => [4,1,1,2] => ([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 0
1001001 => [1,3,3,1] => [2,1,2,1,2] => ([(1,6),(1,7),(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)
 => ? = 0
1001010 => [1,3,2,2] => [1,2,2,1,2] => ([(1,6),(1,7),(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)
 => ? = 0
1001011 => [1,3,2,1,1] => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 0
1001100 => [1,3,1,3] => [1,1,3,1,2] => ([(1,6),(1,7),(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)
 => ? = 0
Description
The maximal number of leaves on a vertex of a graph.
Matching statistic: St001479
Mapping
Mp00178: Binary words —to composition⟶ Integer compositions
Mp00041: Integer compositions —conjugate⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St001479: Graphs ⟶ ℤResult quality: 52% ●values known / values provided: 52%●distinct values known / distinct values provided: 78%
Values
0 => [2] => [1,1] => ([(0,1)],2)
 => 1
1 => [1,1] => [2] => ([],2)
 => 0
00 => [3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 0
01 => [2,1] => [2,1] => ([(0,2),(1,2)],3)
 => 2
10 => [1,2] => [1,2] => ([(1,2)],3)
 => 1
11 => [1,1,1] => [3] => ([],3)
 => 0
000 => [4] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 0
001 => [3,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 0
010 => [2,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 1
011 => [2,1,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
 => 3
100 => [1,3] => [1,1,2] => ([(1,2),(1,3),(2,3)],4)
 => 0
101 => [1,2,1] => [2,2] => ([(1,3),(2,3)],4)
 => 2
110 => [1,1,2] => [1,3] => ([(2,3)],4)
 => 1
111 => [1,1,1,1] => [4] => ([],4)
 => 0
0000 => [5] => [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
0001 => [4,1] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 0
0010 => [3,2] => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 0
0011 => [3,1,1] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 0
0100 => [2,3] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
0101 => [2,2,1] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
0110 => [2,1,2] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
0111 => [2,1,1,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 4
1000 => [1,4] => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 0
1001 => [1,3,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 0
1010 => [1,2,2] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
 => 1
1011 => [1,2,1,1] => [3,2] => ([(1,4),(2,4),(3,4)],5)
 => 3
1100 => [1,1,3] => [1,1,3] => ([(2,3),(2,4),(3,4)],5)
 => 0
1101 => [1,1,2,1] => [2,3] => ([(2,4),(3,4)],5)
 => 2
1110 => [1,1,1,2] => [1,4] => ([(3,4)],5)
 => 1
1111 => [1,1,1,1,1] => [5] => ([],5)
 => 0
00000 => [6] => [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
00001 => [5,1] => [2,1,1,1,1] => ([(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
00010 => [4,2] => [1,2,1,1,1] => ([(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
00011 => [4,1,1] => [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
00100 => [3,3] => [1,1,2,1,1] => ([(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
00101 => [3,2,1] => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 0
00110 => [3,1,2] => [1,3,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 0
00111 => [3,1,1,1] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 0
01000 => [2,4] => [1,1,1,2,1] => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1
01001 => [2,3,1] => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1
01010 => [2,2,2] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1
01011 => [2,2,1,1] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1
01100 => [2,1,3] => [1,1,3,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
01101 => [2,1,2,1] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
01110 => [2,1,1,2] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => 3
01111 => [2,1,1,1,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 5
10000 => [1,5] => [1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 0
10001 => [1,4,1] => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 0
10010 => [1,3,2] => [1,2,1,2] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 0
10011 => [1,3,1,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 0
000000 => [7] => [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
000001 => [6,1] => [2,1,1,1,1,1] => ([(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
000010 => [5,2] => [1,2,1,1,1,1] => ([(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
000100 => [4,3] => [1,1,2,1,1,1] => ([(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
001000 => [3,4] => [1,1,1,2,1,1] => ([(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
010000 => [2,5] => [1,1,1,1,2,1] => ([(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)
 => ? = 1
100000 => [1,6] => [1,1,1,1,1,2] => ([(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
0000000 => [8] => [1,1,1,1,1,1,1,1] => ([(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)
 => ? = 0
0000001 => [7,1] => [2,1,1,1,1,1,1] => ([(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)
 => ? = 0
0001000 => [4,4] => [1,1,1,2,1,1,1] => ([(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)
 => ? = 0
0001001 => [4,3,1] => [2,1,2,1,1,1] => ([(0,5),(0,6),(0,7),(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)
 => ? = 0
0001010 => [4,2,2] => [1,2,2,1,1,1] => ([(0,5),(0,6),(0,7),(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)
 => ? = 0
0001100 => [4,1,3] => [1,1,3,1,1,1] => ([(0,5),(0,6),(0,7),(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)
 => ? = 0
0001110 => [4,1,1,2] => [1,4,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(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)
 => ? = 0
0010001 => [3,4,1] => [2,1,1,2,1,1] => ([(0,6),(0,7),(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)
 => ? = 0
0010010 => [3,3,2] => [1,2,1,2,1,1] => ([(0,6),(0,7),(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)
 => ? = 0
0010100 => [3,2,3] => [1,1,2,2,1,1] => ([(0,6),(0,7),(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)
 => ? = 0
0010101 => [3,2,2,1] => [2,2,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(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)
 => ? = 0
0010110 => [3,2,1,2] => [1,3,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(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)
 => ? = 0
0011001 => [3,1,3,1] => [2,1,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(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)
 => ? = 0
0011010 => [3,1,2,2] => [1,2,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(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)
 => ? = 0
0011100 => [3,1,1,3] => [1,1,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(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)
 => ? = 0
0011101 => [3,1,1,2,1] => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 0
0100010 => [2,4,2] => [1,2,1,1,2,1] => ([(0,7),(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)
 => ? = 1
0100011 => [2,4,1,1] => [3,1,1,2,1] => ([(0,7),(1,4),(1,5),(1,6),(1,7),(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)
 => ? = 1
0100100 => [2,3,3] => [1,1,2,1,2,1] => ([(0,7),(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)
 => ? = 1
0100101 => [2,3,2,1] => [2,2,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(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)
 => ? = 1
0100110 => [2,3,1,2] => [1,3,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(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)
 => ? = 1
0101001 => [2,2,3,1] => [2,1,2,2,1] => ([(0,7),(1,6),(1,7),(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)
 => ? = 1
0101010 => [2,2,2,2] => [1,2,2,2,1] => ([(0,7),(1,6),(1,7),(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)
 => ? = 1
0101011 => [2,2,2,1,1] => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 1
0101100 => [2,2,1,3] => [1,1,3,2,1] => ([(0,7),(1,6),(1,7),(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)
 => ? = 1
0101101 => [2,2,1,2,1] => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 1
0101110 => [2,2,1,1,2] => [1,4,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 1
0101111 => [2,2,1,1,1,1] => [5,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 1
0110010 => [2,1,3,2] => [1,2,1,3,1] => ([(0,7),(1,7),(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)
 => ? = 2
0110011 => [2,1,3,1,1] => [3,1,3,1] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 2
0110100 => [2,1,2,3] => [1,1,2,3,1] => ([(0,7),(1,7),(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)
 => ? = 2
0110101 => [2,1,2,2,1] => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 2
0110110 => [2,1,2,1,2] => [1,3,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 2
0110111 => [2,1,2,1,1,1] => [4,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 2
0111001 => [2,1,1,3,1] => [2,1,4,1] => ([(0,7),(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 3
0111010 => [2,1,1,2,2] => [1,2,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 3
0111011 => [2,1,1,2,1,1] => [3,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 3
0111101 => [2,1,1,1,2,1] => [2,5,1] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 4
0111110 => [2,1,1,1,1,2] => [1,6,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 5
0111111 => [2,1,1,1,1,1,1] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
 => ? = 7
1000000 => [1,7] => [1,1,1,1,1,1,2] => ([(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)
 => ? = 0
1000100 => [1,4,3] => [1,1,2,1,1,2] => ([(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)
 => ? = 0
1000101 => [1,4,2,1] => [2,2,1,1,2] => ([(1,5),(1,6),(1,7),(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)
 => ? = 0
Description
The number of bridges of a graph. A bridge is an edge whose removal increases the number of connected components of the graph.