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Your data matches 2 different statistics following compositions of up to 3 maps.
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Matching statistic: St001179
Mp00178: Binary words —to composition⟶ Integer compositions
Mp00231: Integer compositions —bounce path⟶ Dyck paths
Mp00101: Dyck paths —decomposition reverse⟶ Dyck paths
St001179: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00231: Integer compositions —bounce path⟶ Dyck paths
Mp00101: Dyck paths —decomposition reverse⟶ Dyck paths
St001179: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
0 => [2] => [1,1,0,0]
=> [1,0,1,0]
=> 3
1 => [1,1] => [1,0,1,0]
=> [1,1,0,0]
=> 3
00 => [3] => [1,1,1,0,0,0]
=> [1,0,1,0,1,0]
=> 3
01 => [2,1] => [1,1,0,0,1,0]
=> [1,1,0,0,1,0]
=> 4
10 => [1,2] => [1,0,1,1,0,0]
=> [1,1,0,1,0,0]
=> 4
11 => [1,1,1] => [1,0,1,0,1,0]
=> [1,1,1,0,0,0]
=> 4
000 => [4] => [1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0]
=> 4
001 => [3,1] => [1,1,1,0,0,0,1,0]
=> [1,1,0,0,1,0,1,0]
=> 4
010 => [2,2] => [1,1,0,0,1,1,0,0]
=> [1,1,0,1,0,0,1,0]
=> 4
011 => [2,1,1] => [1,1,0,0,1,0,1,0]
=> [1,1,1,0,0,0,1,0]
=> 5
100 => [1,3] => [1,0,1,1,1,0,0,0]
=> [1,1,0,1,0,1,0,0]
=> 4
101 => [1,2,1] => [1,0,1,1,0,0,1,0]
=> [1,1,1,0,0,1,0,0]
=> 5
110 => [1,1,2] => [1,0,1,0,1,1,0,0]
=> [1,1,1,0,1,0,0,0]
=> 5
111 => [1,1,1,1] => [1,0,1,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0]
=> 5
0000 => [5] => [1,1,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> 5
0001 => [4,1] => [1,1,1,1,0,0,0,0,1,0]
=> [1,1,0,0,1,0,1,0,1,0]
=> 5
0010 => [3,2] => [1,1,1,0,0,0,1,1,0,0]
=> [1,1,0,1,0,0,1,0,1,0]
=> 5
0011 => [3,1,1] => [1,1,1,0,0,0,1,0,1,0]
=> [1,1,1,0,0,0,1,0,1,0]
=> 5
0100 => [2,3] => [1,1,0,0,1,1,1,0,0,0]
=> [1,1,0,1,0,1,0,0,1,0]
=> 5
0101 => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
=> [1,1,1,0,0,1,0,0,1,0]
=> 5
0110 => [2,1,2] => [1,1,0,0,1,0,1,1,0,0]
=> [1,1,1,0,1,0,0,0,1,0]
=> 5
0111 => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0,1,0]
=> 6
1000 => [1,4] => [1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 4
1001 => [1,3,1] => [1,0,1,1,1,0,0,0,1,0]
=> [1,1,1,0,0,1,0,1,0,0]
=> 5
1010 => [1,2,2] => [1,0,1,1,0,0,1,1,0,0]
=> [1,1,1,0,1,0,0,1,0,0]
=> 5
1011 => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,1,0,0,0,1,0,0]
=> 6
1100 => [1,1,3] => [1,0,1,0,1,1,1,0,0,0]
=> [1,1,1,0,1,0,1,0,0,0]
=> 5
1101 => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0]
=> [1,1,1,1,0,0,1,0,0,0]
=> 6
1110 => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0]
=> [1,1,1,1,0,1,0,0,0,0]
=> 6
1111 => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> 6
00000 => [6] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> 6
00001 => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0]
=> [1,1,0,0,1,0,1,0,1,0,1,0]
=> 6
00010 => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0]
=> [1,1,0,1,0,0,1,0,1,0,1,0]
=> 6
00011 => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0]
=> [1,1,1,0,0,0,1,0,1,0,1,0]
=> 6
00100 => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0]
=> [1,1,0,1,0,1,0,0,1,0,1,0]
=> 6
00101 => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0]
=> [1,1,1,0,0,1,0,0,1,0,1,0]
=> 6
00110 => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0]
=> [1,1,1,0,1,0,0,0,1,0,1,0]
=> 6
00111 => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0,1,0,1,0]
=> 6
01000 => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0]
=> [1,1,0,1,0,1,0,1,0,0,1,0]
=> 5
01001 => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0]
=> [1,1,1,0,0,1,0,1,0,0,1,0]
=> 6
01010 => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0]
=> [1,1,1,0,1,0,0,1,0,0,1,0]
=> 6
01011 => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0]
=> [1,1,1,1,0,0,0,1,0,0,1,0]
=> 6
01100 => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0]
=> [1,1,1,0,1,0,1,0,0,0,1,0]
=> 6
01101 => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0]
=> [1,1,1,1,0,0,1,0,0,0,1,0]
=> 6
01110 => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0]
=> [1,1,1,1,0,1,0,0,0,0,1,0]
=> 6
01111 => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0,1,0]
=> 7
10000 => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0]
=> [1,1,0,1,0,1,0,1,0,1,0,0]
=> 5
10001 => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0]
=> [1,1,1,0,0,1,0,1,0,1,0,0]
=> 5
10010 => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0]
=> [1,1,1,0,1,0,0,1,0,1,0,0]
=> 5
10011 => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0]
=> [1,1,1,1,0,0,0,1,0,1,0,0]
=> 6
Description
Number of indecomposable injective modules with projective dimension at most 2 in the corresponding Nakayama algebra.
Matching statistic: St000393
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00316: Binary words —inverse Foata bijection⟶ Binary words
Mp00280: Binary words —path rowmotion⟶ Binary words
St000393: Binary words ⟶ ℤResult quality: 83% ●values known / values provided: 98%●distinct values known / distinct values provided: 83%
Mp00280: Binary words —path rowmotion⟶ Binary words
St000393: Binary words ⟶ ℤResult quality: 83% ●values known / values provided: 98%●distinct values known / distinct values provided: 83%
Values
0 => 0 => 1 => 1 = 3 - 2
1 => 1 => 0 => 1 = 3 - 2
00 => 00 => 01 => 1 = 3 - 2
01 => 01 => 10 => 2 = 4 - 2
10 => 10 => 11 => 2 = 4 - 2
11 => 11 => 00 => 2 = 4 - 2
000 => 000 => 001 => 2 = 4 - 2
001 => 001 => 010 => 2 = 4 - 2
010 => 100 => 011 => 2 = 4 - 2
011 => 011 => 100 => 3 = 5 - 2
100 => 010 => 101 => 2 = 4 - 2
101 => 101 => 110 => 3 = 5 - 2
110 => 110 => 111 => 3 = 5 - 2
111 => 111 => 000 => 3 = 5 - 2
0000 => 0000 => 0001 => 3 = 5 - 2
0001 => 0001 => 0010 => 3 = 5 - 2
0010 => 1000 => 0011 => 3 = 5 - 2
0011 => 0011 => 0100 => 3 = 5 - 2
0100 => 0100 => 1001 => 3 = 5 - 2
0101 => 1001 => 0110 => 3 = 5 - 2
0110 => 1100 => 0111 => 3 = 5 - 2
0111 => 0111 => 1000 => 4 = 6 - 2
1000 => 0010 => 0101 => 2 = 4 - 2
1001 => 0101 => 1010 => 3 = 5 - 2
1010 => 0110 => 1011 => 3 = 5 - 2
1011 => 1011 => 1100 => 4 = 6 - 2
1100 => 1010 => 1101 => 3 = 5 - 2
1101 => 1101 => 1110 => 4 = 6 - 2
1110 => 1110 => 1111 => 4 = 6 - 2
1111 => 1111 => 0000 => 4 = 6 - 2
00000 => 00000 => 00001 => 4 = 6 - 2
00001 => 00001 => 00010 => 4 = 6 - 2
00010 => 10000 => 00011 => 4 = 6 - 2
00011 => 00011 => 00100 => 4 = 6 - 2
00100 => 01000 => 10001 => 4 = 6 - 2
00101 => 10001 => 00110 => 4 = 6 - 2
00110 => 11000 => 00111 => 4 = 6 - 2
00111 => 00111 => 01000 => 4 = 6 - 2
01000 => 00100 => 01001 => 3 = 5 - 2
01001 => 01001 => 10010 => 4 = 6 - 2
01010 => 01100 => 10011 => 4 = 6 - 2
01011 => 10011 => 01100 => 4 = 6 - 2
01100 => 10100 => 11001 => 4 = 6 - 2
01101 => 11001 => 01110 => 4 = 6 - 2
01110 => 11100 => 01111 => 4 = 6 - 2
01111 => 01111 => 10000 => 5 = 7 - 2
10000 => 00010 => 00101 => 3 = 5 - 2
10001 => 00101 => 01010 => 3 = 5 - 2
10010 => 00110 => 01011 => 3 = 5 - 2
10011 => 01011 => 10100 => 4 = 6 - 2
=> ? => ? => ? = 2 - 2
Description
The number of strictly increasing runs in a binary word.
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