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Your data matches 3 different statistics following compositions of up to 3 maps.
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Matching statistic: St001232
Mp00134: Standard tableaux —descent word⟶ Binary words
Mp00097: Binary words —delta morphism⟶ Integer compositions
Mp00231: Integer compositions —bounce path⟶ Dyck paths
St001232: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00097: Binary words —delta morphism⟶ Integer compositions
Mp00231: Integer compositions —bounce path⟶ Dyck paths
St001232: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[[1,2]]
=> 0 => [1] => [1,0]
=> 0
[[1],[2]]
=> 1 => [1] => [1,0]
=> 0
[[1,2,3]]
=> 00 => [2] => [1,1,0,0]
=> 0
[[1,3],[2]]
=> 10 => [1,1] => [1,0,1,0]
=> 1
[[1,2],[3]]
=> 01 => [1,1] => [1,0,1,0]
=> 1
[[1],[2],[3]]
=> 11 => [2] => [1,1,0,0]
=> 0
[[1,2,3,4]]
=> 000 => [3] => [1,1,1,0,0,0]
=> 0
[[1,3,4],[2]]
=> 100 => [1,2] => [1,0,1,1,0,0]
=> 2
[[1,2,3],[4]]
=> 001 => [2,1] => [1,1,0,0,1,0]
=> 1
[[1,4],[2],[3]]
=> 110 => [2,1] => [1,1,0,0,1,0]
=> 1
[[1,2],[3],[4]]
=> 011 => [1,2] => [1,0,1,1,0,0]
=> 2
[[1],[2],[3],[4]]
=> 111 => [3] => [1,1,1,0,0,0]
=> 0
[[1,2,3,4,5]]
=> 0000 => [4] => [1,1,1,1,0,0,0,0]
=> 0
[[1,3,4,5],[2]]
=> 1000 => [1,3] => [1,0,1,1,1,0,0,0]
=> 3
[[1,2,3,4],[5]]
=> 0001 => [3,1] => [1,1,1,0,0,0,1,0]
=> 1
[[1,3,4],[2,5]]
=> 1001 => [1,2,1] => [1,0,1,1,0,0,1,0]
=> 3
[[1,4,5],[2],[3]]
=> 1100 => [2,2] => [1,1,0,0,1,1,0,0]
=> 2
[[1,2,5],[3],[4]]
=> 0110 => [1,2,1] => [1,0,1,1,0,0,1,0]
=> 3
[[1,3,4],[2],[5]]
=> 1001 => [1,2,1] => [1,0,1,1,0,0,1,0]
=> 3
[[1,2,3],[4],[5]]
=> 0011 => [2,2] => [1,1,0,0,1,1,0,0]
=> 2
[[1,2],[3,5],[4]]
=> 0110 => [1,2,1] => [1,0,1,1,0,0,1,0]
=> 3
[[1,5],[2],[3],[4]]
=> 1110 => [3,1] => [1,1,1,0,0,0,1,0]
=> 1
[[1,2],[3],[4],[5]]
=> 0111 => [1,3] => [1,0,1,1,1,0,0,0]
=> 3
[[1],[2],[3],[4],[5]]
=> 1111 => [4] => [1,1,1,1,0,0,0,0]
=> 0
[[1,2,3,4,5,6]]
=> 00000 => [5] => [1,1,1,1,1,0,0,0,0,0]
=> 0
[[1,3,4,5,6],[2]]
=> 10000 => [1,4] => [1,0,1,1,1,1,0,0,0,0]
=> 4
[[1,2,3,4,5],[6]]
=> 00001 => [4,1] => [1,1,1,1,0,0,0,0,1,0]
=> 1
[[1,3,4,5],[2,6]]
=> 10001 => [1,3,1] => [1,0,1,1,1,0,0,0,1,0]
=> 4
[[1,4,5,6],[2],[3]]
=> 11000 => [2,3] => [1,1,0,0,1,1,1,0,0,0]
=> 3
[[1,2,5,6],[3],[4]]
=> 01100 => [1,2,2] => [1,0,1,1,0,0,1,1,0,0]
=> 4
[[1,2,3,6],[4],[5]]
=> 00110 => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
=> 3
[[1,3,4,5],[2],[6]]
=> 10001 => [1,3,1] => [1,0,1,1,1,0,0,0,1,0]
=> 4
[[1,2,3,4],[5],[6]]
=> 00011 => [3,2] => [1,1,1,0,0,0,1,1,0,0]
=> 2
[[1,2,6],[3,5],[4]]
=> 01100 => [1,2,2] => [1,0,1,1,0,0,1,1,0,0]
=> 4
[[1,4,5],[2,6],[3]]
=> 11001 => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
=> 3
[[1,2,3],[4,6],[5]]
=> 00110 => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
=> 3
[[1,3,4],[2,5],[6]]
=> 10011 => [1,2,2] => [1,0,1,1,0,0,1,1,0,0]
=> 4
[[1,5,6],[2],[3],[4]]
=> 11100 => [3,2] => [1,1,1,0,0,0,1,1,0,0]
=> 2
[[1,2,6],[3],[4],[5]]
=> 01110 => [1,3,1] => [1,0,1,1,1,0,0,0,1,0]
=> 4
[[1,4,5],[2],[3],[6]]
=> 11001 => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
=> 3
[[1,3,4],[2],[5],[6]]
=> 10011 => [1,2,2] => [1,0,1,1,0,0,1,1,0,0]
=> 4
[[1,2,3],[4],[5],[6]]
=> 00111 => [2,3] => [1,1,0,0,1,1,1,0,0,0]
=> 3
[[1,2],[3,6],[4],[5]]
=> 01110 => [1,3,1] => [1,0,1,1,1,0,0,0,1,0]
=> 4
[[1,6],[2],[3],[4],[5]]
=> 11110 => [4,1] => [1,1,1,1,0,0,0,0,1,0]
=> 1
[[1,2],[3],[4],[5],[6]]
=> 01111 => [1,4] => [1,0,1,1,1,1,0,0,0,0]
=> 4
[[1],[2],[3],[4],[5],[6]]
=> 11111 => [5] => [1,1,1,1,1,0,0,0,0,0]
=> 0
[[1,2,3,4,5,6,7]]
=> 000000 => [6] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> 0
[[1,3,4,5,6,7],[2]]
=> 100000 => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0]
=> 5
[[1,2,3,4,5,6],[7]]
=> 000001 => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0]
=> 1
[[1,3,4,5,6],[2,7]]
=> 100001 => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0]
=> 5
Description
The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2.
Matching statistic: St001227
Mp00134: Standard tableaux —descent word⟶ Binary words
Mp00097: Binary words —delta morphism⟶ Integer compositions
Mp00231: Integer compositions —bounce path⟶ Dyck paths
St001227: Dyck paths ⟶ ℤResult quality: 47% ●values known / values provided: 47%●distinct values known / distinct values provided: 86%
Mp00097: Binary words —delta morphism⟶ Integer compositions
Mp00231: Integer compositions —bounce path⟶ Dyck paths
St001227: Dyck paths ⟶ ℤResult quality: 47% ●values known / values provided: 47%●distinct values known / distinct values provided: 86%
Values
[[1,2]]
=> 0 => [1] => [1,0]
=> 0
[[1],[2]]
=> 1 => [1] => [1,0]
=> 0
[[1,2,3]]
=> 00 => [2] => [1,1,0,0]
=> 0
[[1,3],[2]]
=> 10 => [1,1] => [1,0,1,0]
=> 1
[[1,2],[3]]
=> 01 => [1,1] => [1,0,1,0]
=> 1
[[1],[2],[3]]
=> 11 => [2] => [1,1,0,0]
=> 0
[[1,2,3,4]]
=> 000 => [3] => [1,1,1,0,0,0]
=> 0
[[1,3,4],[2]]
=> 100 => [1,2] => [1,0,1,1,0,0]
=> 2
[[1,2,3],[4]]
=> 001 => [2,1] => [1,1,0,0,1,0]
=> 1
[[1,4],[2],[3]]
=> 110 => [2,1] => [1,1,0,0,1,0]
=> 1
[[1,2],[3],[4]]
=> 011 => [1,2] => [1,0,1,1,0,0]
=> 2
[[1],[2],[3],[4]]
=> 111 => [3] => [1,1,1,0,0,0]
=> 0
[[1,2,3,4,5]]
=> 0000 => [4] => [1,1,1,1,0,0,0,0]
=> 0
[[1,3,4,5],[2]]
=> 1000 => [1,3] => [1,0,1,1,1,0,0,0]
=> 3
[[1,2,3,4],[5]]
=> 0001 => [3,1] => [1,1,1,0,0,0,1,0]
=> 1
[[1,3,4],[2,5]]
=> 1001 => [1,2,1] => [1,0,1,1,0,0,1,0]
=> 3
[[1,4,5],[2],[3]]
=> 1100 => [2,2] => [1,1,0,0,1,1,0,0]
=> 2
[[1,2,5],[3],[4]]
=> 0110 => [1,2,1] => [1,0,1,1,0,0,1,0]
=> 3
[[1,3,4],[2],[5]]
=> 1001 => [1,2,1] => [1,0,1,1,0,0,1,0]
=> 3
[[1,2,3],[4],[5]]
=> 0011 => [2,2] => [1,1,0,0,1,1,0,0]
=> 2
[[1,2],[3,5],[4]]
=> 0110 => [1,2,1] => [1,0,1,1,0,0,1,0]
=> 3
[[1,5],[2],[3],[4]]
=> 1110 => [3,1] => [1,1,1,0,0,0,1,0]
=> 1
[[1,2],[3],[4],[5]]
=> 0111 => [1,3] => [1,0,1,1,1,0,0,0]
=> 3
[[1],[2],[3],[4],[5]]
=> 1111 => [4] => [1,1,1,1,0,0,0,0]
=> 0
[[1,2,3,4,5,6]]
=> 00000 => [5] => [1,1,1,1,1,0,0,0,0,0]
=> 0
[[1,3,4,5,6],[2]]
=> 10000 => [1,4] => [1,0,1,1,1,1,0,0,0,0]
=> 4
[[1,2,3,4,5],[6]]
=> 00001 => [4,1] => [1,1,1,1,0,0,0,0,1,0]
=> 1
[[1,3,4,5],[2,6]]
=> 10001 => [1,3,1] => [1,0,1,1,1,0,0,0,1,0]
=> 4
[[1,4,5,6],[2],[3]]
=> 11000 => [2,3] => [1,1,0,0,1,1,1,0,0,0]
=> 3
[[1,2,5,6],[3],[4]]
=> 01100 => [1,2,2] => [1,0,1,1,0,0,1,1,0,0]
=> 4
[[1,2,3,6],[4],[5]]
=> 00110 => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
=> 3
[[1,3,4,5],[2],[6]]
=> 10001 => [1,3,1] => [1,0,1,1,1,0,0,0,1,0]
=> 4
[[1,2,3,4],[5],[6]]
=> 00011 => [3,2] => [1,1,1,0,0,0,1,1,0,0]
=> 2
[[1,2,6],[3,5],[4]]
=> 01100 => [1,2,2] => [1,0,1,1,0,0,1,1,0,0]
=> 4
[[1,4,5],[2,6],[3]]
=> 11001 => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
=> 3
[[1,2,3],[4,6],[5]]
=> 00110 => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
=> 3
[[1,3,4],[2,5],[6]]
=> 10011 => [1,2,2] => [1,0,1,1,0,0,1,1,0,0]
=> 4
[[1,5,6],[2],[3],[4]]
=> 11100 => [3,2] => [1,1,1,0,0,0,1,1,0,0]
=> 2
[[1,2,6],[3],[4],[5]]
=> 01110 => [1,3,1] => [1,0,1,1,1,0,0,0,1,0]
=> 4
[[1,4,5],[2],[3],[6]]
=> 11001 => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
=> 3
[[1,3,4],[2],[5],[6]]
=> 10011 => [1,2,2] => [1,0,1,1,0,0,1,1,0,0]
=> 4
[[1,2,3],[4],[5],[6]]
=> 00111 => [2,3] => [1,1,0,0,1,1,1,0,0,0]
=> 3
[[1,2],[3,6],[4],[5]]
=> 01110 => [1,3,1] => [1,0,1,1,1,0,0,0,1,0]
=> 4
[[1,6],[2],[3],[4],[5]]
=> 11110 => [4,1] => [1,1,1,1,0,0,0,0,1,0]
=> 1
[[1,2],[3],[4],[5],[6]]
=> 01111 => [1,4] => [1,0,1,1,1,1,0,0,0,0]
=> 4
[[1],[2],[3],[4],[5],[6]]
=> 11111 => [5] => [1,1,1,1,1,0,0,0,0,0]
=> 0
[[1,2,3,4,5,6,7]]
=> 000000 => [6] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> 0
[[1,3,4,5,6,7],[2]]
=> 100000 => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0]
=> 5
[[1,2,3,4,5,6],[7]]
=> 000001 => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0]
=> 1
[[1,3,4,5,6],[2,7]]
=> 100001 => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0]
=> 5
[[1,2,3,4,5,6,7,8]]
=> 0000000 => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> ? = 0
[[1,3,4,5,6,7,8],[2]]
=> 1000000 => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 6
[[1,2,3,4,5,6,7],[8]]
=> 0000001 => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
=> ? = 1
[[1,3,4,5,6,7],[2,8]]
=> 1000001 => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0]
=> ? = 6
[[1,4,5,6,7,8],[2],[3]]
=> 1100000 => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0]
=> ? = 5
[[1,2,5,6,7,8],[3],[4]]
=> 0110000 => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0]
=> ? = 6
[[1,2,3,6,7,8],[4],[5]]
=> 0011000 => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0]
=> ? = 5
[[1,2,3,4,7,8],[5],[6]]
=> 0001100 => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0]
=> ? = 4
[[1,2,3,4,5,8],[6],[7]]
=> 0000110 => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0]
=> ? = 3
[[1,3,4,5,6,7],[2],[8]]
=> 1000001 => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0]
=> ? = 6
[[1,2,3,4,5,6],[7],[8]]
=> 0000011 => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
=> ? = 2
[[1,2,6,7,8],[3,5],[4]]
=> 0110000 => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0]
=> ? = 6
[[1,2,3,7,8],[4,6],[5]]
=> 0011000 => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0]
=> ? = 5
[[1,3,4,7,8],[2,5],[6]]
=> 1001100 => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0]
=> ? = 6
[[1,2,3,4,8],[5,7],[6]]
=> 0001100 => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0]
=> ? = 4
[[1,3,4,5,8],[2,6],[7]]
=> 1000110 => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0]
=> ? = 6
[[1,4,5,6,7],[2,8],[3]]
=> 1100001 => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0]
=> ? = 5
[[1,2,5,6,7],[3,8],[4]]
=> 0110001 => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
=> ? = 6
[[1,2,3,6,7],[4,8],[5]]
=> 0011001 => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0]
=> ? = 5
[[1,2,3,4,5],[6,8],[7]]
=> 0000110 => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0]
=> ? = 3
[[1,3,4,5,6],[2,7],[8]]
=> 1000011 => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0]
=> ? = 6
[[1,5,6,7,8],[2],[3],[4]]
=> 1110000 => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0]
=> ? = 4
[[1,2,6,7,8],[3],[4],[5]]
=> 0111000 => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0]
=> ? = 6
[[1,3,4,7,8],[2],[5],[6]]
=> 1001100 => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0]
=> ? = 6
[[1,2,3,7,8],[4],[5],[6]]
=> 0011100 => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0]
=> ? = 5
[[1,3,4,5,8],[2],[6],[7]]
=> 1000110 => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0]
=> ? = 6
[[1,2,3,4,8],[5],[6],[7]]
=> 0001110 => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0]
=> ? = 4
[[1,4,5,6,7],[2],[3],[8]]
=> 1100001 => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0]
=> ? = 5
[[1,2,5,6,7],[3],[4],[8]]
=> 0110001 => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
=> ? = 6
[[1,2,3,6,7],[4],[5],[8]]
=> 0011001 => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0]
=> ? = 5
[[1,3,4,5,6],[2],[7],[8]]
=> 1000011 => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0]
=> ? = 6
[[1,2,3,4,5],[6],[7],[8]]
=> 0000111 => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
=> ? = 3
[[1,2,3,8],[4,6,7],[5]]
=> 0011000 => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0]
=> ? = 5
[[1,3,4,8],[2,5,7],[6]]
=> 1001100 => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0]
=> ? = 6
[[1,2,6,7],[3,5,8],[4]]
=> 0110001 => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
=> ? = 6
[[1,2,3,7],[4,6,8],[5]]
=> 0011001 => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0]
=> ? = 5
[[1,2,3,4],[5,7,8],[6]]
=> 0001100 => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0]
=> ? = 4
[[1,3,4,5],[2,6,8],[7]]
=> 1000110 => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0]
=> ? = 6
[[1,4,5,8],[2,6],[3,7]]
=> 1100110 => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0]
=> ? = 5
[[1,3,4,8],[2,5],[6,7]]
=> 1001100 => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0]
=> ? = 6
[[1,2,6,7],[3,5],[4,8]]
=> 0110001 => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
=> ? = 6
[[1,2,3,7],[4,6],[5,8]]
=> 0011001 => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0]
=> ? = 5
[[1,4,5,6],[2,7],[3,8]]
=> 1100011 => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0]
=> ? = 5
[[1,2,5,6],[3,7],[4,8]]
=> 0110011 => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0]
=> ? = 6
[[1,3,4,5],[2,6],[7,8]]
=> 1000110 => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0]
=> ? = 6
[[1,2,7,8],[3,6],[4],[5]]
=> 0111000 => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0]
=> ? = 6
[[1,3,4,8],[2,7],[5],[6]]
=> 1001100 => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0]
=> ? = 6
[[1,2,3,8],[4,7],[5],[6]]
=> 0011100 => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0]
=> ? = 5
[[1,4,5,8],[2,6],[3],[7]]
=> 1100110 => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0]
=> ? = 5
[[1,3,4,8],[2,5],[6],[7]]
=> 1001110 => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
=> ? = 6
Description
The vector space dimension of the first extension group between the socle of the regular module and the Jacobson radical of the corresponding Nakayama algebra.
Matching statistic: St001742
(load all 3 compositions to match this statistic)
(load all 3 compositions to match this statistic)
Mp00207: Standard tableaux —horizontal strip sizes⟶ Integer compositions
Mp00038: Integer compositions —reverse⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St001742: Graphs ⟶ ℤResult quality: 23% ●values known / values provided: 23%●distinct values known / distinct values provided: 71%
Mp00038: Integer compositions —reverse⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St001742: Graphs ⟶ ℤResult quality: 23% ●values known / values provided: 23%●distinct values known / distinct values provided: 71%
Values
[[1,2]]
=> [2] => [2] => ([],2)
=> 0
[[1],[2]]
=> [1,1] => [1,1] => ([(0,1)],2)
=> 0
[[1,2,3]]
=> [3] => [3] => ([],3)
=> 0
[[1,3],[2]]
=> [1,2] => [2,1] => ([(0,2),(1,2)],3)
=> 1
[[1,2],[3]]
=> [2,1] => [1,2] => ([(1,2)],3)
=> 1
[[1],[2],[3]]
=> [1,1,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 0
[[1,2,3,4]]
=> [4] => [4] => ([],4)
=> 0
[[1,3,4],[2]]
=> [1,3] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 2
[[1,2,3],[4]]
=> [3,1] => [1,3] => ([(2,3)],4)
=> 1
[[1,4],[2],[3]]
=> [1,1,2] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 1
[[1,2],[3],[4]]
=> [2,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4)
=> 2
[[1],[2],[3],[4]]
=> [1,1,1,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 0
[[1,2,3,4,5]]
=> [5] => [5] => ([],5)
=> 0
[[1,3,4,5],[2]]
=> [1,4] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 3
[[1,2,3,4],[5]]
=> [4,1] => [1,4] => ([(3,4)],5)
=> 1
[[1,3,4],[2,5]]
=> [1,3,1] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> 3
[[1,4,5],[2],[3]]
=> [1,1,3] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2
[[1,2,5],[3],[4]]
=> [2,1,2] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3
[[1,3,4],[2],[5]]
=> [1,3,1] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> 3
[[1,2,3],[4],[5]]
=> [3,1,1] => [1,1,3] => ([(2,3),(2,4),(3,4)],5)
=> 2
[[1,2],[3,5],[4]]
=> [2,1,2] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3
[[1,5],[2],[3],[4]]
=> [1,1,1,2] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1
[[1,2],[3],[4],[5]]
=> [2,1,1,1] => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3
[[1],[2],[3],[4],[5]]
=> [1,1,1,1,1] => [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
[[1,2,3,4,5,6]]
=> [6] => [6] => ([],6)
=> 0
[[1,3,4,5,6],[2]]
=> [1,5] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> 4
[[1,2,3,4,5],[6]]
=> [5,1] => [1,5] => ([(4,5)],6)
=> 1
[[1,3,4,5],[2,6]]
=> [1,4,1] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> 4
[[1,4,5,6],[2],[3]]
=> [1,1,4] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 3
[[1,2,5,6],[3],[4]]
=> [2,1,3] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 4
[[1,2,3,6],[4],[5]]
=> [3,1,2] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 3
[[1,3,4,5],[2],[6]]
=> [1,4,1] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> 4
[[1,2,3,4],[5],[6]]
=> [4,1,1] => [1,1,4] => ([(3,4),(3,5),(4,5)],6)
=> 2
[[1,2,6],[3,5],[4]]
=> [2,1,3] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 4
[[1,4,5],[2,6],[3]]
=> [1,1,3,1] => [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)
=> 3
[[1,2,3],[4,6],[5]]
=> [3,1,2] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 3
[[1,3,4],[2,5],[6]]
=> [1,3,1,1] => [1,1,3,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 4
[[1,5,6],[2],[3],[4]]
=> [1,1,1,3] => [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)
=> 2
[[1,2,6],[3],[4],[5]]
=> [2,1,1,2] => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 4
[[1,4,5],[2],[3],[6]]
=> [1,1,3,1] => [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)
=> 3
[[1,3,4],[2],[5],[6]]
=> [1,3,1,1] => [1,1,3,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 4
[[1,2,3],[4],[5],[6]]
=> [3,1,1,1] => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 3
[[1,2],[3,6],[4],[5]]
=> [2,1,1,2] => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 4
[[1,6],[2],[3],[4],[5]]
=> [1,1,1,1,2] => [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)
=> 1
[[1,2],[3],[4],[5],[6]]
=> [2,1,1,1,1] => [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)
=> 4
[[1],[2],[3],[4],[5],[6]]
=> [1,1,1,1,1,1] => [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
[[1,2,3,4,5,6,7]]
=> [7] => [7] => ([],7)
=> ? = 0
[[1,3,4,5,6,7],[2]]
=> [1,6] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> ? = 5
[[1,2,3,4,5,6],[7]]
=> [6,1] => [1,6] => ([(5,6)],7)
=> ? = 1
[[1,3,4,5,6],[2,7]]
=> [1,5,1] => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 5
[[1,4,5,6,7],[2],[3]]
=> [1,1,5] => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 4
[[1,2,5,6,7],[3],[4]]
=> [2,1,4] => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 5
[[1,2,3,6,7],[4],[5]]
=> [3,1,3] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 4
[[1,2,3,4,7],[5],[6]]
=> [4,1,2] => [2,1,4] => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 3
[[1,3,4,5,6],[2],[7]]
=> [1,5,1] => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 5
[[1,2,3,4,5],[6],[7]]
=> [5,1,1] => [1,1,5] => ([(4,5),(4,6),(5,6)],7)
=> ? = 2
[[1,2,6,7],[3,5],[4]]
=> [2,1,4] => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 5
[[1,2,3,7],[4,6],[5]]
=> [3,1,3] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 4
[[1,3,4,7],[2,5],[6]]
=> [1,3,1,2] => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 5
[[1,4,5,6],[2,7],[3]]
=> [1,1,4,1] => [1,4,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 4
[[1,2,5,6],[3,7],[4]]
=> [2,1,3,1] => [1,3,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 5
[[1,2,3,4],[5,7],[6]]
=> [4,1,2] => [2,1,4] => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 3
[[1,3,4,5],[2,6],[7]]
=> [1,4,1,1] => [1,1,4,1] => ([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 5
[[1,5,6,7],[2],[3],[4]]
=> [1,1,1,4] => [4,1,1,1] => ([(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)
=> ? = 3
[[1,2,6,7],[3],[4],[5]]
=> [2,1,1,3] => [3,1,1,2] => ([(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)
=> ? = 5
[[1,3,4,7],[2],[5],[6]]
=> [1,3,1,2] => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 5
[[1,2,3,7],[4],[5],[6]]
=> [3,1,1,2] => [2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 4
[[1,4,5,6],[2],[3],[7]]
=> [1,1,4,1] => [1,4,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 4
[[1,2,5,6],[3],[4],[7]]
=> [2,1,3,1] => [1,3,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 5
[[1,3,4,5],[2],[6],[7]]
=> [1,4,1,1] => [1,1,4,1] => ([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 5
[[1,2,3,4],[5],[6],[7]]
=> [4,1,1,1] => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 3
[[1,2,6],[3,5,7],[4]]
=> [2,1,3,1] => [1,3,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 5
[[1,2,3],[4,6,7],[5]]
=> [3,1,3] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 4
[[1,3,4],[2,5,7],[6]]
=> [1,3,1,2] => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 5
[[1,2,6],[3,5],[4,7]]
=> [2,1,3,1] => [1,3,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 5
[[1,4,5],[2,6],[3,7]]
=> [1,1,3,2] => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 4
[[1,3,4],[2,5],[6,7]]
=> [1,3,1,2] => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 5
[[1,2,7],[3,6],[4],[5]]
=> [2,1,1,3] => [3,1,1,2] => ([(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)
=> ? = 5
[[1,5,6],[2,7],[3],[4]]
=> [1,1,1,3,1] => [1,3,1,1,1] => ([(0,4),(0,5),(0,6),(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)
=> ? = 3
[[1,3,4],[2,7],[5],[6]]
=> [1,3,1,2] => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 5
[[1,2,3],[4,7],[5],[6]]
=> [3,1,1,2] => [2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 4
[[1,2,6],[3,5],[4],[7]]
=> [2,1,3,1] => [1,3,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 5
[[1,4,5],[2,6],[3],[7]]
=> [1,1,3,1,1] => [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)
=> ? = 4
[[1,3,4],[2,5],[6],[7]]
=> [1,3,1,1,1] => [1,1,1,3,1] => ([(0,6),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 5
[[1,6,7],[2],[3],[4],[5]]
=> [1,1,1,1,3] => [3,1,1,1,1] => ([(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)
=> ? = 2
[[1,2,7],[3],[4],[5],[6]]
=> [2,1,1,1,2] => [2,1,1,1,2] => ([(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)
=> ? = 5
[[1,5,6],[2],[3],[4],[7]]
=> [1,1,1,3,1] => [1,3,1,1,1] => ([(0,4),(0,5),(0,6),(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)
=> ? = 3
[[1,4,5],[2],[3],[6],[7]]
=> [1,1,3,1,1] => [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)
=> ? = 4
[[1,3,4],[2],[5],[6],[7]]
=> [1,3,1,1,1] => [1,1,1,3,1] => ([(0,6),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 5
[[1,2,3],[4],[5],[6],[7]]
=> [3,1,1,1,1] => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ? = 4
[[1,2],[3,7],[4],[5],[6]]
=> [2,1,1,1,2] => [2,1,1,1,2] => ([(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)
=> ? = 5
[[1,7],[2],[3],[4],[5],[6]]
=> [1,1,1,1,1,2] => [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)
=> ? = 1
[[1,2],[3],[4],[5],[6],[7]]
=> [2,1,1,1,1,1] => [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)
=> ? = 5
[[1],[2],[3],[4],[5],[6],[7]]
=> [1,1,1,1,1,1,1] => [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
[[1,2,3,4,5,6,7,8]]
=> [8] => [8] => ([],8)
=> ? = 0
[[1,3,4,5,6,7,8],[2]]
=> [1,7] => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
=> ? = 6
Description
The difference of the maximal and the minimal degree in a graph.
The graph is regular if and only if this statistic is zero.
Sorry, this statistic was not found in the database
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