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Your data matches 19 different statistics following compositions of up to 3 maps.
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Matching statistic: St001814
(load all 3 compositions to match this statistic)
(load all 3 compositions to match this statistic)
St001814: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1]
=> 2
[2]
=> 3
[1,1]
=> 2
[3]
=> 4
[2,1]
=> 4
[1,1,1]
=> 2
[4]
=> 5
[3,1]
=> 6
[2,2]
=> 3
[2,1,1]
=> 4
[1,1,1,1]
=> 2
[3,2]
=> 6
[2,2,1]
=> 4
[3,3]
=> 4
[2,2,2]
=> 3
Description
The number of partitions interlacing the given partition.
Matching statistic: St000032
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00199: Dyck paths —prime Dyck path⟶ Dyck paths
Mp00032: Dyck paths —inverse zeta map⟶ Dyck paths
St000032: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00199: Dyck paths —prime Dyck path⟶ Dyck paths
Mp00032: Dyck paths —inverse zeta map⟶ Dyck paths
St000032: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1]
=> [1,0,1,0]
=> [1,1,0,1,0,0]
=> [1,1,0,0,1,0]
=> 2
[2]
=> [1,1,0,0,1,0]
=> [1,1,1,0,0,1,0,0]
=> [1,1,0,1,0,0,1,0]
=> 3
[1,1]
=> [1,0,1,1,0,0]
=> [1,1,0,1,1,0,0,0]
=> [1,0,1,1,0,0,1,0]
=> 2
[3]
=> [1,1,1,0,0,0,1,0]
=> [1,1,1,1,0,0,0,1,0,0]
=> [1,1,0,1,0,1,0,0,1,0]
=> 4
[2,1]
=> [1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,0]
=> [1,1,0,0,1,1,0,0]
=> 4
[1,1,1]
=> [1,0,1,1,1,0,0,0]
=> [1,1,0,1,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,0,1,0]
=> 2
[4]
=> [1,1,1,1,0,0,0,0,1,0]
=> [1,1,1,1,1,0,0,0,0,1,0,0]
=> [1,1,0,1,0,1,0,1,0,0,1,0]
=> 5
[3,1]
=> [1,1,0,1,0,0,1,0]
=> [1,1,1,0,1,0,0,1,0,0]
=> [1,1,0,1,0,0,1,1,0,0]
=> 6
[2,2]
=> [1,1,0,0,1,1,0,0]
=> [1,1,1,0,0,1,1,0,0,0]
=> [1,0,1,1,0,1,0,0,1,0]
=> 3
[2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [1,1,0,1,1,0,1,0,0,0]
=> [1,1,0,0,1,0,1,1,0,0]
=> 4
[1,1,1,1]
=> [1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,1,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0]
=> 2
[3,2]
=> [1,1,0,0,1,0,1,0]
=> [1,1,1,0,0,1,0,1,0,0]
=> [1,1,0,0,1,1,0,1,0,0]
=> 6
[2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,1,0,0,0]
=> [1,0,1,1,0,0,1,1,0,0]
=> 4
[3,3]
=> [1,1,1,0,0,0,1,1,0,0]
=> [1,1,1,1,0,0,0,1,1,0,0,0]
=> [1,0,1,1,0,1,0,1,0,0,1,0]
=> 4
[2,2,2]
=> [1,1,0,0,1,1,1,0,0,0]
=> [1,1,1,0,0,1,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,1,0,0,1,0]
=> 3
Description
The number of elements smaller than the given Dyck path in the Tamari Order.
Matching statistic: St000708
Mp00095: Integer partitions —to binary word⟶ Binary words
Mp00178: Binary words —to composition⟶ Integer compositions
Mp00040: Integer compositions —to partition⟶ Integer partitions
St000708: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00178: Binary words —to composition⟶ Integer compositions
Mp00040: Integer compositions —to partition⟶ Integer partitions
St000708: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1]
=> 10 => [1,2] => [2,1]
=> 2
[2]
=> 100 => [1,3] => [3,1]
=> 3
[1,1]
=> 110 => [1,1,2] => [2,1,1]
=> 2
[3]
=> 1000 => [1,4] => [4,1]
=> 4
[2,1]
=> 1010 => [1,2,2] => [2,2,1]
=> 4
[1,1,1]
=> 1110 => [1,1,1,2] => [2,1,1,1]
=> 2
[4]
=> 10000 => [1,5] => [5,1]
=> 5
[3,1]
=> 10010 => [1,3,2] => [3,2,1]
=> 6
[2,2]
=> 1100 => [1,1,3] => [3,1,1]
=> 3
[2,1,1]
=> 10110 => [1,2,1,2] => [2,2,1,1]
=> 4
[1,1,1,1]
=> 11110 => [1,1,1,1,2] => [2,1,1,1,1]
=> 2
[3,2]
=> 10100 => [1,2,3] => [3,2,1]
=> 6
[2,2,1]
=> 11010 => [1,1,2,2] => [2,2,1,1]
=> 4
[3,3]
=> 11000 => [1,1,4] => [4,1,1]
=> 4
[2,2,2]
=> 11100 => [1,1,1,3] => [3,1,1,1]
=> 3
Description
The product of the parts of an integer partition.
Matching statistic: St001959
Mp00095: Integer partitions —to binary word⟶ Binary words
Mp00178: Binary words —to composition⟶ Integer compositions
Mp00231: Integer compositions —bounce path⟶ Dyck paths
St001959: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00178: Binary words —to composition⟶ Integer compositions
Mp00231: Integer compositions —bounce path⟶ Dyck paths
St001959: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1]
=> 10 => [1,2] => [1,0,1,1,0,0]
=> 2
[2]
=> 100 => [1,3] => [1,0,1,1,1,0,0,0]
=> 3
[1,1]
=> 110 => [1,1,2] => [1,0,1,0,1,1,0,0]
=> 2
[3]
=> 1000 => [1,4] => [1,0,1,1,1,1,0,0,0,0]
=> 4
[2,1]
=> 1010 => [1,2,2] => [1,0,1,1,0,0,1,1,0,0]
=> 4
[1,1,1]
=> 1110 => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0]
=> 2
[4]
=> 10000 => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0]
=> 5
[3,1]
=> 10010 => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0]
=> 6
[2,2]
=> 1100 => [1,1,3] => [1,0,1,0,1,1,1,0,0,0]
=> 3
[2,1,1]
=> 10110 => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0]
=> 4
[1,1,1,1]
=> 11110 => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0]
=> 2
[3,2]
=> 10100 => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0]
=> 6
[2,2,1]
=> 11010 => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0]
=> 4
[3,3]
=> 11000 => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0]
=> 4
[2,2,2]
=> 11100 => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0]
=> 3
Description
The product of the heights of the peaks of a Dyck path.
Matching statistic: St001232
(load all 12 compositions to match this statistic)
(load all 12 compositions to match this statistic)
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00101: Dyck paths —decomposition reverse⟶ Dyck paths
Mp00327: Dyck paths —inverse Kreweras complement⟶ Dyck paths
St001232: Dyck paths ⟶ ℤResult quality: 73% ●values known / values provided: 73%●distinct values known / distinct values provided: 80%
Mp00101: Dyck paths —decomposition reverse⟶ Dyck paths
Mp00327: Dyck paths —inverse Kreweras complement⟶ Dyck paths
St001232: Dyck paths ⟶ ℤResult quality: 73% ●values known / values provided: 73%●distinct values known / distinct values provided: 80%
Values
[1]
=> [1,0,1,0]
=> [1,1,0,0]
=> [1,0,1,0]
=> 1 = 2 - 1
[2]
=> [1,1,0,0,1,0]
=> [1,1,0,0,1,0]
=> [1,0,1,1,0,0]
=> 2 = 3 - 1
[1,1]
=> [1,0,1,1,0,0]
=> [1,1,0,1,0,0]
=> [1,1,0,0,1,0]
=> 1 = 2 - 1
[3]
=> [1,1,1,0,0,0,1,0]
=> [1,1,0,0,1,0,1,0]
=> [1,0,1,1,1,0,0,0]
=> 3 = 4 - 1
[2,1]
=> [1,0,1,0,1,0]
=> [1,1,1,0,0,0]
=> [1,0,1,0,1,0]
=> ? = 4 - 1
[1,1,1]
=> [1,0,1,1,1,0,0,0]
=> [1,1,0,1,0,1,0,0]
=> [1,1,1,0,0,0,1,0]
=> 1 = 2 - 1
[4]
=> [1,1,1,1,0,0,0,0,1,0]
=> [1,1,0,0,1,0,1,0,1,0]
=> [1,0,1,1,1,1,0,0,0,0]
=> 4 = 5 - 1
[3,1]
=> [1,1,0,1,0,0,1,0]
=> [1,1,0,0,1,1,0,0]
=> [1,0,1,1,0,1,0,0]
=> ? = 6 - 1
[2,2]
=> [1,1,0,0,1,1,0,0]
=> [1,1,0,1,0,0,1,0]
=> [1,1,0,0,1,1,0,0]
=> 2 = 3 - 1
[2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [1,1,0,1,1,0,0,0]
=> [1,1,0,0,1,0,1,0]
=> ? = 4 - 1
[1,1,1,1]
=> [1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> [1,1,1,1,0,0,0,0,1,0]
=> 1 = 2 - 1
[3,2]
=> [1,1,0,0,1,0,1,0]
=> [1,1,1,0,0,0,1,0]
=> [1,0,1,0,1,1,0,0]
=> ? = 6 - 1
[2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [1,1,1,0,1,0,0,0]
=> [1,0,1,1,0,0,1,0]
=> 3 = 4 - 1
[3,3]
=> [1,1,1,0,0,0,1,1,0,0]
=> [1,1,0,1,0,0,1,0,1,0]
=> [1,1,0,0,1,1,1,0,0,0]
=> 3 = 4 - 1
[2,2,2]
=> [1,1,0,0,1,1,1,0,0,0]
=> [1,1,0,1,0,1,0,0,1,0]
=> [1,1,1,0,0,0,1,1,0,0]
=> 2 = 3 - 1
Description
The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2.
Matching statistic: St001000
Mp00095: Integer partitions —to binary word⟶ Binary words
Mp00178: Binary words —to composition⟶ Integer compositions
Mp00231: Integer compositions —bounce path⟶ Dyck paths
St001000: Dyck paths ⟶ ℤResult quality: 47% ●values known / values provided: 47%●distinct values known / distinct values provided: 60%
Mp00178: Binary words —to composition⟶ Integer compositions
Mp00231: Integer compositions —bounce path⟶ Dyck paths
St001000: Dyck paths ⟶ ℤResult quality: 47% ●values known / values provided: 47%●distinct values known / distinct values provided: 60%
Values
[1]
=> 10 => [1,2] => [1,0,1,1,0,0]
=> 2
[2]
=> 100 => [1,3] => [1,0,1,1,1,0,0,0]
=> 3
[1,1]
=> 110 => [1,1,2] => [1,0,1,0,1,1,0,0]
=> 2
[3]
=> 1000 => [1,4] => [1,0,1,1,1,1,0,0,0,0]
=> 4
[2,1]
=> 1010 => [1,2,2] => [1,0,1,1,0,0,1,1,0,0]
=> 4
[1,1,1]
=> 1110 => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0]
=> 2
[4]
=> 10000 => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0]
=> ? = 5
[3,1]
=> 10010 => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0]
=> ? = 6
[2,2]
=> 1100 => [1,1,3] => [1,0,1,0,1,1,1,0,0,0]
=> 3
[2,1,1]
=> 10110 => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0]
=> ? = 4
[1,1,1,1]
=> 11110 => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0]
=> ? = 2
[3,2]
=> 10100 => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0]
=> ? = 6
[2,2,1]
=> 11010 => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0]
=> ? = 4
[3,3]
=> 11000 => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0]
=> ? = 4
[2,2,2]
=> 11100 => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0]
=> ? = 3
Description
Number of indecomposable modules with projective dimension equal to the global dimension in the Nakayama algebra corresponding to the Dyck path.
Matching statistic: St000483
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00146: Dyck paths —to tunnel matching⟶ Perfect matchings
Mp00283: Perfect matchings —non-nesting-exceedence permutation⟶ Permutations
St000483: Permutations ⟶ ℤResult quality: 33% ●values known / values provided: 33%●distinct values known / distinct values provided: 60%
Mp00146: Dyck paths —to tunnel matching⟶ Perfect matchings
Mp00283: Perfect matchings —non-nesting-exceedence permutation⟶ Permutations
St000483: Permutations ⟶ ℤResult quality: 33% ●values known / values provided: 33%●distinct values known / distinct values provided: 60%
Values
[1]
=> [1,0,1,0]
=> [(1,2),(3,4)]
=> [2,1,4,3] => 2
[2]
=> [1,1,0,0,1,0]
=> [(1,4),(2,3),(5,6)]
=> [3,4,2,1,6,5] => 3
[1,1]
=> [1,0,1,1,0,0]
=> [(1,2),(3,6),(4,5)]
=> [2,1,5,6,4,3] => 2
[3]
=> [1,1,1,0,0,0,1,0]
=> [(1,6),(2,5),(3,4),(7,8)]
=> [4,5,6,3,2,1,8,7] => ? = 4
[2,1]
=> [1,0,1,0,1,0]
=> [(1,2),(3,4),(5,6)]
=> [2,1,4,3,6,5] => 4
[1,1,1]
=> [1,0,1,1,1,0,0,0]
=> [(1,2),(3,8),(4,7),(5,6)]
=> [2,1,6,7,8,5,4,3] => ? = 2
[4]
=> [1,1,1,1,0,0,0,0,1,0]
=> [(1,8),(2,7),(3,6),(4,5),(9,10)]
=> [5,6,7,8,4,3,2,1,10,9] => ? = 5
[3,1]
=> [1,1,0,1,0,0,1,0]
=> [(1,6),(2,3),(4,5),(7,8)]
=> [3,5,2,6,4,1,8,7] => ? = 6
[2,2]
=> [1,1,0,0,1,1,0,0]
=> [(1,4),(2,3),(5,8),(6,7)]
=> [3,4,2,1,7,8,6,5] => 3
[2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [(1,2),(3,8),(4,5),(6,7)]
=> [2,1,5,7,4,8,6,3] => ? = 4
[1,1,1,1]
=> [1,0,1,1,1,1,0,0,0,0]
=> [(1,2),(3,10),(4,9),(5,8),(6,7)]
=> [2,1,7,8,9,10,6,5,4,3] => ? = 2
[3,2]
=> [1,1,0,0,1,0,1,0]
=> [(1,4),(2,3),(5,6),(7,8)]
=> [3,4,2,1,6,5,8,7] => ? = 6
[2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [(1,2),(3,4),(5,8),(6,7)]
=> [2,1,4,3,7,8,6,5] => ? = 4
[3,3]
=> [1,1,1,0,0,0,1,1,0,0]
=> [(1,6),(2,5),(3,4),(7,10),(8,9)]
=> [4,5,6,3,2,1,9,10,8,7] => ? = 4
[2,2,2]
=> [1,1,0,0,1,1,1,0,0,0]
=> [(1,4),(2,3),(5,10),(6,9),(7,8)]
=> [3,4,2,1,8,9,10,7,6,5] => ? = 3
Description
The number of times a permutation switches from increasing to decreasing or decreasing to increasing.
This is the same as the number of inner peaks plus the number of inner valleys and called alternating runs in [2]
Matching statistic: St001583
(load all 4 compositions to match this statistic)
(load all 4 compositions to match this statistic)
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00201: Dyck paths —Ringel⟶ Permutations
Mp00149: Permutations —Lehmer code rotation⟶ Permutations
St001583: Permutations ⟶ ℤResult quality: 27% ●values known / values provided: 27%●distinct values known / distinct values provided: 60%
Mp00201: Dyck paths —Ringel⟶ Permutations
Mp00149: Permutations —Lehmer code rotation⟶ Permutations
St001583: Permutations ⟶ ℤResult quality: 27% ●values known / values provided: 27%●distinct values known / distinct values provided: 60%
Values
[1]
=> [1,0,1,0]
=> [3,1,2] => [1,3,2] => 2
[2]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => [3,1,4,2] => 3
[1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => [4,2,1,3] => 2
[3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => [3,4,1,5,2] => ? = 4
[2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => [1,3,4,2] => 4
[1,1,1]
=> [1,0,1,1,1,0,0,0]
=> [3,1,4,5,2] => [4,2,5,1,3] => ? = 2
[4]
=> [1,1,1,1,0,0,0,0,1,0]
=> [2,3,4,6,1,5] => [3,4,5,1,6,2] => ? = 5
[3,1]
=> [1,1,0,1,0,0,1,0]
=> [5,3,1,2,4] => [1,5,3,4,2] => ? = 6
[2,2]
=> [1,1,0,0,1,1,0,0]
=> [2,4,1,5,3] => [3,5,2,1,4] => ? = 3
[2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => [1,3,2,5,4] => ? = 4
[1,1,1,1]
=> [1,0,1,1,1,1,0,0,0,0]
=> [3,1,4,5,6,2] => [4,2,5,6,1,3] => ? = 2
[3,2]
=> [1,1,0,0,1,0,1,0]
=> [2,5,1,3,4] => [3,1,4,5,2] => ? = 6
[2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [4,1,2,5,3] => [5,2,3,1,4] => ? = 4
[3,3]
=> [1,1,1,0,0,0,1,1,0,0]
=> [2,3,5,1,6,4] => [3,4,6,2,1,5] => ? = 4
[2,2,2]
=> [1,1,0,0,1,1,1,0,0,0]
=> [2,4,1,5,6,3] => [3,5,2,6,1,4] => ? = 3
Description
The projective dimension of the simple module corresponding to the point in the poset of the symmetric group under bruhat order.
Matching statistic: St001582
(load all 7 compositions to match this statistic)
(load all 7 compositions to match this statistic)
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00101: Dyck paths —decomposition reverse⟶ Dyck paths
Mp00201: Dyck paths —Ringel⟶ Permutations
St001582: Permutations ⟶ ℤResult quality: 27% ●values known / values provided: 27%●distinct values known / distinct values provided: 60%
Mp00101: Dyck paths —decomposition reverse⟶ Dyck paths
Mp00201: Dyck paths —Ringel⟶ Permutations
St001582: Permutations ⟶ ℤResult quality: 27% ●values known / values provided: 27%●distinct values known / distinct values provided: 60%
Values
[1]
=> [1,0,1,0]
=> [1,1,0,0]
=> [2,3,1] => 1 = 2 - 1
[2]
=> [1,1,0,0,1,0]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => 2 = 3 - 1
[1,1]
=> [1,0,1,1,0,0]
=> [1,1,0,1,0,0]
=> [4,3,1,2] => 1 = 2 - 1
[3]
=> [1,1,1,0,0,0,1,0]
=> [1,1,0,0,1,0,1,0]
=> [2,5,1,3,4] => ? = 4 - 1
[2,1]
=> [1,0,1,0,1,0]
=> [1,1,1,0,0,0]
=> [2,3,4,1] => 3 = 4 - 1
[1,1,1]
=> [1,0,1,1,1,0,0,0]
=> [1,1,0,1,0,1,0,0]
=> [5,4,1,2,3] => ? = 2 - 1
[4]
=> [1,1,1,1,0,0,0,0,1,0]
=> [1,1,0,0,1,0,1,0,1,0]
=> [2,6,1,3,4,5] => ? = 5 - 1
[3,1]
=> [1,1,0,1,0,0,1,0]
=> [1,1,0,0,1,1,0,0]
=> [2,4,1,5,3] => ? = 6 - 1
[2,2]
=> [1,1,0,0,1,1,0,0]
=> [1,1,0,1,0,0,1,0]
=> [5,3,1,2,4] => ? = 3 - 1
[2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [1,1,0,1,1,0,0,0]
=> [4,3,1,5,2] => ? = 4 - 1
[1,1,1,1]
=> [1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> [5,6,1,2,3,4] => ? = 2 - 1
[3,2]
=> [1,1,0,0,1,0,1,0]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 6 - 1
[2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [1,1,1,0,1,0,0,0]
=> [5,3,4,1,2] => ? = 4 - 1
[3,3]
=> [1,1,1,0,0,0,1,1,0,0]
=> [1,1,0,1,0,0,1,0,1,0]
=> [6,3,1,2,4,5] => ? = 4 - 1
[2,2,2]
=> [1,1,0,0,1,1,1,0,0,0]
=> [1,1,0,1,0,1,0,0,1,0]
=> [6,4,1,2,3,5] => ? = 3 - 1
Description
The grades of the simple modules corresponding to the points in the poset of the symmetric group under the Bruhat order.
Matching statistic: St001645
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00100: Dyck paths —touch composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St001645: Graphs ⟶ ℤResult quality: 27% ●values known / values provided: 27%●distinct values known / distinct values provided: 80%
Mp00100: Dyck paths —touch composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St001645: Graphs ⟶ ℤResult quality: 27% ●values known / values provided: 27%●distinct values known / distinct values provided: 80%
Values
[1]
=> [1,0]
=> [1] => ([],1)
=> 1 = 2 - 1
[2]
=> [1,0,1,0]
=> [1,1] => ([(0,1)],2)
=> 2 = 3 - 1
[1,1]
=> [1,1,0,0]
=> [2] => ([],2)
=> ? = 2 - 1
[3]
=> [1,0,1,0,1,0]
=> [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 3 = 4 - 1
[2,1]
=> [1,0,1,1,0,0]
=> [1,2] => ([(1,2)],3)
=> ? = 4 - 1
[1,1,1]
=> [1,1,0,1,0,0]
=> [3] => ([],3)
=> ? = 2 - 1
[4]
=> [1,0,1,0,1,0,1,0]
=> [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 4 = 5 - 1
[3,1]
=> [1,0,1,0,1,1,0,0]
=> [1,1,2] => ([(1,2),(1,3),(2,3)],4)
=> ? = 6 - 1
[2,2]
=> [1,1,1,0,0,0]
=> [3] => ([],3)
=> ? = 3 - 1
[2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [1,3] => ([(2,3)],4)
=> ? = 4 - 1
[1,1,1,1]
=> [1,1,0,1,0,1,0,0]
=> [4] => ([],4)
=> ? = 2 - 1
[3,2]
=> [1,0,1,1,1,0,0,0]
=> [1,3] => ([(2,3)],4)
=> ? = 6 - 1
[2,2,1]
=> [1,1,1,0,0,1,0,0]
=> [4] => ([],4)
=> ? = 4 - 1
[3,3]
=> [1,1,1,0,1,0,0,0]
=> [4] => ([],4)
=> ? = 4 - 1
[2,2,2]
=> [1,1,1,1,0,0,0,0]
=> [4] => ([],4)
=> ? = 3 - 1
Description
The pebbling number of a connected graph.
The following 9 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
St001375The pancake length of a permutation. St001491The number of indecomposable projective-injective modules in the algebra corresponding to a subset. St000307The number of rowmotion orbits of a poset. St000632The jump number of the poset. St000717The number of ordinal summands of a poset. St001060The distinguishing index of a graph. St001208The number of connected components of the quiver of $A/T$ when $T$ is the 1-tilting module corresponding to the permutation in the Auslander algebra $A$ of $K[x]/(x^n)$. St001722The number of minimal chains with small intervals between a binary word and the top element. St001811The Castelnuovo-Mumford regularity of a permutation.
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