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Your data matches 132 different statistics following compositions of up to 3 maps.
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Matching statistic: St001884
(load all 7 compositions to match this statistic)
(load all 7 compositions to match this statistic)
St001884: Binary words ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
0 => 1 = 2 - 1
1 => 1 = 2 - 1
00 => 2 = 3 - 1
01 => 1 = 2 - 1
10 => 1 = 2 - 1
11 => 2 = 3 - 1
000 => 3 = 4 - 1
001 => 1 = 2 - 1
010 => 2 = 3 - 1
011 => 1 = 2 - 1
100 => 1 = 2 - 1
101 => 2 = 3 - 1
110 => 1 = 2 - 1
111 => 3 = 4 - 1
0000 => 4 = 5 - 1
1111 => 4 = 5 - 1
00000 => 5 = 6 - 1
11111 => 5 = 6 - 1
000000 => 6 = 7 - 1
111111 => 6 = 7 - 1
Description
The number of borders of a binary word.
A border of a binary word $w$ is a word which is both a prefix and a suffix of $w$.
Matching statistic: St000295
(load all 7 compositions to match this statistic)
(load all 7 compositions to match this statistic)
St000295: Binary words ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
0 => 0 = 2 - 2
1 => 0 = 2 - 2
00 => 1 = 3 - 2
01 => 0 = 2 - 2
10 => 0 = 2 - 2
11 => 1 = 3 - 2
000 => 2 = 4 - 2
001 => 0 = 2 - 2
010 => 1 = 3 - 2
011 => 0 = 2 - 2
100 => 0 = 2 - 2
101 => 1 = 3 - 2
110 => 0 = 2 - 2
111 => 2 = 4 - 2
0000 => 3 = 5 - 2
1111 => 3 = 5 - 2
00000 => 4 = 6 - 2
11111 => 4 = 6 - 2
000000 => 5 = 7 - 2
111111 => 5 = 7 - 2
Description
The length of the border of a binary word.
The border of a word is the longest word which is both a proper prefix and a proper suffix, including a possible empty border.
Matching statistic: St000469
(load all 3 compositions to match this statistic)
(load all 3 compositions to match this statistic)
Values
0 => ([(0,1)],2)
=> ([],2)
=> 2
1 => ([(0,1)],2)
=> ([],2)
=> 2
00 => ([(0,2),(2,1)],3)
=> ([],3)
=> 3
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)
=> 3
000 => ([(0,3),(2,1),(3,2)],4)
=> ([],4)
=> 4
001 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(2,5),(3,4),(4,5)],6)
=> 2
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)
=> 2
100 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(2,5),(3,4),(4,5)],6)
=> 2
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)
=> 2
111 => ([(0,3),(2,1),(3,2)],4)
=> ([],4)
=> 4
0000 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([],5)
=> 5
1111 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([],5)
=> 5
00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([],6)
=> 6
11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([],6)
=> 6
000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ([],7)
=> 7
111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ([],7)
=> 7
Description
The distinguishing number of a graph.
This is the minimal number of colours needed to colour the vertices of a graph, such that only the trivial automorphism of the graph preserves the colouring.
For connected graphs, this statistic is at most one plus the maximal degree of the graph, with equality attained for complete graphs, complete bipartite graphs and the cycle with five vertices, see Theorem 4.2 of [2].
Matching statistic: St000382
(load all 3 compositions to match this statistic)
(load all 3 compositions to match this statistic)
Mp00136: Binary words —rotate back-to-front⟶ Binary words
Mp00097: Binary words —delta morphism⟶ Integer compositions
St000382: Integer compositions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00097: Binary words —delta morphism⟶ Integer compositions
St000382: Integer compositions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
0 => 0 => [1] => 1 = 2 - 1
1 => 1 => [1] => 1 = 2 - 1
00 => 00 => [2] => 2 = 3 - 1
01 => 10 => [1,1] => 1 = 2 - 1
10 => 01 => [1,1] => 1 = 2 - 1
11 => 11 => [2] => 2 = 3 - 1
000 => 000 => [3] => 3 = 4 - 1
001 => 100 => [1,2] => 1 = 2 - 1
010 => 001 => [2,1] => 2 = 3 - 1
011 => 101 => [1,1,1] => 1 = 2 - 1
100 => 010 => [1,1,1] => 1 = 2 - 1
101 => 110 => [2,1] => 2 = 3 - 1
110 => 011 => [1,2] => 1 = 2 - 1
111 => 111 => [3] => 3 = 4 - 1
0000 => 0000 => [4] => 4 = 5 - 1
1111 => 1111 => [4] => 4 = 5 - 1
00000 => 00000 => [5] => 5 = 6 - 1
11111 => 11111 => [5] => 5 = 6 - 1
000000 => 000000 => [6] => 6 = 7 - 1
111111 => 111111 => [6] => 6 = 7 - 1
Description
The first part of an integer composition.
Matching statistic: St000383
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00135: Binary words —rotate front-to-back⟶ Binary words
Mp00097: Binary words —delta morphism⟶ Integer compositions
St000383: Integer compositions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00097: Binary words —delta morphism⟶ Integer compositions
St000383: Integer compositions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
0 => 0 => [1] => 1 = 2 - 1
1 => 1 => [1] => 1 = 2 - 1
00 => 00 => [2] => 2 = 3 - 1
01 => 10 => [1,1] => 1 = 2 - 1
10 => 01 => [1,1] => 1 = 2 - 1
11 => 11 => [2] => 2 = 3 - 1
000 => 000 => [3] => 3 = 4 - 1
001 => 010 => [1,1,1] => 1 = 2 - 1
010 => 100 => [1,2] => 2 = 3 - 1
011 => 110 => [2,1] => 1 = 2 - 1
100 => 001 => [2,1] => 1 = 2 - 1
101 => 011 => [1,2] => 2 = 3 - 1
110 => 101 => [1,1,1] => 1 = 2 - 1
111 => 111 => [3] => 3 = 4 - 1
0000 => 0000 => [4] => 4 = 5 - 1
1111 => 1111 => [4] => 4 = 5 - 1
00000 => 00000 => [5] => 5 = 6 - 1
11111 => 11111 => [5] => 5 = 6 - 1
000000 => 000000 => [6] => 6 = 7 - 1
111111 => 111111 => [6] => 6 = 7 - 1
Description
The last part of an integer composition.
Matching statistic: St000773
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00097: Binary words —delta morphism⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000773: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000773: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
0 => [1] => ([],1)
=> 1 = 2 - 1
1 => [1] => ([],1)
=> 1 = 2 - 1
00 => [2] => ([],2)
=> 2 = 3 - 1
01 => [1,1] => ([(0,1)],2)
=> 1 = 2 - 1
10 => [1,1] => ([(0,1)],2)
=> 1 = 2 - 1
11 => [2] => ([],2)
=> 2 = 3 - 1
000 => [3] => ([],3)
=> 3 = 4 - 1
001 => [2,1] => ([(0,2),(1,2)],3)
=> 1 = 2 - 1
010 => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 2 = 3 - 1
011 => [1,2] => ([(1,2)],3)
=> 1 = 2 - 1
100 => [1,2] => ([(1,2)],3)
=> 1 = 2 - 1
101 => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 2 = 3 - 1
110 => [2,1] => ([(0,2),(1,2)],3)
=> 1 = 2 - 1
111 => [3] => ([],3)
=> 3 = 4 - 1
0000 => [4] => ([],4)
=> 4 = 5 - 1
1111 => [4] => ([],4)
=> 4 = 5 - 1
00000 => [5] => ([],5)
=> 5 = 6 - 1
11111 => [5] => ([],5)
=> 5 = 6 - 1
000000 => [6] => ([],6)
=> 6 = 7 - 1
111111 => [6] => ([],6)
=> 6 = 7 - 1
Description
The multiplicity of the largest Laplacian eigenvalue in a graph.
Matching statistic: St000776
(load all 3 compositions to match this statistic)
(load all 3 compositions to match this statistic)
Mp00097: Binary words —delta morphism⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000776: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000776: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
0 => [1] => ([],1)
=> 1 = 2 - 1
1 => [1] => ([],1)
=> 1 = 2 - 1
00 => [2] => ([],2)
=> 2 = 3 - 1
01 => [1,1] => ([(0,1)],2)
=> 1 = 2 - 1
10 => [1,1] => ([(0,1)],2)
=> 1 = 2 - 1
11 => [2] => ([],2)
=> 2 = 3 - 1
000 => [3] => ([],3)
=> 3 = 4 - 1
001 => [2,1] => ([(0,2),(1,2)],3)
=> 1 = 2 - 1
010 => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 2 = 3 - 1
011 => [1,2] => ([(1,2)],3)
=> 1 = 2 - 1
100 => [1,2] => ([(1,2)],3)
=> 1 = 2 - 1
101 => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 2 = 3 - 1
110 => [2,1] => ([(0,2),(1,2)],3)
=> 1 = 2 - 1
111 => [3] => ([],3)
=> 3 = 4 - 1
0000 => [4] => ([],4)
=> 4 = 5 - 1
1111 => [4] => ([],4)
=> 4 = 5 - 1
00000 => [5] => ([],5)
=> 5 = 6 - 1
11111 => [5] => ([],5)
=> 5 = 6 - 1
000000 => [6] => ([],6)
=> 6 = 7 - 1
111111 => [6] => ([],6)
=> 6 = 7 - 1
Description
The maximal multiplicity of an eigenvalue in a graph.
Matching statistic: St000439
Mp00136: Binary words —rotate back-to-front⟶ Binary words
Mp00097: Binary words —delta morphism⟶ Integer compositions
Mp00231: Integer compositions —bounce path⟶ Dyck paths
St000439: 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
St000439: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
0 => 0 => [1] => [1,0]
=> 2
1 => 1 => [1] => [1,0]
=> 2
00 => 00 => [2] => [1,1,0,0]
=> 3
01 => 10 => [1,1] => [1,0,1,0]
=> 2
10 => 01 => [1,1] => [1,0,1,0]
=> 2
11 => 11 => [2] => [1,1,0,0]
=> 3
000 => 000 => [3] => [1,1,1,0,0,0]
=> 4
001 => 100 => [1,2] => [1,0,1,1,0,0]
=> 2
010 => 001 => [2,1] => [1,1,0,0,1,0]
=> 3
011 => 101 => [1,1,1] => [1,0,1,0,1,0]
=> 2
100 => 010 => [1,1,1] => [1,0,1,0,1,0]
=> 2
101 => 110 => [2,1] => [1,1,0,0,1,0]
=> 3
110 => 011 => [1,2] => [1,0,1,1,0,0]
=> 2
111 => 111 => [3] => [1,1,1,0,0,0]
=> 4
0000 => 0000 => [4] => [1,1,1,1,0,0,0,0]
=> 5
1111 => 1111 => [4] => [1,1,1,1,0,0,0,0]
=> 5
00000 => 00000 => [5] => [1,1,1,1,1,0,0,0,0,0]
=> 6
11111 => 11111 => [5] => [1,1,1,1,1,0,0,0,0,0]
=> 6
000000 => 000000 => [6] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> 7
111111 => 111111 => [6] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> 7
Description
The position of the first down step of a Dyck path.
Matching statistic: St000675
(load all 4 compositions to match this statistic)
(load all 4 compositions to match this statistic)
Mp00097: Binary words —delta morphism⟶ Integer compositions
Mp00231: Integer compositions —bounce path⟶ Dyck paths
Mp00199: Dyck paths —prime Dyck path⟶ Dyck paths
St000675: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00231: Integer compositions —bounce path⟶ Dyck paths
Mp00199: Dyck paths —prime Dyck path⟶ Dyck paths
St000675: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
0 => [1] => [1,0]
=> [1,1,0,0]
=> 2
1 => [1] => [1,0]
=> [1,1,0,0]
=> 2
00 => [2] => [1,1,0,0]
=> [1,1,1,0,0,0]
=> 3
01 => [1,1] => [1,0,1,0]
=> [1,1,0,1,0,0]
=> 2
10 => [1,1] => [1,0,1,0]
=> [1,1,0,1,0,0]
=> 2
11 => [2] => [1,1,0,0]
=> [1,1,1,0,0,0]
=> 3
000 => [3] => [1,1,1,0,0,0]
=> [1,1,1,1,0,0,0,0]
=> 4
001 => [2,1] => [1,1,0,0,1,0]
=> [1,1,1,0,0,1,0,0]
=> 2
010 => [1,1,1] => [1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,0]
=> 3
011 => [1,2] => [1,0,1,1,0,0]
=> [1,1,0,1,1,0,0,0]
=> 2
100 => [1,2] => [1,0,1,1,0,0]
=> [1,1,0,1,1,0,0,0]
=> 2
101 => [1,1,1] => [1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,0]
=> 3
110 => [2,1] => [1,1,0,0,1,0]
=> [1,1,1,0,0,1,0,0]
=> 2
111 => [3] => [1,1,1,0,0,0]
=> [1,1,1,1,0,0,0,0]
=> 4
0000 => [4] => [1,1,1,1,0,0,0,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> 5
1111 => [4] => [1,1,1,1,0,0,0,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> 5
00000 => [5] => [1,1,1,1,1,0,0,0,0,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> 6
11111 => [5] => [1,1,1,1,1,0,0,0,0,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> 6
000000 => [6] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> 7
111111 => [6] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> 7
Description
The number of centered multitunnels of a Dyck path.
This is the number of factorisations $D = A B C$ of a Dyck path, such that $B$ is a Dyck path and $A$ and $B$ have the same length.
Matching statistic: St001290
Mp00097: Binary words —delta morphism⟶ Integer compositions
Mp00231: Integer compositions —bounce path⟶ Dyck paths
Mp00122: Dyck paths —Elizalde-Deutsch bijection⟶ Dyck paths
St001290: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00231: Integer compositions —bounce path⟶ Dyck paths
Mp00122: Dyck paths —Elizalde-Deutsch bijection⟶ Dyck paths
St001290: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
0 => [1] => [1,0]
=> [1,0]
=> 2
1 => [1] => [1,0]
=> [1,0]
=> 2
00 => [2] => [1,1,0,0]
=> [1,0,1,0]
=> 3
01 => [1,1] => [1,0,1,0]
=> [1,1,0,0]
=> 2
10 => [1,1] => [1,0,1,0]
=> [1,1,0,0]
=> 2
11 => [2] => [1,1,0,0]
=> [1,0,1,0]
=> 3
000 => [3] => [1,1,1,0,0,0]
=> [1,0,1,0,1,0]
=> 4
001 => [2,1] => [1,1,0,0,1,0]
=> [1,1,1,0,0,0]
=> 2
010 => [1,1,1] => [1,0,1,0,1,0]
=> [1,1,0,0,1,0]
=> 3
011 => [1,2] => [1,0,1,1,0,0]
=> [1,1,0,1,0,0]
=> 2
100 => [1,2] => [1,0,1,1,0,0]
=> [1,1,0,1,0,0]
=> 2
101 => [1,1,1] => [1,0,1,0,1,0]
=> [1,1,0,0,1,0]
=> 3
110 => [2,1] => [1,1,0,0,1,0]
=> [1,1,1,0,0,0]
=> 2
111 => [3] => [1,1,1,0,0,0]
=> [1,0,1,0,1,0]
=> 4
0000 => [4] => [1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0]
=> 5
1111 => [4] => [1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0]
=> 5
00000 => [5] => [1,1,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> 6
11111 => [5] => [1,1,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> 6
000000 => [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]
=> 7
111111 => [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]
=> 7
Description
The first natural number n such that the tensor product of n copies of D(A) is zero for the corresponding Nakayama algebra A.
The following 122 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
St000010The length of the partition. St000011The number of touch points (or returns) of a Dyck path. St000025The number of initial rises of a Dyck path. St000026The position of the first return of a Dyck path. St000031The number of cycles in the cycle decomposition of a permutation. St000056The decomposition (or block) number of a permutation. St000273The domination number of a graph. St000287The number of connected components of a graph. St000544The cop number of a graph. St000617The number of global maxima of a Dyck path. St000723The maximal cardinality of a set of vertices with the same neighbourhood in a graph. St000757The length of the longest weakly inreasing subsequence of parts of an integer composition. St000765The number of weak records in an integer composition. St000772The multiplicity of the largest distance Laplacian eigenvalue in a connected graph. St000916The packing number of a graph. St000930The k-Gorenstein degree of the corresponding Nakayama algebra with linear quiver. St000999Number of indecomposable projective module with injective dimension equal to the global dimension in the Nakayama algebra corresponding to the Dyck path. St001009Number of indecomposable injective modules with projective dimension g when g is the global dimension of the Nakayama algebra corresponding to the Dyck path. St001052The length of the exterior of a permutation. St001096The size of the overlap set of a permutation. St001135The projective dimension of the first simple module in the Nakayama algebra corresponding to the Dyck path. St001184Number of indecomposable injective modules with grade at least 1 in the corresponding Nakayama algebra. St001201The grade of the simple module $S_0$ in the special CNakayama algebra corresponding to the Dyck path. St001202Call a CNakayama algebra (a Nakayama algebra with a cyclic quiver) with Kupisch series $L=[c_0,c_1,...,c_{n−1}]$ such that $n=c_0 < c_i$ for all $i > 0$ a special CNakayama algebra. St001210Gives the maximal vector space dimension of the first Ext-group between an indecomposable module X and the regular module A, when A is the Nakayama algebra corresponding to the Dyck path. St001322The size of a minimal independent dominating set in a graph. St001339The irredundance number of a graph. St001363The Euler characteristic of a graph according to Knill. St001461The number of topologically connected components of the chord diagram of a permutation. St001481The minimal height of a peak of a Dyck path. St001652The length of a longest interval of consecutive numbers. St001662The length of the longest factor of consecutive numbers in a permutation. St001778The largest greatest common divisor of an element and its image in a permutation. St001829The common independence number of a graph. St000234The number of global ascents of a permutation. St000377The dinv defect of an integer partition. St000441The number of successions of a permutation. St000954Number of times the corresponding LNakayama algebra has $Ext^i(D(A),A)=0$ for $i>0$. St001176The size of a partition minus its first part. St001233The number of indecomposable 2-dimensional modules with projective dimension one. St001265The maximal i such that the i-th simple module has projective dimension equal to the global dimension in the corresponding Nakayama algebra. St001777The number of weak descents in an integer composition. St001366The maximal multiplicity of a degree of a vertex of a graph. St001844The maximal degree of a generator of the invariant ring of the automorphism group of a graph. St000489The number of cycles of a permutation of length at most 3. St000678The number of up steps after the last double rise of a Dyck path. St000887The maximal number of nonzero entries on a diagonal of a permutation matrix. St001038The minimal height of a column in the parallelogram polyomino associated with the Dyck path. St000689The maximal n such that the minimal generator-cogenerator module in the LNakayama algebra of a Dyck path is n-rigid. St001232The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2. St001330The hat guessing number of a graph. St000454The largest eigenvalue of a graph if it is integral. St001880The number of 2-Gorenstein indecomposable injective modules in the incidence algebra of the lattice. St001879The number of indecomposable summands of the top of the first syzygy of the dual of the regular module in the incidence algebra of the lattice. St001200The number of simple modules in $eAe$ with projective dimension at most 2 in the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. St000771The largest multiplicity of a distance Laplacian eigenvalue in a connected graph. St000806The semiperimeter of the associated bargraph. St001199The dominant dimension of $eAe$ for the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. St001198The number of simple modules in the algebra $eAe$ with projective dimension at most 1 in the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. St001206The maximal dimension of an indecomposable projective $eAe$-module (that is the height of the corresponding Dyck path) of the corresponding Nakayama algebra with minimal faithful projective-injective module $eA$. St000460The hook length of the last cell along the main diagonal of an integer partition. St000510The number of invariant oriented cycles when acting with a permutation of given cycle type. St000681The Grundy value of Chomp on Ferrers diagrams. St000870The product of the hook lengths of the diagonal cells in an integer partition. St001247The number of parts of a partition that are not congruent 2 modulo 3. St001249Sum of the odd parts of a partition. St001250The number of parts of a partition that are not congruent 0 modulo 3. St001281The normalized isoperimetric number of a graph. St001360The number of covering relations in Young's lattice below a partition. St001378The product of the cohook lengths of the integer partition. St001380The number of monomer-dimer tilings of a Ferrers diagram. St001432The order dimension of the partition. St001498The normalised height of a Nakayama algebra with magnitude 1. St001592The maximal number of simple paths between any two different vertices of a graph. St001607The number of coloured graphs such that the multiplicities of colours are given by a partition. St001608The number of coloured rooted trees such that the multiplicities of colours are given by a partition. St001609The number of coloured trees such that the multiplicities of colours are given by a partition. St001611The number of multiset partitions such that the multiplicities of elements are given by a partition. St001780The order of promotion on the set of standard tableaux of given shape. St001785The number of ways to obtain a partition as the multiset of antidiagonal lengths of the Ferrers diagram of a partition. St001899The total number of irreducible representations contained in the higher Lie character for an integer partition. St001900The number of distinct irreducible representations contained in the higher Lie character for an integer partition. St001908The number of semistandard tableaux of distinct weight whose maximal entry is the length of the partition. St001913The number of preimages of an integer partition in Bulgarian solitaire. St001914The size of the orbit of an integer partition in Bulgarian solitaire. St001933The largest multiplicity of a part in an integer partition. St001936The number of transitive factorisations of a permutation of given cycle type into star transpositions. St000175Degree of the polynomial counting the number of semistandard Young tableaux when stretching the shape. St000225Difference between largest and smallest parts in a partition. St000379The number of Hamiltonian cycles in a graph. St000506The number of standard desarrangement tableaux of shape equal to the given partition. St000512The number of invariant subsets of size 3 when acting with a permutation of given cycle type. St000661The number of rises of length 3 of a Dyck path. St000749The smallest integer d such that the restriction of the representation corresponding to a partition of n to the symmetric group on n-d letters has a constituent of odd degree. St000931The number of occurrences of the pattern UUU in a Dyck path. St000944The 3-degree of an integer partition. St001035The convexity degree of the parallelogram polyomino associated with the Dyck path. St001141The number of occurrences of hills of size 3 in a Dyck path. St001384The number of boxes in the diagram of a partition that do not lie in the largest triangle it contains. St001440The number of standard Young tableaux whose major index is congruent one modulo the size of a given integer partition. St001586The number of odd parts smaller than the largest even part in an integer partition. St001714The number of subpartitions of an integer partition that do not dominate the conjugate subpartition. St001767The largest minimal number of arrows pointing to a cell in the Ferrers diagram in any assignment. St001961The sum of the greatest common divisors of all pairs of parts. St000515The number of invariant set partitions when acting with a permutation of given cycle type. St001207The Lowey length of the algebra $A/T$ when $T$ is the 1-tilting module corresponding to the permutation in the Auslander algebra of $K[x]/(x^n)$. St000704The number of semistandard tableaux on a given integer partition with minimal maximal entry. St001128The exponens consonantiae of a partition. St000938The number of zeros of the symmetric group character corresponding to the partition. St000940The number of characters of the symmetric group whose value on the partition is zero. St000941The number of characters of the symmetric group whose value on the partition is even. St001124The multiplicity of the standard representation in the Kronecker square corresponding to a partition. St001060The distinguishing index of a graph. St000464The Schultz index of a connected graph. St000817The sum of the entries in the column specified by the composition of the change of basis matrix from dual immaculate quasisymmetric functions to monomial quasisymmetric functions. St000818The sum of the entries in the column specified by the composition of the change of basis matrix from quasisymmetric Schur functions to monomial quasisymmetric functions. St001545The second Elser number of a connected graph. St000285The size of the preimage of the map 'to inverse des composition' from Parking functions to Integer compositions. St000456The monochromatic index of a connected graph. St000762The sum of the positions of the weak records of an integer composition. St001118The acyclic chromatic index of a graph. St000455The second largest eigenvalue of a graph if it is integral.
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