- FindStat

Your data matches 646 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)

Matching statistic: St000552
(load all 8 compositions to match this statistic)

Mapping

St000552: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%

Values

([],1)
 => 0
([],2)
 => 0
([(0,1)],2)
 => 0
([],3)
 => 0
([(1,2)],3)
 => 0
([(0,2),(1,2)],3)
 => 1
([(0,1),(0,2),(1,2)],3)
 => 0
([],4)
 => 0
([(2,3)],4)
 => 0
([(1,3),(2,3)],4)
 => 1
([(0,3),(1,3),(2,3)],4)
 => 1
([(0,3),(1,2)],4)
 => 0
([(0,3),(1,2),(2,3)],4)
 => 2
([(1,2),(1,3),(2,3)],4)
 => 0
([(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => 0
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 0
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 0

Description

The number of cut vertices of a graph. A cut vertex is one whose deletion increases the number of connected components.

Matching statistic: St001323
(load all 15 compositions to match this statistic)

Mapping

St001323: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%

Values

([],1)
 => 0
([],2)
 => 0
([(0,1)],2)
 => 0
([],3)
 => 0
([(1,2)],3)
 => 0
([(0,2),(1,2)],3)
 => 1
([(0,1),(0,2),(1,2)],3)
 => 0
([],4)
 => 0
([(2,3)],4)
 => 0
([(1,3),(2,3)],4)
 => 1
([(0,3),(1,3),(2,3)],4)
 => 2
([(0,3),(1,2)],4)
 => 0
([(0,3),(1,2),(2,3)],4)
 => 0
([(1,2),(1,3),(2,3)],4)
 => 0
([(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => 0
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 0

Description

The independence gap of a graph. This is the difference between the independence number [[St000093]] and the minimal size of a maximally independent set of a graph. In particular, this statistic is

$0$ for well covered graphs

Matching statistic: St001336
(load all 25 compositions to match this statistic)

Mapping

St001336: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%

Values

([],1)
 => 0
([],2)
 => 0
([(0,1)],2)
 => 0
([],3)
 => 0
([(1,2)],3)
 => 0
([(0,2),(1,2)],3)
 => 0
([(0,1),(0,2),(1,2)],3)
 => 1
([],4)
 => 0
([(2,3)],4)
 => 0
([(1,3),(2,3)],4)
 => 0
([(0,3),(1,3),(2,3)],4)
 => 0
([(0,3),(1,2)],4)
 => 0
([(0,3),(1,2),(2,3)],4)
 => 0
([(1,2),(1,3),(2,3)],4)
 => 1
([(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => 0
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2

Description

The minimal number of vertices in a graph whose complement is triangle-free.

Matching statistic: St001572
(load all 25 compositions to match this statistic)

Mapping

St001572: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%

Values

([],1)
 => 0
([],2)
 => 0
([(0,1)],2)
 => 0
([],3)
 => 0
([(1,2)],3)
 => 0
([(0,2),(1,2)],3)
 => 0
([(0,1),(0,2),(1,2)],3)
 => 1
([],4)
 => 0
([(2,3)],4)
 => 0
([(1,3),(2,3)],4)
 => 0
([(0,3),(1,3),(2,3)],4)
 => 0
([(0,3),(1,2)],4)
 => 0
([(0,3),(1,2),(2,3)],4)
 => 0
([(1,2),(1,3),(2,3)],4)
 => 1
([(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => 0
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2

Description

The minimal number of edges to remove to make a graph bipartite.

Matching statistic: St001573
(load all 25 compositions to match this statistic)

Mapping

St001573: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%

Values

([],1)
 => 0
([],2)
 => 0
([(0,1)],2)
 => 0
([],3)
 => 0
([(1,2)],3)
 => 0
([(0,2),(1,2)],3)
 => 0
([(0,1),(0,2),(1,2)],3)
 => 1
([],4)
 => 0
([(2,3)],4)
 => 0
([(1,3),(2,3)],4)
 => 0
([(0,3),(1,3),(2,3)],4)
 => 0
([(0,3),(1,2)],4)
 => 0
([(0,3),(1,2),(2,3)],4)
 => 0
([(1,2),(1,3),(2,3)],4)
 => 1
([(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => 0
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2

Description

The minimal number of edges to remove to make a graph triangle-free.

Matching statistic: St001689
(load all 8 compositions to match this statistic)

Mapping

St001689: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%

Values

([],1)
 => 0
([],2)
 => 0
([(0,1)],2)
 => 0
([],3)
 => 0
([(1,2)],3)
 => 0
([(0,2),(1,2)],3)
 => 1
([(0,1),(0,2),(1,2)],3)
 => 0
([],4)
 => 0
([(2,3)],4)
 => 0
([(1,3),(2,3)],4)
 => 1
([(0,3),(1,3),(2,3)],4)
 => 1
([(0,3),(1,2)],4)
 => 0
([(0,3),(1,2),(2,3)],4)
 => 0
([(1,2),(1,3),(2,3)],4)
 => 0
([(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => 0
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 0

Description

The number of celebrities in a graph. A celebrity is a vertex such that more than half of its neighbours have smaller degree.

Matching statistic: St000091
(load all 16 compositions to match this statistic)

Mapping

Mp00152: Graphs —Laplacian multiplicities⟶ Integer compositions
St000091: Integer compositions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%

Values

([],1)
 => [1] => 0
([],2)
 => [2] => 0
([(0,1)],2)
 => [1,1] => 0
([],3)
 => [3] => 0
([(1,2)],3)
 => [1,2] => 1
([(0,2),(1,2)],3)
 => [1,1,1] => 0
([(0,1),(0,2),(1,2)],3)
 => [2,1] => 0
([],4)
 => [4] => 0
([(2,3)],4)
 => [1,3] => 2
([(1,3),(2,3)],4)
 => [1,1,2] => 1
([(0,3),(1,3),(2,3)],4)
 => [1,2,1] => 1
([(0,3),(1,2)],4)
 => [2,2] => 0
([(0,3),(1,2),(2,3)],4)
 => [1,1,1,1] => 0
([(1,2),(1,3),(2,3)],4)
 => [2,2] => 0
([(0,3),(1,2),(1,3),(2,3)],4)
 => [1,1,1,1] => 0
([(0,2),(0,3),(1,2),(1,3)],4)
 => [1,2,1] => 1
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => [2,1,1] => 0
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => [3,1] => 0

Description

The descent variation of a composition. Defined in [1].

Matching statistic: St000225
(load all 24 compositions to match this statistic)

Mapping

Mp00251: Graphs —clique sizes⟶ Integer partitions
St000225: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%

Values

([],1)
 => [1]
 => 0
([],2)
 => [1,1]
 => 0
([(0,1)],2)
 => [2]
 => 0
([],3)
 => [1,1,1]
 => 0
([(1,2)],3)
 => [2,1]
 => 1
([(0,2),(1,2)],3)
 => [2,2]
 => 0
([(0,1),(0,2),(1,2)],3)
 => [3]
 => 0
([],4)
 => [1,1,1,1]
 => 0
([(2,3)],4)
 => [2,1,1]
 => 1
([(1,3),(2,3)],4)
 => [2,2,1]
 => 1
([(0,3),(1,3),(2,3)],4)
 => [2,2,2]
 => 0
([(0,3),(1,2)],4)
 => [2,2]
 => 0
([(0,3),(1,2),(2,3)],4)
 => [2,2,2]
 => 0
([(1,2),(1,3),(2,3)],4)
 => [3,1]
 => 2
([(0,3),(1,2),(1,3),(2,3)],4)
 => [3,2]
 => 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => [2,2,2,2]
 => 0
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => [3,3]
 => 0
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => [4]
 => 0

Description

Difference between largest and smallest parts in a partition.

Matching statistic: St000362
(load all 6 compositions to match this statistic)

Mapping

Mp00274: Graphs —block-cut tree⟶ Graphs
St000362: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%

Values

([],1)
 => ([],1)
 => 0
([],2)
 => ([],2)
 => 0
([(0,1)],2)
 => ([],1)
 => 0
([],3)
 => ([],3)
 => 0
([(1,2)],3)
 => ([],2)
 => 0
([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => 1
([(0,1),(0,2),(1,2)],3)
 => ([],1)
 => 0
([],4)
 => ([],4)
 => 0
([(2,3)],4)
 => ([],3)
 => 0
([(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => 1
([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => 1
([(0,3),(1,2)],4)
 => ([],2)
 => 0
([(0,3),(1,2),(2,3)],4)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 2
([(1,2),(1,3),(2,3)],4)
 => ([],2)
 => 0
([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(1,2)],3)
 => 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([],1)
 => 0
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],1)
 => 0
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],1)
 => 0

Description

The size of a minimal vertex cover of a graph. A '''vertex cover''' of a graph

$G$ is a subset

$S$ of the vertices of

$G$ such that each edge of

$G$ contains at least one vertex of

$S$ . Finding a minimal vertex cover is an NP-hard optimization problem.

Matching statistic: St000387
(load all 8 compositions to match this statistic)

Mapping

Mp00274: Graphs —block-cut tree⟶ Graphs
St000387: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%

Values

([],1)
 => ([],1)
 => 0
([],2)
 => ([],2)
 => 0
([(0,1)],2)
 => ([],1)
 => 0
([],3)
 => ([],3)
 => 0
([(1,2)],3)
 => ([],2)
 => 0
([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => 1
([(0,1),(0,2),(1,2)],3)
 => ([],1)
 => 0
([],4)
 => ([],4)
 => 0
([(2,3)],4)
 => ([],3)
 => 0
([(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => 1
([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => 1
([(0,3),(1,2)],4)
 => ([],2)
 => 0
([(0,3),(1,2),(2,3)],4)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 2
([(1,2),(1,3),(2,3)],4)
 => ([],2)
 => 0
([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,2),(1,2)],3)
 => 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([],1)
 => 0
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],1)
 => 0
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([],1)
 => 0

Description

The matching number of a graph. For a graph

$G$ , this is defined as the maximal size of a '''matching''' or '''independent edge set''' (a set of edges without common vertices) contained in

$G$ .

The following 636 statistics, ordered by result quality, also match your data. Click on any of them to see the details.

St000537The cutwidth of a graph. St000752The Grundy value for the game 'Couples are forever' on an integer partition. St000766The number of inversions of an integer composition. St000985The number of positive eigenvalues of the adjacency matrix of the graph. St001214The aft of an integer partition. St001270The bandwidth of a graph. St001271The competition number of a graph. St001331The size of the minimal feedback vertex set. St001349The number of different graphs obtained from the given graph by removing an edge. St001393The induced matching number of a graph. St001459The number of zero columns in the nullspace of a graph. St001479The number of bridges of a graph. St001638The book thickness of a graph. St001644The dimension of a graph. St001723The differential of a graph. St001724The 2-packing differential of a graph. St001812The biclique partition number of a graph. St001826The maximal number of leaves on a vertex of a graph. St001962The proper pathwidth of a graph. St000172The Grundy number of a graph. St000482The (zero)-forcing number of a graph. St000771The largest multiplicity of a distance Laplacian eigenvalue in a connected graph. St000772The multiplicity of the largest distance Laplacian eigenvalue in a connected graph. St000773The multiplicity of the largest Laplacian eigenvalue in a graph. St000774The maximal multiplicity of a Laplacian eigenvalue in a graph. St000776The maximal multiplicity of an eigenvalue in a graph. St001112The 3-weak dynamic number of a graph. St001116The game chromatic number of a graph. St001261The Castelnuovo-Mumford regularity of a graph. St001581The achromatic number of a graph. St001670The connected partition number of a graph. St001734The lettericity of a graph. St001774The degree of the minimal polynomial of the smallest eigenvalue of a graph. St001775The degree of the minimal polynomial of the largest eigenvalue of a graph. St001883The mutual visibility number of a graph. St001951The number of factors in the disjoint direct product decomposition of the automorphism group of a graph. St001963The tree-depth of a graph. St000089The absolute variation of a composition. St000171The degree of the graph. St000185The weighted size of a partition. St000272The treewidth of a graph. St000377The dinv defect of an integer partition. St000535The rank-width of a graph. St000536The pathwidth of a graph. St000697The number of 3-rim hooks removed from an integer partition to obtain its associated 3-core. St000769The major index of a composition regarded as a word. St000877The depth of the binary word interpreted as a path. St001026The maximum of the projective dimensions of the indecomposable non-projective injective modules minus the minimum in the Nakayama algebra corresponding to the Dyck path. St001033The normalized area of the parallelogram polyomino associated with the Dyck path. St001071The beta invariant of the graph. St001167The number of simple modules that appear as the top of an indecomposable non-projective modules that is reflexive in the corresponding Nakayama algebra. St001172The number of 1-rises at odd height of a Dyck path. St001176The size of a partition minus its first part. St001219Number of simple modules S in the corresponding Nakayama algebra such that the Auslander-Reiten sequence ending at S has the property that all modules in the exact sequence are reflexive. St001231The number of simple modules that are non-projective and non-injective with the property that they have projective dimension equal to one and that also the Auslander-Reiten translates of the module and the inverse Auslander-Reiten translate of the module have the same projective dimension. St001234The number of indecomposable three dimensional modules with projective dimension one. St001252Half the sum of the even parts of a partition. St001253The number of non-projective indecomposable reflexive modules in the corresponding Nakayama algebra. St001264The smallest index i such that the i-th simple module has projective dimension equal to the global dimension of the corresponding Nakayama algebra. St001266The largest vector space dimension of an indecomposable non-projective module that is reflexive in the corresponding Nakayama algebra. St001277The degeneracy of a graph. St001340The cardinality of a minimal non-edge isolating set of a graph. St001358The largest degree of a regular subgraph of a graph. St001395The number of strictly unfriendly partitions of a graph. St001512The minimum rank of a graph. St001578The minimal number of edges to add or remove to make a graph a line graph. St001587Half of the largest even part of an integer partition. St001647The number of edges that can be added without increasing the clique number. St001648The number of edges that can be added without increasing the chromatic number. St001692The number of vertices with higher degree than the average degree in a graph. St001712The number of natural descents of a standard Young tableau. St001742The difference of the maximal and the minimal degree in a graph. St001743The discrepancy of a graph. St001792The arboricity of a graph. St001794Half the number of sets of vertices in a graph which are dominating and non-blocking. St001798The difference of the number of edges in a graph and the number of edges in the complement of the Turán graph. St001961The sum of the greatest common divisors of all pairs of parts. St000003The number of standard Young tableaux of the partition. St000047The number of standard immaculate tableaux of a given shape. St000097The order of the largest clique of the graph. St000098The chromatic number of a graph. St000159The number of distinct parts of the integer partition. St000258The burning number of a graph. St000277The number of ribbon shaped standard tableaux. St000299The number of nonisomorphic vertex-induced subtrees. St000381The largest part of an integer composition. St000382The first part of an integer composition. St000388The number of orbits of vertices of a graph under automorphisms. St000452The number of distinct eigenvalues of a graph. St000453The number of distinct Laplacian eigenvalues of a graph. St000533The minimum of the number of parts and the size of the first part of an integer partition. St000636The hull number of a graph. 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. St000767The number of runs in an integer composition. St000775The multiplicity of the largest eigenvalue in a graph. St000778The metric dimension of a graph. St000808The number of up steps of the associated bargraph. St000810The sum of the entries in the column specified by the partition of the change of basis matrix from powersum symmetric functions to monomial symmetric functions. St000814The sum of the entries in the column specified by the partition of the change of basis matrix from elementary symmetric functions to Schur symmetric functions. St000822The Hadwiger number of the graph. St000899The maximal number of repetitions of an integer composition. St000900The minimal number of repetitions of a part in an integer composition. St000902 The minimal number of repetitions of an integer composition. St000904The maximal number of repetitions of an integer composition. St001029The size of the core of a graph. St001066The number of simple reflexive modules in the corresponding Nakayama algebra. St001093The detour number of a graph. St001108The 2-dynamic chromatic number of a graph. St001110The 3-dynamic chromatic number of a graph. St001236The dominant dimension of the corresponding Comp-Nakayama algebra. St001238The number of simple modules S such that the Auslander-Reiten translate of S is isomorphic to the Nakayama functor applied to the second syzygy of S. St001302The number of minimally dominating sets of vertices of a graph. St001304The number of maximally independent sets of vertices of a graph. St001330The hat guessing number of a graph. St001352The number of internal nodes in the modular decomposition of a graph. St001354The number of series nodes in the modular decomposition of a graph. St001366The maximal multiplicity of a degree of a vertex of a graph. St001368The number of vertices of maximal degree in a graph. St001463The number of distinct columns in the nullspace of a graph. St001483The number of simple module modules that appear in the socle of the regular module but have no nontrivial selfextensions with the regular module. St001494The Alon-Tarsi number of a graph. St001580The acyclic chromatic number of a graph. St001642The Prague dimension of a graph. St001654The monophonic hull number of a graph. St001655The general position number of a graph. St001656The monophonic position number of a graph. St001674The number of vertices of the largest induced star graph in the graph. St001740The number of graphs with the same symmetric edge polytope as the given graph. St001765The number of connected components of the friends and strangers graph. St001780The order of promotion on the set of standard tableaux of given shape. St001804The minimal height of the rectangular inner shape in a cylindrical tableau associated to a tableau. St001908The number of semistandard tableaux of distinct weight whose maximal entry is the length of the partition. St001917The order of toric promotion on the set of labellings of a graph. St001924The number of cells in an integer partition whose arm and leg length coincide. St001949The rigidity index of a graph. St000318The number of addable cells of the Ferrers diagram of an integer partition. St000469The distinguishing number of a graph. St001391The disjunction number of a graph. St001844The maximal degree of a generator of the invariant ring of the automorphism group of a graph. St000024The number of double up and double down steps of a Dyck path. St000052The number of valleys of a Dyck path not on the x-axis. St000057The Shynar inversion number of a standard tableau. St000090The variation of a composition. St000142The number of even parts of a partition. St000143The largest repeated part of a partition. St000147The largest part of an integer partition. St000150The floored half-sum of the multiplicities of a partition. St000169The cocharge of a standard tableau. St000175Degree of the polynomial counting the number of semistandard Young tableaux when stretching the shape. St000228The size of a partition. St000261The edge connectivity of a graph. St000262The vertex connectivity of a graph. St000293The number of inversions of a binary word. St000310The minimal degree of a vertex of a graph. St000313The number of degree 2 vertices of a graph. St000319The spin of an integer partition. St000320The dinv adjustment of an integer partition. St000330The (standard) major index of a standard tableau. St000336The leg major index of a standard tableau. St000369The dinv deficit of a Dyck path. St000378The diagonal inversion number of an integer partition. St000384The maximal part of the shifted composition of an integer partition. St000394The sum of the heights of the peaks of a Dyck path minus the number of peaks. St000454The largest eigenvalue of a graph if it is integral. St000459The hook length of the base cell of a partition. St000473The number of parts of a partition that are strictly bigger than the number of ones. St000483The number of times a permutation switches from increasing to decreasing or decreasing to increasing. St000663The number of right floats of a permutation. St000682The Grundy value of Welter's game on a binary word. St000688The global dimension minus the dominant dimension of the LNakayama algebra associated to a Dyck path. St000741The Colin de Verdière graph invariant. 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. St000784The maximum of the length and the largest part of the integer partition. St000835The minimal difference in size when partitioning the integer partition into two subpartitions. St000921The number of internal inversions of a binary word. St000931The number of occurrences of the pattern UUU in a Dyck path. St000970Number of peaks minus the dominant dimension of the corresponding LNakayama algebra. St000987The number of positive eigenvalues of the Laplacian matrix of the graph. St000992The alternating sum of the parts of an integer partition. St001021Sum of the differences between projective and codominant dimension of the non-projective indecomposable injective modules in the Nakayama algebra corresponding to the Dyck path. St001055The Grundy value for the game of removing cells of a row in an integer partition. St001087The number of occurrences of the vincular pattern |12-3 in a permutation. St001089Number of indecomposable projective non-injective modules minus the number of indecomposable projective non-injective modules with dominant dimension equal to the injective dimension in the corresponding Nakayama algebra. St001091The number of parts in an integer partition whose next smaller part has the same size. St001113Number of indecomposable projective non-injective modules with reflexive Auslander-Reiten sequences in the corresponding Nakayama algebra. St001119The length of a shortest maximal path in a graph. St001120The length of a longest path in a graph. St001137Number of simple modules that are 3-regular in the corresponding Nakayama algebra. St001163The number of simple modules with dominant dimension at least three in the corresponding Nakayama algebra. St001164Number of indecomposable injective modules whose socle has projective dimension at most g-1 (g the global dimension) minus the number of indecomposable projective-injective modules. St001189The number of simple modules with dominant and codominant dimension equal to zero in the Nakayama algebra corresponding to the Dyck path. St001229The vector space dimension of the first extension group between the Jacobson radical J and J^2. St001233The number of indecomposable 2-dimensional modules with projective dimension one. St001251The number of parts of a partition that are not congruent 1 modulo 3. St001265The maximal i such that the i-th simple module has projective dimension equal to the global dimension in the corresponding Nakayama algebra. St001280The number of parts of an integer partition that are at least two. St001314The number of tilting modules of arbitrary projective dimension that have no simple modules as a direct summand in the corresponding Nakayama algebra. St001320The minimal number of occurrences of the path-pattern in a linear ordering of the vertices of the graph. St001345The Hamming dimension of a graph. St001355Number of non-empty prefixes of a binary word that contain equally many 0's and 1's. St001357The maximal degree of a regular spanning subgraph of a graph. St001435The number of missing boxes in the first row. St001436The index of a given binary word in the lex-order among all its cyclic shifts. St001438The number of missing boxes of a skew partition. St001584The area statistic between a Dyck path and its bounce path. St001657The number of twos in an integer partition. St001695The natural comajor index of a standard Young tableau. St001697The shifted natural comajor index of a standard Young tableau. St001699The major index of a standard tableau minus the weighted size of its shape. St001702The absolute value of the determinant of the adjacency matrix of a graph. St001744The number of occurrences of the arrow pattern 1-2 with an arrow from 1 to 2 in a permutation. St001777The number of weak descents in an integer composition. St001810The number of fixed points of a permutation smaller than its largest moved point. St001869The maximum cut size of a graph. St001912The length of the preperiod in Bulgarian solitaire corresponding to an integer partition. St001918The degree of the cyclic sieving polynomial corresponding to an integer partition. St000013The height of a Dyck path. St000025The number of initial rises of a Dyck path. St000026The position of the first return of a Dyck path. St000063The number of linear extensions of a certain poset defined for an integer partition. St000075The orbit size of a standard tableau under promotion. St000087The number of induced subgraphs. St000093The cardinality of a maximal independent set of vertices of a graph. St000108The number of partitions contained in the given partition. St000160The multiplicity of the smallest part of a partition. St000182The number of permutations whose cycle type is the given integer partition. St000208Number of integral Gelfand-Tsetlin polytopes with prescribed top row and integer partition weight. St000271The chromatic index of a graph. St000278The size of the preimage of the map 'to partition' from Integer compositions to Integer partitions. St000286The number of connected components of the complement of a graph. St000321The number of integer partitions of n that are dominated by an integer partition. St000326The position of the first one in a binary word after appending a 1 at the end. St000335The difference of lower and upper interactions. St000345The number of refinements of a partition. St000346The number of coarsenings of a partition. St000363The number of minimal vertex covers of a graph. St000383The last part of an integer composition. St000443The number of long tunnels of a Dyck path. St000532The total number of rook placements on a Ferrers board. St000553The number of blocks of a graph. St000626The minimal period of a binary word. St000657The smallest part of an integer composition. St000722The number of different neighbourhoods in a graph. St000738The first entry in the last row of a standard tableau. St000786The maximal number of occurrences of a colour in a proper colouring of a graph. St000820The number of compositions obtained by rotating the composition. St000876The number of factors in the Catalan decomposition of a binary word. St000926The clique-coclique number of a graph. St000935The number of ordered refinements of an integer partition. St001007Number of simple modules with projective dimension 1 in the Nakayama algebra corresponding to the Dyck path. St001014Number of indecomposable injective modules with codominant dimension equal to the dominant dimension of the Nakayama algebra corresponding to the Dyck path. St001015Number of indecomposable injective modules with codominant dimension equal to one in the Nakayama algebra corresponding to the Dyck path. St001016Number of indecomposable injective modules with codominant dimension at most 1 in the Nakayama algebra corresponding to the Dyck path. St001027Number of simple modules with projective dimension equal to injective dimension in the Nakayama algebra corresponding to the Dyck path. St001088Number of indecomposable projective non-injective modules with dominant dimension equal to the injective dimension in the corresponding Nakayama algebra. St001184Number of indecomposable injective modules with grade at least 1 in the corresponding Nakayama algebra. St001187The number of simple modules with grade at least one in the corresponding Nakayama 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. St001224Let X be the direct sum of all simple modules of the corresponding Nakayama algebra. St001235The global dimension of the corresponding Comp-Nakayama algebra. St001241The number of non-zero radicals of the indecomposable projective modules that have injective dimension and projective dimension at most one. St001282The number of graphs with the same chromatic polynomial. St001286The annihilation number of a graph. St001297The number of indecomposable non-injective projective modules minus the number of indecomposable non-injective projective modules that have reflexive Auslander-Reiten sequences in the corresponding Nakayama algebra. St001313The number of Dyck paths above the lattice path given by a binary word. St001316The domatic number of a graph. St001337The upper domination number of a graph. St001338The upper irredundance number of a graph. St001342The number of vertices in the center of a graph. St001387Number of standard Young tableaux of the skew shape tracing the border of the given partition. St001389The number of partitions of the same length below the given integer partition. St001400The total number of Littlewood-Richardson tableaux of given shape. St001514The dimension of the top of the Auslander-Reiten translate of the regular modules as a bimodule. St001515The vector space dimension of the socle of the first syzygy module of the regular module (as a bimodule). St001595The number of standard Young tableaux of the skew partition. St001645The pebbling number of a connected graph. St001707The length of a longest path in a graph such that the remaining vertices can be partitioned into two sets of the same size without edges between them. St001716The 1-improper chromatic number of a graph. St001725The harmonious chromatic number of a graph. St001746The coalition number of a graph. St001786The number of total orderings of the north steps of a Dyck path such that steps after the k-th east step are not among the first k positions in the order. St001809The index of the step at the first peak of maximal height in a Dyck path. St001814The number of partitions interlacing the given 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. St001929The number of meanders with top half given by the noncrossing matching corresponding to the Dyck path. 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. St000300The number of independent sets of vertices of a graph. St000301The number of facets of the stable set polytope of a graph. St000312The number of leaves in a graph. St000439The position of the first down step of a Dyck path. St001180Number of indecomposable injective modules with projective dimension at most 1. St001211The number of simple modules in the corresponding Nakayama algebra that have vanishing second Ext-group with the regular module. St001226The number of integers i such that the radical of the i-th indecomposable projective module has vanishing first extension group with the Jacobson radical J in the corresponding Nakayama algebra. St001315The dissociation number of a graph. St001492The number of simple modules that do not appear in the socle of the regular module or have no nontrivial selfextensions with the regular module in the corresponding Nakayama algebra. St001504The sum of all indegrees of vertices with indegree at least two in the resolution quiver of a Nakayama algebra corresponding to the Dyck path. St001526The Loewy length of the Auslander-Reiten translate of the regular module as a bimodule of the Nakayama algebra corresponding to the Dyck path. St001166Number of indecomposable projective non-injective modules with dominant dimension equal to the global dimension plus the number of indecomposable projective injective modules in the corresponding Nakayama algebra. St001237The number of simple modules with injective dimension at most one or dominant dimension at least one. St000938The number of zeros of the symmetric group character corresponding to the partition. St000260The radius of a connected graph. St000940The number of characters of the symmetric group whose value on the partition is zero. St001124The multiplicity of the standard representation in the Kronecker square corresponding to a partition. St001845The number of join irreducibles minus the rank of a lattice. St001499The number of indecomposable projective-injective modules of a magnitude 1 Nakayama algebra. St001624The breadth of a lattice. St000376The bounce deficit of a Dyck path. St000691The number of changes of a binary word. St001629The coefficient of the integer composition in the quasisymmetric expansion of the relabelling action of the symmetric group on cycles. St000524The number of posets with the same order polynomial. St000525The number of posets with the same zeta polynomial. St000526The number of posets with combinatorially isomorphic order polytopes. St000983The length of the longest alternating subword. St000988The orbit size of a permutation under Foata's bijection. St001714The number of subpartitions of an integer partition that do not dominate the conjugate subpartition. St000282The size of the preimage of the map 'to poset' from Ordered trees to Posets. St000506The number of standard desarrangement tableaux of shape equal to the given partition. St000671The maximin edge-connectivity for choosing a subgraph. St000944The 3-degree of an integer partition. St001440The number of standard Young tableaux whose major index is congruent one modulo the size of a given integer partition. St001574The minimal number of edges to add or remove to make a graph regular. St001576The minimal number of edges to add or remove to make a graph vertex transitive. St001646The number of edges that can be added without increasing the maximal degree of a graph. St000259The diameter of a connected graph. St000274The number of perfect matchings of a graph. St000512The number of invariant subsets of size 3 when acting with a permutation of given cycle type. St000620The number of standard tableaux of shape equal to the given partition such that the minimal cyclic descent is odd. St000658The number of rises of length 2 of a Dyck path. St000661The number of rises of length 3 of a Dyck path. St000680The Grundy value for Hackendot on posets. St000699The toughness times the least common multiple of 1,. St000928The sum of the coefficients of the character polynomial of an integer partition. St000934The 2-degree of an integer partition. St001025Number of simple modules with projective dimension 4 in the Nakayama algebra corresponding to the Dyck path. St001056The Grundy value for the game of deleting vertices of a graph until it has no edges. St001092The number of distinct even parts of a partition. St001097The coefficient of the monomial symmetric function indexed by the partition in the formal group law for linear orders. St001141The number of occurrences of hills of size 3 in a Dyck path. St001175The size of a partition minus the hook length of the base cell. St001263The index of the maximal parabolic seaweed algebra associated with the composition. St001281The normalized isoperimetric number of a graph. St001484The number of singletons of an integer partition. St001586The number of odd parts smaller than the largest even part in an integer partition. St001588The number of distinct odd parts smaller than the largest even part in an integer partition. St001673The degree of asymmetry of an integer composition. St001797The number of overfull subgraphs of a graph. St001871The number of triconnected components of a graph. St000273The domination number of a graph. St000544The cop number of a graph. St001829The common independence number of a graph. St000148The number of odd parts of a partition. St000442The maximal area to the right of an up step of a Dyck path. St000475The number of parts equal to 1 in a partition. St000549The number of odd partial sums of an integer partition. St000566The number of ways to select a row of a Ferrers shape and two cells in this row. St000674The number of hills of a Dyck path. St000693The modular (standard) major index of a standard tableau. St000761The number of ascents in an integer composition. St000790The number of pairs of centered tunnels, one strictly containing the other, of a Dyck path. St000874The position of the last double rise in a Dyck path. St000929The constant term of the character polynomial of an integer partition. St000941The number of characters of the symmetric group whose value on the partition is even. St000954Number of times the corresponding LNakayama algebra has

$Ext^i(D(A),A)=0$ for

$i>0$ . St000966Number of peaks minus the global dimension of the corresponding LNakayama algebra. St001022Number of simple modules with projective dimension 3 in the Nakayama algebra corresponding to the Dyck path. St001036The number of inner corners of the parallelogram polyomino associated with the Dyck path. St001037The number of inner corners of the upper path of the parallelogram polyomino associated with the Dyck path. St001067The number of simple modules of dominant dimension at least two in the corresponding Nakayama algebra. St001125The number of simple modules that satisfy the 2-regular condition in the corresponding Nakayama algebra. St001139The number of occurrences of hills of size 2 in a Dyck path. St001181Number of indecomposable injective modules with grade at least 3 in the corresponding Nakayama algebra. St001186Number of simple modules with grade at least 3 in the corresponding Nakayama algebra. St001216The number of indecomposable injective modules in the corresponding Nakayama algebra that have non-vanishing second Ext-group with the regular module. St001222Number of simple modules in the corresponding LNakayama algebra that have a unique 2-extension with the regular module. St001223Number of indecomposable projective non-injective modules P such that the modules X and Y in a an Auslander-Reiten sequence ending at P are torsionless. St001230The number of simple modules with injective dimension equal to the dominant dimension equal to one and the dual property. St001274The number of indecomposable injective modules with projective dimension equal to two. St001276The number of 2-regular indecomposable modules in the corresponding Nakayama algebra. St001392The largest nonnegative integer which is not a part and is smaller than the largest part of the partition. St001480The number of simple summands of the module J^2/J^3. St001541The Gini index of an integer partition. St001730The number of times the path corresponding to a binary word crosses the base line. St001827The number of two-component spanning forests of a graph. St001931The weak major index of an integer composition regarded as a word. St001932The number of pairs of singleton blocks in the noncrossing set partition corresponding to a Dyck path, that can be merged to create another noncrossing set partition. St001232The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2. St000422The energy of a graph, if it is integral. St001001The number of indecomposable modules with projective and injective dimension equal to the global dimension of the Nakayama algebra corresponding to the Dyck path. St001193The dimension of

$Ext_A^1(A/AeA,A)$ in the corresponding Nakayama algebra

$A$ such that

$eA$ is a minimal faithful projective-injective module. St001217The projective dimension of the indecomposable injective module I[n-2] in the corresponding Nakayama algebra with simples enumerated from 0 to n-1. St001305The number of induced cycles on four vertices in a graph. St001324The minimal number of occurrences of the chordal-pattern in a linear ordering of the vertices of the graph. St001326The minimal number of occurrences of the interval-pattern in a linear ordering of the vertices of the graph. St001327The minimal number of occurrences of the split-pattern in a linear ordering of the vertices of the graph. St001575The minimal number of edges to add or remove to make a graph edge transitive. St001651The Frankl number of a lattice. St000777The number of distinct eigenvalues of the distance Laplacian of a connected graph. St000302The determinant of the distance matrix of a connected graph. St000466The Gutman (or modified Schultz) index of a connected graph. St000467The hyper-Wiener index of a connected graph. St000689The maximal n such that the minimal generator-cogenerator module in the LNakayama algebra of a Dyck path is n-rigid. St001008Number of indecomposable injective modules with projective dimension 1 in the Nakayama algebra corresponding to the Dyck path. St001010Number of indecomposable injective modules with projective dimension g-1 when g is the global dimension of the Nakayama algebra corresponding to the Dyck path. St001017Number of indecomposable injective modules with projective dimension equal to the codominant dimension in the Nakayama algebra corresponding to the Dyck path. St001140Number of indecomposable modules with projective and injective dimension at least two in the corresponding Nakayama algebra. St001204Call 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. St001221The number of simple modules in the corresponding LNakayama algebra that have 2 dimensional second Extension group with the regular module. St001292The injective dimension of the tensor product of two copies of the dual of the Nakayama algebra associated to a Dyck path. St000379The number of Hamiltonian cycles in a graph. St000455The second largest eigenvalue of a graph if it is integral. St000621The number of standard tableaux of shape equal to the given partition such that the minimal cyclic descent is even. St000936The number of even values of the symmetric group character corresponding to the partition. St001396Number of triples of incomparable elements in a finite poset. St001592The maximal number of simple paths between any two different vertices of a graph. St001964The interval resolution global dimension of a poset. St001322The size of a minimal independent dominating set in a graph. St001532The leading coefficient of the Poincare polynomial of the poset cone. St000281The size of the preimage of the map 'to poset' from Binary trees to Posets. St001101The coefficient times the product of the factorials of the parts of the monomial symmetric function indexed by the partition in the formal group law for increasing trees. St001668The number of points of the poset minus the width of the poset. St001123The multiplicity of the dual of the standard representation in the Kronecker square corresponding to a partition. St000478Another weight of a partition according to Alladi. St000683The number of points below the Dyck path such that the diagonal to the north-east hits the path between two down steps, and the diagonal to the north-west hits the path between two up steps. St001339The irredundance number of a graph. St001363The Euler characteristic of a graph according to Knill. St001626The number of maximal proper sublattices of a lattice. St000791The number of pairs of left tunnels, one strictly containing the other, of a Dyck path. St000932The number of occurrences of the pattern UDU in a Dyck path. St001035The convexity degree of the parallelogram polyomino associated with the Dyck path. St001498The normalised height of a Nakayama algebra with magnitude 1. St001502The global dimension minus the dominant dimension of magnitude 1 Nakayama algebras. St001207The Lowey length of the algebra

$A/T$ when

$T$ is the 1-tilting module corresponding to the permutation in the Auslander algebra of

$K[x]/(x^n)$ . 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

$eA$ . St001431Half of the Loewy length minus one of a modified stable Auslander algebra of the Nakayama algebra corresponding to the Dyck path. St001462The number of factors of a standard tableaux under concatenation. St001553The number of indecomposable summands of the square of the Jacobson radical as a bimodule in the Nakayama algebra corresponding to the Dyck path. St001570The minimal number of edges to add to make a graph Hamiltonian. St001604The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on polygons. St001122The multiplicity of the sign representation in the Kronecker square corresponding to a partition. St001525The number of symmetric hooks on the diagonal of a partition. St001593This is the number of standard Young tableaux of the given shifted shape. St001601The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on trees. St001606The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on set partitions. St001939The number of parts that are equal to their multiplicity in the integer partition. St001940The number of distinct parts that are equal to their multiplicity in the integer partition. St001195The global dimension of the algebra

$A/AfA$ of the corresponding Nakayama algebra

$A$ with minimal left faithful projective-injective module

$Af$ . St000205Number of non-integral Gelfand-Tsetlin polytopes with prescribed top row and partition weight. St000206Number of non-integral Gelfand-Tsetlin polytopes with prescribed top row and integer composition weight. St001095The number of non-isomorphic posets with precisely one further covering relation. St001178Twelve times the variance of the major index among all standard Young tableaux of a partition. St001248Sum of the even parts of a partition. St001279The sum of the parts of an integer partition that are at least two. St001384The number of boxes in the diagram of a partition that do not lie in the largest triangle it contains. St001767The largest minimal number of arrows pointing to a cell in the Ferrers diagram in any assignment. St000005The bounce statistic of a Dyck path. St000006The dinv of a Dyck path. St000010The length of the partition. St000012The area of a Dyck path. St000016The number of attacking pairs of a standard tableau. St000017The number of inversions of a standard tableau. St000053The number of valleys of the Dyck path. St000117The number of centered tunnels of a Dyck path. St000120The number of left tunnels of a Dyck path. St000149The number of cells of the partition whose leg is zero and arm is odd. St000183The side length of the Durfee square of an integer partition. St000256The number of parts from which one can substract 2 and still get an integer partition. St000257The number of distinct parts of a partition that occur at least twice. St000290The major index of a binary word. St000291The number of descents of a binary word. St000292The number of ascents of a binary word. St000295The length of the border of a binary word. St000296The length of the symmetric border of a binary word. St000306The bounce count of a Dyck path. St000329The number of evenly positioned ascents of the Dyck path, with the initial position equal to 1. St000331The number of upper interactions of a Dyck path. St000340The number of non-final maximal constant sub-paths of length greater than one. St000347The inversion sum of a binary word. St000348The non-inversion sum of a binary word. St000480The number of lower covers of a partition in dominance order. St000481The number of upper covers of a partition in dominance order. St000513The number of invariant subsets of size 2 when acting with a permutation of given cycle type. St000519The largest length of a factor maximising the subword complexity. St000547The number of even non-empty partial sums of an integer partition. St000548The number of different non-empty partial sums of an integer partition. St000628The balance of a binary word. St000629The defect of a binary word. St000659The number of rises of length at least 2 of a Dyck path. St000687The dimension of

$Hom(I,P)$ for the LNakayama algebra of a Dyck path. St000714The number of semistandard Young tableau of given shape, with entries at most 2. St000783The side length of the largest staircase partition fitting into a partition. St000867The sum of the hook lengths in the first row of an integer partition. St000875The semilength of the longest Dyck word in the Catalan factorisation of a binary word. St000885The number of critical steps in the Catalan decomposition of a binary word. St000897The number of different multiplicities of parts of an integer partition. St000980The number of boxes weakly below the path and above the diagonal that lie below at least two peaks. St000995The largest even part of an integer partition. St001011Number of simple modules of projective dimension 2 in the Nakayama algebra corresponding to the Dyck path. St001031The height of the bicoloured Motzkin path associated with the Dyck path. St001107The number of times one can erase the first up and the last down step in a Dyck path and still remain a Dyck path. St001126Number of simple module that are 1-regular in the corresponding Nakayama algebra. St001127The sum of the squares of the parts of a partition. St001142The projective dimension of the socle of the regular module as a bimodule in the Nakayama algebra corresponding to the Dyck path. St001161The major index north count of a Dyck path. St001169Number of simple modules with projective dimension at least two in the corresponding Nakayama algebra. St001177Twice the mean value of the major index among all standard Young tableaux of a partition. St001185The number of indecomposable injective modules of grade at least 2 in the corresponding Nakayama algebra. St001188The number of simple modules

$S$ with grade

$\inf \{ i \geq 0 | Ext^i(S,A) \neq 0 \}$ at least two in the Nakayama algebra

$A$ corresponding to the Dyck path. St001192The maximal dimension of

$Ext_A^2(S,A)$ for a simple module

$S$ over the corresponding Nakayama algebra

$A$ . St001194The injective dimension of

$A/AfA$ in the corresponding Nakayama algebra

$A$ when

$Af$ is the minimal faithful projective-injective left

$A$ -module St001197The global dimension of

$eAe$ for the corresponding Nakayama algebra

$A$ with minimal faithful projective-injective module

$eA$ . St001205The number of non-simple indecomposable projective-injective modules of the algebra

$eAe$ in the corresponding Nakayama algebra

$A$ with minimal faithful projective-injective module

$eA$ . St001212The number of simple modules in the corresponding Nakayama algebra that have non-zero second Ext-group with the regular module. St001215Let X be the direct sum of all simple modules of the corresponding Nakayama algebra. St001225The vector space dimension of the first extension group between J and itself when J is the Jacobson radical of the corresponding Nakayama algebra. St001227The vector space dimension of the first extension group between the socle of the regular module and the Jacobson radical of the corresponding Nakayama algebra. St001244The number of simple modules of projective dimension one that are not 1-regular for the Nakayama algebra associated to a Dyck path. St001273The projective dimension of the first term in an injective coresolution of the regular module. St001278The number of indecomposable modules that are fixed by

$\tau \Omega^1$ composed with its inverse in the corresponding Nakayama algebra. St001294The maximal torsionfree index of a simple non-projective module in the corresponding Nakayama algebra. St001295Gives the vector space dimension of the homomorphism space between J^2 and J^2. St001296The maximal torsionfree index of an indecomposable non-projective module in the corresponding Nakayama algebra. St001371The length of the longest Yamanouchi prefix of a binary word. St001382The number of boxes in the diagram of a partition that do not lie in its Durfee square. St001413Half the length of the longest even length palindromic prefix of a binary word. St001414Half the length of the longest odd length palindromic prefix of a binary word. St001418Half of the global dimension of the stable Auslander algebra of the Nakayama algebra corresponding to the Dyck path. St001420Half the length of a longest factor which is its own reverse-complement of a binary word. St001421Half the length of a longest factor which is its own reverse-complement and begins with a one of a binary word. St001423The number of distinct cubes in a binary word. St001424The number of distinct squares in a binary word. St001485The modular major index of a binary word. St001506Half the projective dimension of the unique simple module with even projective dimension in a magnitude 1 Nakayama algebra. St001507The sum of projective dimension of simple modules with even projective dimension divided by 2 in the LNakayama algebra corresponding to Dyck paths. St001508The degree of the standard monomial associated to a Dyck path relative to the diagonal boundary. St001509The degree of the standard monomial associated to a Dyck path relative to the trivial lower boundary. St001524The degree of symmetry of a binary word. St001594The number of indecomposable projective modules in the Nakayama algebra corresponding to the Dyck path such that the UC-condition is satisfied. St001596The number of two-by-two squares inside a skew partition. St001698The comajor index of a standard tableau minus the weighted size of its shape. St001721The degree of a binary word. St001803The maximal overlap of the cylindrical tableau associated with a tableau. St001873For a Nakayama algebra corresponding to a Dyck path, we define the matrix C with entries the Hom-spaces between

$e_i J$ and

$e_j J$ (the radical of the indecomposable projective modules). St001910The height of the middle non-run of a Dyck path. St001955The number of natural descents for set-valued two row standard Young tableaux. St001491The number of indecomposable projective-injective modules in the algebra corresponding to a subset. St001722The number of minimal chains with small intervals between a binary word and the top element. St000567The sum of the products of all pairs of parts. St001098The coefficient times the product of the factorials of the parts of the monomial symmetric function indexed by the partition in the formal group law for vertex labelled trees. St001099The coefficient times the product of the factorials of the parts of the monomial symmetric function indexed by the partition in the formal group law for leaf labelled binary trees. St001100The coefficient times the product of the factorials of the parts of the monomial symmetric function indexed by the partition in the formal group law for leaf labelled trees. St000046The largest eigenvalue of the random to random operator acting on the simple module corresponding to the given partition. St000137The Grundy value of an integer partition. St001383The BG-rank of an integer partition. St001442The number of standard Young tableaux whose major index is divisible by the size of a given integer partition. St001600The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on simple graphs. St001628The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on simple connected graphs. St001876The number of 2-regular simple modules in the incidence algebra of the lattice. St000145The Dyson rank of a partition. St001247The number of parts of a partition that are not congruent 2 modulo 3. St001249Sum of the odd parts of a partition. St001283The number of finite solvable groups that are realised by the given partition over the complex numbers. St001284The number of finite groups that are realised by the given partition over the complex numbers. St001561The value of the elementary symmetric function evaluated at 1. St001785The number of ways to obtain a partition as the multiset of antidiagonal lengths of the Ferrers diagram of a partition. St001913The number of preimages of an integer partition in Bulgarian solitaire. St001118The acyclic chromatic index of a graph. St000207Number of integral Gelfand-Tsetlin polytopes with prescribed top row and integer composition weight. St000460The hook length of the last cell along the main diagonal of an integer partition. St000667The greatest common divisor of the parts of the partition. St000713The dimension of the irreducible representation of Sp(4) labelled by an integer partition. St000755The number of real roots of the characteristic polynomial of a linear recurrence associated with an integer partition. St000870The product of the hook lengths of the diagonal cells in an integer partition. 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. St001527The cyclic permutation representation number of an integer partition. St001571The Cartan determinant of the integer partition. St001603The number of colourings of a polygon such that the multiplicities of a colour are given by a partition. St001605The number of colourings of a cycle such that the multiplicities of colours are given by a partition. St001607The number of coloured graphs 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. St001914The size of the orbit of an integer partition in Bulgarian solitaire. St000456The monochromatic index of a connected graph. St001632The number of indecomposable injective modules

$I$ with

$dim Ext^1(I,A)=1$ for the incidence algebra A of a poset. St000284The Plancherel distribution on integer partitions. St000510The number of invariant oriented cycles when acting with a permutation of given cycle type. St000668The least common multiple of the parts of the partition. St000681The Grundy value of Chomp on Ferrers diagrams. St000698The number of 2-rim hooks removed from an integer partition to obtain its associated 2-core. St000704The number of semistandard tableaux on a given integer partition with minimal maximal entry. St000707The product of the factorials of the parts. St000708The product of the parts of an integer partition. St000770The major index of an integer partition when read from bottom to top. St000815The number of semistandard Young tableaux of partition weight of given shape. St000901The cube of the number of standard Young tableaux with shape given by the partition. St000933The number of multipartitions of sizes given by an integer partition. St001128The exponens consonantiae of a partition. St001846The number of elements which do not have a complement in the lattice. St001877Number of indecomposable injective modules with projective dimension 2. St001719The number of shortest chains of small intervals from the bottom to the top in a lattice. St001820The size of the image of the pop stack sorting operator. St001720The minimal length of a chain of small intervals in a lattice. St000419The number of Dyck paths that are weakly above the Dyck path, except for the path itself. St000476The sum of the semi-lengths of tunnels before a valley of a Dyck path. St000706The product of the factorials of the multiplicities of an integer partition. St000735The last entry on the main diagonal of a standard tableau. St000744The length of the path to the largest entry in a standard Young tableau. St000939The number of characters of the symmetric group whose value on the partition is positive. St000946The sum of the skew hook positions in a Dyck path. St000947The major index east count of a Dyck path. St000976The sum of the positions of double up-steps of a Dyck path. St000984The number of boxes below precisely one peak. St000993The multiplicity of the largest part of an integer partition. St001032The number of horizontal steps in the bicoloured Motzkin path associated with the Dyck path. St001038The minimal height of a column in the parallelogram polyomino associated with the Dyck path. St001039The maximal height of a column in the parallelogram polyomino associated with a Dyck path. St001568The smallest positive integer that does not appear twice in the partition. St000618The number of self-evacuating tableaux of given shape. St000781The number of proper colouring schemes of a Ferrers diagram. St001250The number of parts of a partition that are not congruent 0 modulo 3. St001364The number of permutations whose cube equals a fixed permutation of given cycle type. St001432The order dimension of the partition. St001599The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on rooted trees. St001602The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on endofunctions. 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. St001627The number of coloured connected graphs such that the multiplicities of colours are given by a partition. St001763The Hurwitz number of an integer partition. St001901The largest multiplicity of an irreducible representation contained in the higher Lie character for an integer partition. St001934The number of monotone factorisations of genus zero of a permutation of given cycle type. St001938The number of transitive monotone factorizations of genus zero of a permutation of given cycle type. St000782The indicator function of whether a given perfect matching is an L & P matching.