St000911The number of maximal antichains of maximal size in a poset. St000914The sum of the values of the Möbius function of a poset. St001301The first Betti number of the order complex associated with the poset. St001534The alternating sum of the coefficients of the Poincare polynomial of the poset cone. St001634The trace of the Coxeter matrix of the incidence algebra of a poset. St000097The order of the largest clique of the graph. St000098The chromatic number of a graph. St000183The side length of the Durfee square of an integer partition. St000311The number of vertices of odd degree in a graph. St000845The maximal number of elements covered by an element in a poset. St001029The size of the core of a graph. St001109The number of proper colourings of a graph with as few colours as possible. St001111The weak 2-dynamic chromatic number of a graph. St001261The Castelnuovo-Mumford regularity of a graph. St001316The domatic number of a graph. St001352The number of internal nodes in the modular decomposition of a graph. St001368The number of vertices of maximal degree in a graph. St001494The Alon-Tarsi number of a graph. St001618The cardinality of the Frattini sublattice of a lattice. St001624The breadth of a lattice. St001630The global dimension of the incidence algebra of the lattice over the rational numbers. St001692The number of vertices with higher degree than the average degree in a graph. St001716The 1-improper chromatic number of a graph. St001878The projective dimension of the simple modules corresponding to the minimum of L in the incidence algebra of the lattice L. St001913The number of preimages of an integer partition in Bulgarian solitaire. St000068The number of minimal elements in a poset. St000160The multiplicity of the smallest part of a partition. St000261The edge connectivity of a graph. St000262The vertex connectivity of a graph. St000286The number of connected components of the complement of a graph. St000287The number of connected components of a graph. St000310The minimal degree of a vertex of a graph. St000363The number of minimal vertex covers of a graph. St000475The number of parts equal to 1 in a partition. St000535The rank-width of a graph. St000667The greatest common divisor of the parts of the partition. St000706The product of the factorials of the multiplicities of an integer partition. St000773The multiplicity of the largest Laplacian eigenvalue in a graph. St000775The multiplicity of the largest eigenvalue in a graph. St000785The number of distinct colouring schemes of a graph. St000897The number of different multiplicities of parts of an integer partition. St000993The multiplicity of the largest part of an integer partition. St001070The absolute value of the derivative of the chromatic polynomial of the graph at 1. St001071The beta invariant of the graph. St001108The 2-dynamic chromatic number of a graph. St001247The number of parts of a partition that are not congruent 2 modulo 3. St001282The number of graphs with the same chromatic polynomial. St001333The cardinality of a minimal edge-isolating set of a graph. St001393The induced matching number of a graph. St001395The number of strictly unfriendly partitions of a graph. St001496The number of graphs with the same Laplacian spectrum as the given graph. St001518The number of graphs with the same ordinary spectrum as the given graph. St001568The smallest positive integer that does not appear twice in the partition. St001613The binary logarithm of the size of the center of a lattice. St001657The number of twos in an integer partition. St001719The number of shortest chains of small intervals from the bottom to the top in a lattice. St001740The number of graphs with the same symmetric edge polytope as the given graph. St001743The discrepancy of a graph. St001774The degree of the minimal polynomial of the smallest eigenvalue of a graph. St001881The number of factors of a lattice as a Cartesian product of lattices. St001933The largest multiplicity of a part in an integer partition. 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. St000095The number of triangles of a graph. St000096The number of spanning trees of a graph. St000143The largest repeated part of a partition. St000150The floored half-sum of the multiplicities of a partition. St000257The number of distinct parts of a partition that occur at least twice. St000268The number of strongly connected orientations of a graph. St000274The number of perfect matchings of a graph. St000276The size of the preimage of the map 'to graph' from Ordered trees to Graphs. St000281The size of the preimage of the map 'to poset' from Binary trees to Posets. St000282The size of the preimage of the map 'to poset' from Ordered trees to Posets. St000283The size of the preimage of the map 'to graph' from Binary trees to Graphs. St000303The determinant of the product of the incidence matrix and its transpose of a graph divided by $4$. St000315The number of isolated vertices of a graph. St000322The skewness of a graph. St000323The minimal crossing number of a graph. St000344The number of strongly connected outdegree sequences of a graph. St000351The determinant of the adjacency matrix of a graph. St000368The Altshuler-Steinberg determinant of a graph. St000370The genus of a graph. St000379The number of Hamiltonian cycles in a graph. St000447The number of pairs of vertices of a graph with distance 3. St000449The number of pairs of vertices of a graph with distance 4. St000510The number of invariant oriented cycles when acting with a permutation of given cycle type. St000552The number of cut vertices of a graph. St000671The maximin edge-connectivity for choosing a subgraph. St000699The toughness times the least common multiple of 1,. St000929The constant term of the character polynomial of an integer partition. St000948The chromatic discriminant of a graph. St001069The coefficient of the monomial xy of the Tutte polynomial of the graph. St001073The number of nowhere zero 3-flows of a graph. St001091The number of parts in an integer partition whose next smaller part has the same size. St001119The length of a shortest maximal path in a graph. St001271The competition number of a graph. St001281The normalized isoperimetric number of a graph. 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. St001307The number of induced stars on four vertices in a graph. St001309The number of four-cliques in a graph. St001310The number of induced diamond graphs in a graph. St001323The independence gap of a graph. St001325The minimal number of occurrences of the comparability-pattern in a linear ordering of the vertices of the graph. St001328The minimal number of occurrences of the bipartite-pattern in a linear ordering of the vertices of the graph. St001329The minimal number of occurrences of the outerplanar pattern in a linear ordering of the vertices of the graph. St001334The minimal number of occurrences of the 3-colorable pattern in a linear ordering of the vertices of the graph. St001336The minimal number of vertices in a graph whose complement is triangle-free. St001341The number of edges in the center of a graph. St001357The maximal degree of a regular spanning subgraph of a graph. St001367The smallest number which does not occur as degree of a vertex in a graph. St001477The number of nowhere zero 5-flows of a graph. St001478The number of nowhere zero 4-flows of a graph. St001510The number of self-evacuating linear extensions of a finite poset. St001561The value of the elementary symmetric function evaluated at 1. St001572The minimal number of edges to remove to make a graph bipartite. St001573The minimal number of edges to remove to make a graph triangle-free. St001578The minimal number of edges to add or remove to make a graph a line graph. 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. St001690The length of a longest path in a graph such that after removing the paths edges, every vertex of the path has distance two from some other vertex of the path. St001702The absolute value of the determinant of the adjacency matrix of a graph. St001714The number of subpartitions of an integer partition that do not dominate the conjugate subpartition. St001783The number of odd automorphisms of a graph. St001785The number of ways to obtain a partition as the multiset of antidiagonal lengths of the Ferrers diagram of a partition. St001793The difference between the clique number and the chromatic number of a graph. St001794Half the number of sets of vertices in a graph which are dominating and non-blocking. St001795The binary logarithm of the evaluation of the Tutte polynomial of the graph at (x,y) equal to (-1,-1). St001796The absolute value of the quotient of the Tutte polynomial of the graph at (1,1) and (-1,-1). St001797The number of overfull subgraphs of a graph. St001845The number of join irreducibles minus the rank of a lattice. St001871The number of triconnected components of a graph. St000093The cardinality of a maximal independent set of vertices of a graph. St000159The number of distinct parts of the integer partition. St000244The cardinality of the automorphism group of a graph. St000258The burning number of a graph. St000259The diameter of a connected graph. St000273The domination number of a graph. St000299The number of nonisomorphic vertex-induced subtrees. St000312The number of leaves in a graph. St000318The number of addable cells of the Ferrers diagram of an integer partition. St000335The difference of lower and upper interactions. St000364The exponent of the automorphism group of a graph. St000378The diagonal inversion number of an integer partition. St000388The number of orbits of vertices of a graph under automorphisms. St000439The position of the first down step of a Dyck path. St000453The number of distinct Laplacian eigenvalues of a graph. St000469The distinguishing number of a graph. St000511The number of invariant subsets when acting with a permutation of given cycle type. St000533The minimum of the number of parts and the size of the first part of an integer partition. St000544The cop number of a graph. St000553The number of blocks of a graph. St000630The length of the shortest palindromic decomposition of a binary word. St000636The hull number of a graph. St000675The number of centered multitunnels of a Dyck path. St000745The index of the last row whose first entry is the row number in a standard Young tableau. St000758The length of the longest staircase fitting into an integer composition. St000759The smallest missing part in an integer partition. St000764The number of strong records in an integer composition. St000767The number of runs in an integer composition. St000774The maximal multiplicity of a Laplacian eigenvalue in a graph. St000783The side length of the largest staircase partition fitting into a partition. St000786The maximal number of occurrences of a colour in a proper colouring of a graph. St000822The Hadwiger number of the graph. St000876The number of factors in the Catalan decomposition of a binary word. St000903The number of different parts of an integer composition. St000916The packing number of a graph. St000917The open packing number of a graph. St000918The 2-limited packing number of a graph. St000951The dimension of $Ext^{1}(D(A),A)$ of the corresponding LNakayama algebra. St000955Number of times one has $Ext^i(D(A),A)>0$ for $i>0$ for the corresponding LNakayama algebra. St000995The largest even part of an integer partition. St001060The distinguishing index of a graph. St001088Number of indecomposable projective non-injective modules with dominant dimension equal to the injective dimension in the corresponding Nakayama algebra. St001093The detour number of a graph. St001184Number of indecomposable injective modules with grade at least 1 in the corresponding Nakayama algebra. 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 $eA$. 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. St001248Sum of the even parts of a partition. St001257The dominant dimension of the double dual of A/J when A is the corresponding Nakayama algebra with Jacobson radical J. St001322The size of a minimal independent dominating set in a graph. St001330The hat guessing number of a graph. St001337The upper domination number of a graph. St001338The upper irredundance number of a graph. St001339The irredundance number of a graph. St001358The largest degree of a regular subgraph of a graph. St001432The order dimension of the partition. St001459The number of zero columns in the nullspace of a graph. St001503The largest distance of a vertex to a vertex in a cycle in the resolution quiver of the corresponding Nakayama algebra. St001545The second Elser number of a connected graph. St001570The minimal number of edges to add to make a graph Hamiltonian. 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. St001732The number of peaks visible from the left. St001734The lettericity of a graph. St001792The arboricity of a graph. St001829The common independence number of a graph. St001844The maximal degree of a generator of the invariant ring of the automorphism group 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. St000003The number of standard Young tableaux of the partition. St000010The length of the partition. St000025The number of initial rises of a Dyck path. St000026The position of the first return of a Dyck path. St000047The number of standard immaculate tableaux of a given shape. St000048The multinomial of the parts of a partition. St000049The number of set partitions whose sorted block sizes correspond to the partition. St000088The row sums of the character table of the symmetric group. St000137The Grundy value of an integer partition. St000142The number of even parts of a partition. St000146The Andrews-Garvan crank of a partition. St000148The number of odd parts of a partition. St000181The number of connected components of the Hasse diagram for the poset. St000212The number of standard Young tableaux for an integer partition such that no two consecutive entries appear in the same row. St000256The number of parts from which one can substract 2 and still get an integer partition. St000260The radius of a connected graph. St000264The girth of a graph, which is not a tree. St000266The number of spanning subgraphs of a graph with the same connected components. St000267The number of maximal spanning forests contained in a graph. St000272The treewidth of a graph. St000275Number of permutations whose sorted list of non zero multiplicities of the Lehmer code is the given partition. St000278The size of the preimage of the map 'to partition' from Integer compositions to Integer partitions. St000284The Plancherel distribution on integer partitions. St000297The number of leading ones in a binary word. St000326The position of the first one in a binary word after appending a 1 at the end. St000346The number of coarsenings of a partition. St000382The first part of an integer composition. St000383The last part of an integer composition. St000392The length of the longest run of ones in a binary word. St000450The number of edges minus the number of vertices plus 2 of a graph. St000452The number of distinct eigenvalues of a graph. St000456The monochromatic index of a connected graph. St000473The number of parts of a partition that are strictly bigger than the number of ones. St000480The number of lower covers of a partition in dominance order. St000481The number of upper covers of a partition in dominance order. St000482The (zero)-forcing number of a graph. St000517The Kreweras number of an integer partition. St000531The leading coefficient of the rook polynomial of an integer partition. St000536The pathwidth of a graph. St000537The cutwidth of a graph. St000548The number of different non-empty partial sums of an integer partition. St000617The number of global maxima of a Dyck path. St000618The number of self-evacuating tableaux of given shape. St000628The balance of a binary word. St000655The length of the minimal rise of a Dyck path. St000657The smallest part of an integer composition. St000659The number of rises of length at least 2 of a Dyck path. St000685The dominant dimension of the LNakayama algebra associated to a Dyck path. St000704The number of semistandard tableaux on a given integer partition with minimal maximal entry. St000723The maximal cardinality of a set of vertices with the same neighbourhood in a graph. St000733The row containing the largest entry of a standard tableau. St000741The Colin de Verdière graph invariant. St000755The number of real roots of the characteristic polynomial of a linear recurrence associated with an integer partition. St000760The length of the longest strictly decreasing subsequence of parts of an integer composition. St000761The number of ascents in an integer composition. St000771The largest multiplicity of a distance Laplacian eigenvalue in a connected graph. St000772The multiplicity of the largest distance Laplacian eigenvalue in a connected graph. St000776The maximal multiplicity of an eigenvalue in a graph. St000778The metric dimension of a graph. St000781The number of proper colouring schemes of a Ferrers diagram. St000805The number of peaks 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. St000813The number of zero-one matrices with weakly decreasing column sums and row sums given by the partition. 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. St000816The number of standard composition tableaux of the composition. St000835The minimal difference in size when partitioning the integer partition into two subpartitions. St000900The minimal number of repetitions of a part in an integer composition. St000901The cube of the number of standard Young tableaux with shape given by the partition. St000902 The minimal number of repetitions of an integer composition. St000913The number of ways to refine the partition into singletons. St000968We make a CNakayama algebra out of the LNakayama algebra (corresponding to the Dyck path) $[c_0,c_1,...,c_{n−1}]$ by adding $c_0$ to $c_{n−1}$. St000985The number of positive eigenvalues of the adjacency matrix of the graph. St000992The alternating sum of the parts of an integer partition. St001006Number of simple modules with projective dimension equal to the global dimension of 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. St001011Number of simple modules of projective dimension 2 in the Nakayama algebra corresponding to the Dyck path. St001013Number of indecomposable injective modules with codominant dimension equal to the global dimension in 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. St001022Number of simple modules with projective dimension 3 in the Nakayama algebra corresponding to the Dyck path. St001031The height of the bicoloured Motzkin path associated with the Dyck path. St001035The convexity degree of the parallelogram polyomino associated with the Dyck path. St001038The minimal height of a column in the parallelogram polyomino associated with the Dyck path. St001055The Grundy value for the game of removing cells of a row in an integer partition. St001092The number of distinct even parts of a partition. St001103The number of words with multiplicities of the letters given by the partition, avoiding the consecutive pattern 123. St001112The 3-weak dynamic number of a graph. St001121The multiplicity of the irreducible representation indexed by the partition in the Kronecker square corresponding to the partition. St001122The multiplicity of the sign representation in the Kronecker square corresponding to a partition. St001124The multiplicity of the standard representation in the Kronecker square corresponding to a partition. St001126Number of simple module that are 1-regular in the corresponding Nakayama algebra. St001128The exponens consonantiae of a partition. St001159Number of simple modules with dominant dimension equal to the global dimension 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. St001181Number of indecomposable injective modules with grade at least 3 in the corresponding Nakayama algebra. St001185The number of indecomposable injective modules of grade at least 2 in the corresponding Nakayama algebra. St001186Number of simple modules with grade at least 3 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. St001189The number of simple modules with dominant and codominant dimension equal to zero in the Nakayama algebra corresponding to the Dyck path. St001191Number of simple modules $S$ with $Ext_A^i(S,A)=0$ for all $i=0,1,...,g-1$ in the corresponding Nakayama algebra $A$ with global dimension $g$. St001196The global dimension of $A$ minus the global dimension of $eAe$ for the corresponding Nakayama algebra with minimal faithful projective-injective module $eA$. 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. St001212The number of simple modules in the corresponding Nakayama algebra that have non-zero second Ext-group with the regular module. St001214The aft of an integer partition. St001222Number of simple modules in the corresponding LNakayama algebra that have a unique 2-extension with the regular module. St001236The dominant dimension of the corresponding Comp-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. St001249Sum of the odd parts of a partition. St001251The number of parts of a partition that are not congruent 1 modulo 3. St001252Half the sum of the even parts of a partition. St001256Number of simple reflexive modules that are 2-stable reflexive. St001270The bandwidth of a graph. St001272The number of graphs with the same degree sequence. St001277The degeneracy of a graph. St001280The number of parts of an integer partition that are at least two. St001335The cardinality of a minimal cycle-isolating set of a graph. St001340The cardinality of a minimal non-edge isolating set of a graph. St001342The number of vertices in the center of a graph. St001349The number of different graphs obtained from the given graph by removing an edge. St001354The number of series nodes in the modular decomposition of a graph. St001363The Euler characteristic of a graph according to Knill. St001364The number of permutations whose cube equals a fixed permutation of given cycle type. St001372The length of a longest cyclic run of ones of a binary word. St001385The number of conjugacy classes of subgroups with connected subgroups of sizes prescribed by an integer partition. St001387Number of standard Young tableaux of the skew shape tracing the border of the given partition. St001440The number of standard Young tableaux whose major index is congruent one modulo the size of a given integer partition. St001442The number of standard Young tableaux whose major index is divisible by the size of a given integer partition. St001475The evaluation of the Tutte polynomial of the graph at (x,y) equal to (1,0). St001476The evaluation of the Tutte polynomial of the graph at (x,y) equal to (1,-1). St001481The minimal height of a peak of a Dyck path. St001484The number of singletons of an integer partition. St001486The number of corners of the ribbon associated with an integer composition. St001493The number of simple modules with maximal even projective dimension in the corresponding Nakayama algebra. St001498The normalised height of a Nakayama algebra with magnitude 1. St001501The dominant dimension of magnitude 1 Nakayama algebras. St001512The minimum rank of a graph. St001525The number of symmetric hooks on the diagonal of a partition. St001527The cyclic permutation representation number of an integer partition. St001532The leading coefficient of the Poincare polynomial of the poset cone. St001533The largest coefficient of the Poincare polynomial of the poset cone. St001546The number of monomials in the Tutte polynomial of a graph. St001562The value of the complete homogeneous symmetric function evaluated at 1. St001563The value of the power-sum symmetric function evaluated at 1. St001564The value of the forgotten symmetric functions when all variables set to 1. St001571The Cartan determinant of the integer partition. St001587Half of the largest even part of an integer partition. St001592The maximal number of simple paths between any two different vertices of a graph. 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. St001603The number of colourings of a polygon such that the multiplicities of a colour are given by a partition. St001604The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on polygons. St001605The number of colourings of a cycle such that the multiplicities of colours are given by a partition. St001606The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on set partitions. St001621The number of atoms of a lattice. St001628The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on simple connected graphs. St001644The dimension of a graph. St001659The number of ways to place as many non-attacking rooks as possible on a Ferrers board. St001672The restrained domination number of a graph. St001673The degree of asymmetry of an integer composition. St001681The number of inclusion-wise minimal subsets of a lattice, whose meet is the bottom element. St001689The number of celebrities in a graph. St001691The number of kings in a graph. St001694The number of maximal dissociation sets in a graph. St001711The number of permutations such that conjugation with a permutation of given cycle type yields the squared permutation. St001722The number of minimal chains with small intervals between a binary word and the top element. St001739The number of graphs with the same edge polytope as the given graph. St001767The largest minimal number of arrows pointing to a cell in the Ferrers diagram in any assignment. St001775The degree of the minimal polynomial of the largest eigenvalue of a graph. St001776The degree of the minimal polynomial of the largest Laplacian eigenvalue of a graph. St001780The order of promotion on the set of standard tableaux of given shape. St001803The maximal overlap of the cylindrical tableau associated with a tableau. St001826The maximal number of leaves on a vertex of a graph. St001828The Euler characteristic of a graph. St001890The maximum magnitude of the Möbius function of a poset. St001901The largest multiplicity of an irreducible representation 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. St001914The size of the orbit of an integer partition in Bulgarian solitaire. St001924The number of cells in an integer partition whose arm and leg length coincide. St001934The number of monotone factorisations of genus zero of a permutation of given cycle type. St001936The number of transitive factorisations of a permutation of given cycle type into star transpositions. St001949The rigidity index of a graph. St001962The proper pathwidth of a graph. St000090The variation of a composition. St000145The Dyson rank of a partition. St000149The number of cells of the partition whose leg is zero and arm is odd. St000175Degree of the polynomial counting the number of semistandard Young tableaux when stretching the shape. St000185The weighted size of a partition. 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. St000225Difference between largest and smallest parts in a partition. St000296The length of the symmetric border of a binary word. St000313The number of degree 2 vertices of a graph. St000376The bounce deficit of a Dyck path. St000377The dinv defect of an integer partition. St000403The Szeged index minus the Wiener index of a graph. St000448The number of pairs of vertices of a graph with distance 2. St000455The second largest eigenvalue of a graph if it is integral. St000477The weight of a partition according to Alladi. St000478Another weight of a partition according to Alladi. St000506The number of standard desarrangement tableaux of shape equal to the given partition. St000508Eigenvalues of the random-to-random operator acting on a simple module. St000513The number of invariant subsets of size 2 when acting with a permutation of given cycle type. St000567The sum of the products of all pairs of parts. St000629The defect of a binary word. St000637The length of the longest cycle in a graph. St000661The number of rises of length 3 of a Dyck path. St000687The dimension of $Hom(I,P)$ for the LNakayama algebra 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. St000752The Grundy value for the game 'Couples are forever' on an integer partition. St000766The number of inversions of an integer composition. St000768The number of peaks in an integer composition. St000769The major index of a composition regarded as a word. St000790The number of pairs of centered tunnels, one strictly containing the other, of a Dyck path. St000791The number of pairs of left tunnels, one strictly containing the other, of a Dyck path. St000807The sum of the heights of the valleys of the associated bargraph. St000811The sum of the entries in the column specified by the partition of the change of basis matrix from powersum symmetric functions to Schur symmetric functions. St000921The number of internal inversions of a binary word. St000936The number of even values of the symmetric group character corresponding to the partition. St000938The number of zeros of the symmetric group character corresponding to the partition. St000966Number of peaks minus the global dimension of the corresponding LNakayama algebra. St000980The number of boxes weakly below the path and above the diagonal that lie below at least two peaks. St001008Number of indecomposable injective modules with projective dimension 1 in the Nakayama algebra corresponding to the Dyck path. St001037The number of inner corners of the upper path of the parallelogram polyomino associated with the Dyck path. St001057The Grundy value of the game of creating an independent set in a graph. St001095The number of non-isomorphic posets with precisely one further covering relation. St001097The coefficient of the monomial symmetric function indexed by the partition in the formal group law for linear orders. 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. 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. 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. St001110The 3-dynamic chromatic number of a graph. St001123The multiplicity of the dual of the standard representation in the Kronecker square corresponding to a partition. 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. 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. St001176The size of a partition minus its first part. St001177Twice the mean value of the major index among all standard Young tableaux of a partition. St001178Twelve times the variance of the major index among all standard Young tableaux of a partition. 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. St001230The number of simple modules with injective dimension equal to the dominant dimension equal to one and the dual property. 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. St001241The number of non-zero radicals of the indecomposable projective modules that have injective dimension and projective dimension at most one. St001264The smallest index i such that the i-th simple module has projective dimension equal to the global dimension of the corresponding Nakayama algebra. St001265The maximal i such that the i-th simple module has projective dimension equal to the global dimension in the corresponding Nakayama algebra. St001275The projective dimension of the second term in a minimal injective coresolution of the regular module. St001276The number of 2-regular indecomposable modules in the corresponding Nakayama algebra. St001292The injective dimension of the tensor product of two copies of the dual of the Nakayama algebra associated to a Dyck path. St001305The number of induced cycles on four vertices in a graph. St001306The number of induced paths on four vertices in a graph. St001308The number of induced paths on three vertices in a graph. St001311The cyclomatic number of a graph. St001317The minimal number of occurrences of the forest-pattern in a linear ordering of the vertices of the graph. St001320The minimal number of occurrences of the path-pattern in a linear ordering of the vertices of the 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. St001331The size of the minimal feedback vertex set. St001347The number of pairs of vertices of a graph having the same neighbourhood. St001350Half of the Albertson index of a graph. St001351The Albertson index of a graph. St001353The number of prime nodes in the modular decomposition of a graph. St001356The number of vertices in prime modules of a graph. St001371The length of the longest Yamanouchi prefix of a binary word. St001374The Padmakar-Ivan index of a graph. St001384The number of boxes in the diagram of a partition that do not lie in the largest triangle it contains. St001392The largest nonnegative integer which is not a part and is smaller than the largest part of the partition. St001396Number of triples of incomparable elements in a finite poset. St001423The number of distinct cubes in a binary word. St001479The number of bridges of a graph. St001575The minimal number of edges to add or remove to make a graph edge transitive. St001577The minimal number of edges to add or remove to make a graph a cograph. St001594The number of indecomposable projective modules in the Nakayama algebra corresponding to the Dyck path such that the UC-condition is satisfied. St001638The book thickness of a graph. St001651The Frankl number of a lattice. St001677The number of non-degenerate subsets of a lattice whose meet is the bottom element. St001695The natural comajor index of a standard Young tableau. St001696The natural major index of a standard Young tableau. St001698The comajor index of a standard tableau minus the weighted size of its shape. St001699The major index of a standard tableau minus the weighted size of its shape. St001712The number of natural descents of a standard Young tableau. St001730The number of times the path corresponding to a binary word crosses the base line. St001736The total number of cycles in a graph. St001764The number of non-convex subsets of vertices in a graph. St001814The number of partitions interlacing the given partition. St001816Eigenvalues of the top-to-random operator acting on a simple module. St001912The length of the preperiod in Bulgarian solitaire corresponding to an integer partition. St001957The number of Hasse diagrams with a given underlying undirected graph. St001961The sum of the greatest common divisors of all pairs of parts. St000307The number of rowmotion orbits of a poset. St000422The energy of a graph, if it is integral. St000718The largest Laplacian eigenvalue of a graph if it is integral. St000454The largest eigenvalue of a graph if it is integral. St000460The hook length of the last cell along the main diagonal of an integer partition. St001876The number of 2-regular simple modules in the incidence algebra of the lattice. St000208Number of integral Gelfand-Tsetlin polytopes with prescribed top row and integer partition weight. St000566The number of ways to select a row of a Ferrers shape and two cells in this row. St000668The least common multiple of the parts of the partition. St001703The villainy of a graph. St001720The minimal length of a chain of small intervals in a lattice. St000319The spin of an integer partition. St000320The dinv adjustment of an integer partition. St000321The number of integer partitions of n that are dominated by an integer partition. St000345The number of refinements of a partition. St000935The number of ordered refinements of an integer partition. St001000Number of indecomposable modules with projective dimension equal to the global dimension in the Nakayama algebra corresponding to the Dyck path. St001195The global dimension of the algebra $A/AfA$ of the corresponding Nakayama algebra $A$ with minimal left faithful projective-injective module $Af$. 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 $eA$. St001738The minimal order of a graph which is not an induced subgraph of the given graph. St001820The size of the image of the pop stack sorting operator. St000689The maximal n such that the minimal generator-cogenerator module in the LNakayama algebra of a Dyck path is n-rigid. St000707The product of the factorials of the parts. St000708The product of the parts of an integer partition. St000713The dimension of the irreducible representation of Sp(4) labelled by an integer partition. St000714The number of semistandard Young tableau of given shape, with entries at most 2. St000933The number of multipartitions of sizes given by an integer partition. St001001The number of indecomposable modules with projective and injective dimension equal to the global dimension of the Nakayama algebra corresponding to the Dyck path. St001846The number of elements which do not have a complement in the lattice. St001834The number of non-isomorphic minors of a graph. St001129The product of the squares of the parts of a partition.