St001743The discrepancy of a graph. St001792The arboricity of a graph. St000093The cardinality of a maximal independent set of vertices of a graph. St000147The largest part of an integer partition. St000298The order dimension or Dushnik-Miller dimension of a poset. St000318The number of addable cells of the Ferrers diagram of an integer partition. St000755The number of real roots of the characteristic polynomial of a linear recurrence associated with an integer partition. St000759The smallest missing part in an integer partition. St000786The maximal number of occurrences of a colour in a proper colouring of a graph. St001720The minimal length of a chain of small intervals in a lattice. St001814The number of partitions interlacing the given partition. St001883The mutual visibility number of a graph. St000159The number of distinct parts of the integer partition. St000183The side length of the Durfee square of an integer partition. St000319The spin of an integer partition. St000320The dinv adjustment of an integer partition. St000378The diagonal inversion number of an integer partition. St000480The number of lower covers of a partition in dominance order. St000533The minimum of the number of parts and the size of the first part of an integer partition. St000537The cutwidth of a graph. St000783The side length of the largest staircase partition fitting into a partition. St000897The number of different multiplicities of parts of an integer partition. St001092The number of distinct even parts of a partition. St001270The bandwidth of a graph. St001587Half of the largest even part of an integer partition. St001644The dimension of a graph. St001777The number of weak descents in an integer composition. St001826The maximal number of leaves on a vertex of a graph. St001918The degree of the cyclic sieving polynomial corresponding to an integer partition. St001931The weak major index of an integer composition regarded as a word. St001962The proper pathwidth of a graph. St000010The length of the partition. St000172The Grundy number of a graph. St000258The burning number of a graph. St000288The number of ones in a binary word. St000346The number of coarsenings of a partition. St000381The largest part of an integer composition. St000382The first part of an integer composition. St000511The number of invariant subsets when acting with a permutation of given cycle type. St000757The length of the longest weakly inreasing subsequence of parts of an integer composition. St000765The number of weak records in an integer composition. St000808The number of up steps of the associated bargraph. St001116The game chromatic number of a graph. St001261The Castelnuovo-Mumford regularity of a graph. St001302The number of minimally dominating sets of vertices of a graph. St001304The number of maximally independent sets of vertices of a graph. St001486The number of corners of the ribbon associated with an integer composition. St001581The achromatic number of a graph. St001654The monophonic hull number of a graph. St001670The connected partition number of a graph. St001784The minimum of the smallest closer and the second element of the block containing 1 in a set partition. St001884The number of borders of a binary word. St001963The tree-depth of a graph. St000160The multiplicity of the smallest part of a partition. St000292The number of ascents of a binary word. St000362The size of a minimal vertex cover of a graph. St000387The matching number of a graph. St000481The number of upper covers of a partition in dominance order. St000548The number of different non-empty partial sums of an integer partition. St000651The maximal size of a rise in a permutation. St000985The number of positive eigenvalues of the adjacency matrix of the graph. St001333The cardinality of a minimal edge-isolating set 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. St001393The induced matching number of a graph. St001484The number of singletons of an integer partition. St001613The binary logarithm of the size of the center of a lattice. St001621The number of atoms of a lattice. St001592The maximal number of simple paths between any two different vertices of a graph. St000668The least common multiple of the parts of the partition. St000822The Hadwiger number of the graph. St001330The hat guessing number of a graph. St000818The sum of the entries in the column specified by the composition of the change of basis matrix from quasisymmetric Schur functions to monomial quasisymmetric functions. St001337The upper domination number of a graph. St001338The upper irredundance number of a graph. St001642The Prague dimension of a graph. St000253The crossing number of a set partition. St000254The nesting number of a set partition. St000659The number of rises of length at least 2 of a Dyck path. St000730The maximal arc length of a set partition. St001031The height of the bicoloured Motzkin path associated with the Dyck path. St001340The cardinality of a minimal non-edge isolating set of a graph. St000636The hull number of a graph. St000917The open packing number of a graph. St000918The 2-limited packing number of a graph. St001109The number of proper colourings of a graph with as few colours as possible. St001315The dissociation number of a graph. St001656The monophonic position number of a graph. St001395The number of strictly unfriendly partitions of a graph. St001942The number of loops of the quiver corresponding to the reduced incidence algebra of a poset. St000640The rank of the largest boolean interval in a poset. St001625The Möbius invariant of a lattice. St001335The cardinality of a minimal cycle-isolating set of a graph. St000207Number of integral Gelfand-Tsetlin polytopes with prescribed top row and integer composition weight. St000208Number of integral Gelfand-Tsetlin polytopes with prescribed top row and integer partition weight. St000618The number of self-evacuating tableaux of given shape. St000667The greatest common divisor of the parts of the partition. St000781The number of proper colouring schemes of a Ferrers diagram. St000785The number of distinct colouring schemes of a graph. St001272The number of graphs with the same degree sequence. St001282The number of graphs with the same chromatic polynomial. 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. St001389The number of partitions of the same length below the given integer partition. St001432The order dimension of the partition. St001476The evaluation of the Tutte polynomial of the graph at (x,y) equal to (1,-1). 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. St001571The Cartan determinant of the integer partition. St001599The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on rooted trees. St001739The number of graphs with the same edge polytope as the given graph. St001740The number of graphs with the same symmetric edge polytope as the given 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. 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. 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. 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. St000175Degree of the polynomial counting the number of semistandard Young tableaux when stretching the shape. 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. St000322The skewness of a graph. St000323The minimal crossing number of a graph. St000370The genus of a graph. St000379The number of Hamiltonian cycles in a graph. St000403The Szeged index minus the Wiener index of 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. St000671The maximin edge-connectivity for choosing a subgraph. 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. St000944The 3-degree of an integer partition. St001069The coefficient of the monomial xy of the Tutte polynomial of the graph. St001175The size of a partition minus the hook length of the base cell. 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. St001280The number of parts of an integer partition that are at least two. St001301The first Betti number of the order complex associated with the poset. St001305The number of induced cycles on four vertices in a graph. St001306The number of induced paths on four vertices in a graph. 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. St001324The minimal number of occurrences of the chordal-pattern in a linear ordering of the vertices of the graph. St001325The minimal number of occurrences of the comparability-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. 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. St001392The largest nonnegative integer which is not a part and is smaller than the largest part of the partition. St001398Number of subsets of size 3 of elements in a poset that form a "v". St001541The Gini index of an integer partition. 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. 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. St001633The number of simple modules with projective dimension two in the incidence algebra of the poset. St001651The Frankl number of a lattice. St001657The number of twos in an integer partition. St001793The difference between the clique number and the chromatic number of a graph. St001871The number of triconnected components of a graph. St000092The number of outer peaks of a permutation. St000099The number of valleys of a permutation, including the boundary. St000023The number of inner peaks of a permutation. St000353The number of inner valleys of a permutation. St000806The semiperimeter of the associated bargraph. St000993The multiplicity of the largest part of an integer partition. St001442The number of standard Young tableaux whose major index is divisible by the size of a given integer partition. 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. St001568The smallest positive integer that does not appear twice in the 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. St001609The number of coloured trees such that the multiplicities of colours are given by a partition. St001913The number of preimages of an integer partition in Bulgarian solitaire. St001933The largest multiplicity of a part in an integer partition. St001936The number of transitive factorisations of a permutation of given cycle type into star transpositions. 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. St000506The number of standard desarrangement tableaux of shape equal to the given partition. St000929The constant term of the character polynomial of an integer partition. 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. St001440The number of standard Young tableaux whose major index is congruent one modulo the size of a given integer partition. St001714The number of subpartitions of an integer partition that do not dominate the conjugate subpartition. St001961The sum of the greatest common divisors of all pairs of parts. St000914The sum of the values of the Möbius function of a poset. St001890The maximum magnitude of the Möbius function of a poset. St000907The number of maximal antichains of minimal length in a poset. St000699The toughness times the least common multiple of 1,. St001281The normalized isoperimetric number of a graph. St001964The interval resolution global dimension of a poset. St000741The Colin de Verdière graph invariant. St001878The projective dimension of the simple modules corresponding to the minimum of L in the incidence algebra of the lattice L. St001704The size of the largest multi-subset-intersection of the deck of a graph with the deck of another graph. St000284The Plancherel distribution on integer partitions. St000620The number of standard tableaux of shape equal to the given partition such that the minimal cyclic descent is odd. 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. St000478Another weight of a partition according to Alladi. St000566The number of ways to select a row of a Ferrers shape and two cells in this row. St000621The number of standard tableaux of shape equal to the given partition such that the minimal cyclic descent is even. St000934The 2-degree of an integer partition. 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. 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. St000716The dimension of the irreducible representation of Sp(6) labelled by an integer partition. St000514The number of invariant simple graphs when acting with a permutation of given cycle type. St000515The number of invariant set partitions when acting with a permutation of given cycle type. St000706The product of the factorials of the multiplicities of an integer partition. St000813The number of zero-one matrices with weakly decreasing column sums and row sums given by the partition. St000567The sum of the products of all pairs of parts. St000941The number of characters of the symmetric group whose value on the partition is even. 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. St000454The largest eigenvalue of a graph if it is integral. St000264The girth of a graph, which is not a tree. St001095The number of non-isomorphic posets with precisely one further covering relation. St000086The number of subgraphs. St000087The number of induced subgraphs. St000244The cardinality of the automorphism group of a graph. St000259The diameter of a connected graph. St000269The number of acyclic orientations of a graph. St000270The number of forests contained in a graph. St000283The size of the preimage of the map 'to graph' from Binary trees to Graphs. St000286The number of connected components of the complement of a graph. St000299The number of nonisomorphic vertex-induced subtrees. St000343The number of spanning subgraphs of a graph. St000363The number of minimal vertex covers of a graph. St000364The exponent of the automorphism group of a graph. St000452The number of distinct eigenvalues of a graph. St000453The number of distinct Laplacian eigenvalues of a graph. St000468The Hosoya index of a graph. St000469The distinguishing number of a graph. St000479The Ramsey number of a graph. St000722The number of different neighbourhoods in a graph. St000777The number of distinct eigenvalues of the distance Laplacian of a connected graph. St000926The clique-coclique number of a graph. St000972The composition number of a graph. St001093The detour number of a graph. St001108The 2-dynamic chromatic number of a graph. St001110The 3-dynamic chromatic number of a graph. St001235The global dimension of the corresponding Comp-Nakayama algebra. St001316The domatic number of a graph. St001318The number of vertices of the largest induced subforest with the same number of connected components of a graph. St001321The number of vertices of the largest induced subforest of a graph. St001342The number of vertices in the center 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. St001474The evaluation of the Tutte polynomial of the graph at (x,y) equal to (2,-1). St001645The pebbling number of a connected graph. St001655The general position number of a graph. St001672The restrained domination number of a graph. St001674The number of vertices of the largest induced star graph in the 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. St001725The harmonious chromatic number of a graph. St001746The coalition number of a graph. St001757The number of orbits of toric promotion on a graph. St001758The number of orbits of promotion on a graph. St001802The number of endomorphisms of a graph. St001844The maximal degree of a generator of the invariant ring of the automorphism group of a graph. St000081The number of edges of a graph. St000171The degree of the graph. St000260The radius of a connected graph. St000261The edge connectivity of a graph. St000262The vertex connectivity of a graph. St000263The Szeged index of a graph. St000265The Wiener index of a graph. St000274The number of perfect matchings of a graph. St000300The number of independent sets of vertices of a graph. St000301The number of facets of the stable set polytope of a graph. St000310The minimal degree of a vertex of a graph. St000361The second Zagreb index of a graph. St000466The Gutman (or modified Schultz) index of a connected graph. St000778The metric dimension of a graph. St000987The number of positive eigenvalues of the Laplacian matrix of the graph. St001056The Grundy value for the game of deleting vertices of a graph until it has no edges. St001071The beta invariant of the graph. St001117The game chromatic index of a graph. St001119The length of a shortest maximal path in a graph. St001120The length of a longest path in a graph. St001271The competition number of a graph. St001331The size of the minimal feedback vertex set. St001336The minimal number of vertices in a graph whose complement is triangle-free. St001341The number of edges in the center of a graph. St001345The Hamming dimension of a graph. St001357The maximal degree of a regular spanning subgraph of a graph. St001362The normalized Knill dimension of a graph. St001391The disjunction number of a graph. St001479The number of bridges of a graph. St001512The minimum rank of a graph. St001649The length of a longest trail in a graph. St001702The absolute value of the determinant of the adjacency matrix of a graph. St001783The number of odd automorphisms of a graph. St001794Half the number of sets of vertices in a graph which are dominating and non-blocking. St001812The biclique partition number of a graph. St001827The number of two-component spanning forests of a graph. St001869The maximum cut size of a graph. St001949The rigidity index of a graph. St000088The row sums of the character table of the symmetric group. St000179The product of the hook lengths of the integer partition. St000184The size of the centralizer of any permutation of given cycle type. St000228The size of a partition. St000273The domination number of a graph. St000287The number of connected components of a graph. St000309The number of vertices with even degree. St000315The number of isolated vertices of a graph. St000321The number of integer partitions of n that are dominated by an integer partition. St000345The number of refinements of a partition. St000384The maximal part of the shifted composition of an integer partition. St000450The number of edges minus the number of vertices plus 2 of a graph. St000459The hook length of the base cell of a partition. St000460The hook length of the last cell along the main diagonal of an integer partition. St000482The (zero)-forcing number of a graph. St000531The leading coefficient of the rook polynomial of an integer partition. St000544The cop number of a graph. St000553The number of blocks of a graph. St000644The number of graphs with given frequency partition. St000723The maximal cardinality of a set of vertices with the same neighbourhood in 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. St000775The multiplicity of the largest eigenvalue in a graph. St000776The maximal multiplicity of an eigenvalue in a graph. St000784The maximum of the length and the largest part of the integer partition. St000812The sum of the entries in the column specified by the partition of the change of basis matrix from complete homogeneous symmetric functions to monomial symmetric functions. St000835The minimal difference in size when partitioning the integer partition into two subpartitions. St000870The product of the hook lengths of the diagonal cells in an integer partition. 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. St000916The packing number of a graph. St000935The number of ordered refinements of an integer partition. St000948The chromatic discriminant of a graph. St000986The multiplicity of the eigenvalue zero of the adjacency matrix of the graph. St000992The alternating sum of the parts of an integer partition. St001055The Grundy value for the game of removing cells of a row in an integer partition. St001057The Grundy value of the game of creating an independent set in a graph. St001070The absolute value of the derivative of the chromatic polynomial of the graph at 1. St001102The number of words with multiplicities of the letters given by the composition, avoiding the consecutive pattern 132. St001236The dominant dimension of the corresponding Comp-Nakayama algebra. St001239The largest vector space dimension of the double dual of a simple module in the corresponding Nakayama algebra. St001286The annihilation number of a graph. St001312Number of parabolic noncrossing partitions indexed by the composition. St001322The size of a minimal independent dominating set in a graph. St001339The irredundance number of a graph. St001360The number of covering relations in Young's lattice below a partition. St001363The Euler characteristic of a graph according to Knill. St001373The logarithm of the number of winning configurations of the lights out game on a graph. St001378The product of the cohook lengths of the integer partition. St001380The number of monomer-dimer tilings of a Ferrers diagram. St001441The number of non-empty connected induced subgraphs of a graph. St001463The number of distinct columns in the nullspace of a graph. St001475The evaluation of the Tutte polynomial of the graph at (x,y) equal to (1,0). St001527The cyclic permutation representation number of an integer partition. St001600The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on simple graphs. St001606The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on set partitions. 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. St001612The number of coloured multisets of cycles such that the multiplicities of colours are given by a partition. St001659The number of ways to place as many non-attacking rooks as possible on a Ferrers board. St001675The number of parts equal to the part in the reversed composition. St001691The number of kings in a graph. St001710The number of permutations such that conjugation with a permutation of given cycle type yields the inverse permutation. St001716The 1-improper chromatic number of a graph. St001765The number of connected components of the friends and strangers graph. St001828The Euler characteristic of a graph. St001829The common independence number of a graph. St001914The size of the orbit of an integer partition in Bulgarian solitaire. St000008The major index of the composition. St000063The number of linear extensions of a certain poset defined for an integer partition. St000095The number of triangles of a graph. St000108The number of partitions contained in the given partition. St000142The number of even parts of a partition. St000145The Dyson rank of a partition. St000149The number of cells of the partition whose leg is zero and arm is odd. St000256The number of parts from which one can substract 2 and still get an integer partition. St000303The determinant of the product of the incidence matrix and its transpose of a graph divided by $4$. St000344The number of strongly connected outdegree sequences of a graph. St000380Half of the maximal perimeter of a rectangle fitting into the diagram of an integer partition. St000473The number of parts of a partition that are strictly bigger than the number of ones. St000513The number of invariant subsets of size 2 when acting with a permutation of given cycle type. St000532The total number of rook placements on a Ferrers board. St000547The number of even non-empty partial sums of an integer partition. St000718The largest Laplacian eigenvalue of a graph if it is integral. St001192The maximal dimension of $Ext_A^2(S,A)$ for a simple module $S$ over the corresponding Nakayama algebra $A$. St001251The number of parts of a partition that are not congruent 1 modulo 3. St001252Half the sum of the even parts of a partition. 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. St001319The minimal number of occurrences of the star-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. St001328The minimal number of occurrences of the bipartite-pattern in a linear ordering of the vertices of the graph. St001347The number of pairs of vertices of a graph having the same neighbourhood. St001382The number of boxes in the diagram of a partition that do not lie in its Durfee square. St001384The number of boxes in the diagram of a partition that do not lie in the largest triangle it contains. St001400The total number of Littlewood-Richardson tableaux of given shape. St001458The rank of the adjacency matrix of a graph. St001459The number of zero columns in the nullspace of a graph. 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. St001638The book thickness of a graph. St001723The differential of a graph. St001724The 2-packing differential of a graph. St001736The total number of cycles in a graph. St001767The largest minimal number of arrows pointing to a cell in the Ferrers diagram in any assignment. St001797The number of overfull subgraphs of a graph. St001799The number of proper separations of a graph. St001834The number of non-isomorphic minors of a graph. St001706The number of closed sets in a graph. St000455The second largest eigenvalue of a graph if it is integral. St001044The number of pairs whose larger element is at most one more than half the size of the perfect matching. St000464The Schultz index of a connected graph. St001545The second Elser number of a connected graph. St000456The monochromatic index of a connected graph. St001118The acyclic chromatic index of a graph. St000285The size of the preimage of the map 'to inverse des composition' from Parking functions to Integer compositions. St000477The weight of a partition according to Alladi. St000937The number of positive values of the symmetric group character corresponding to the partition. St000997The even-odd crank of an integer partition. 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 $eA$. St000509The diagonal index (content) of a partition. St000510The number of invariant oriented cycles when acting with a permutation of given cycle type. St000681The Grundy value of Chomp on Ferrers diagrams. St000714The number of semistandard Young tableau of given shape, with entries at most 2. St000762The sum of the positions of the weak records of an integer composition. St000817The sum of the entries in the column specified by the composition of the change of basis matrix from dual immaculate quasisymmetric functions to monomial quasisymmetric functions. St000927The alternating sum of the coefficients of the character polynomial of an integer partition. St000939The number of characters of the symmetric group whose value on the partition is positive. St001060The distinguishing index of a graph. St001123The multiplicity of the dual of the standard representation in the Kronecker square corresponding to a partition. St000512The number of invariant subsets of size 3 when acting with a permutation of given cycle type. St000928The sum of the coefficients of the character polynomial of an integer partition. St001570The minimal number of edges to add to make a graph Hamiltonian. St000713The dimension of the irreducible representation of Sp(4) labelled by an integer partition. St001603The number of colourings of a polygon such that the multiplicities of a colour are given by a partition. 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. St001605The number of colourings of a cycle such that the multiplicities of colours are given by a partition. St001604The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on polygons. St001195The global dimension of the algebra $A/AfA$ of the corresponding Nakayama algebra $A$ with minimal left faithful projective-injective module $Af$. St001876The number of 2-regular simple modules in the incidence algebra of the lattice. St001323The independence gap of a graph. St001630The global dimension of the incidence algebra of the lattice over the rational numbers. St001875The number of simple modules with projective dimension at most 1. St001877Number of indecomposable injective modules with projective dimension 2. St001879The number of indecomposable summands of the top of the first syzygy of the dual of the regular module in the incidence algebra of the lattice. St001880The number of 2-Gorenstein indecomposable injective modules in the incidence algebra of the lattice. St001632The number of indecomposable injective modules $I$ with $dim Ext^1(I,A)=1$ for the incidence algebra A of a poset. St000660The number of rises of length at least 3 of a Dyck path. St001738The minimal order of a graph which is not an induced subgraph of the given graph. St001035The convexity degree of the parallelogram polyomino associated with the Dyck path. St001199The dominant dimension of $eAe$ for the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. St001498The normalised height of a Nakayama algebra with magnitude 1. St001526The Loewy length of the Auslander-Reiten translate of the regular module as a bimodule of the Nakayama algebra corresponding to the Dyck path. St000302The determinant of the distance matrix of a connected graph. St000467The hyper-Wiener index of a connected graph.