St000260The radius of a connected graph. St000261The edge connectivity of a graph. St000262The vertex connectivity of a graph. St000272The treewidth of a graph. St000274The number of perfect matchings of a graph. St000310The minimal degree of a vertex of a graph. St000319The spin of an integer partition. St000320The dinv adjustment of an integer partition. St000362The size of a minimal vertex cover of a graph. St000387The matching number of a graph. St000454The largest eigenvalue of a graph if it is integral. St000536The pathwidth of a graph. St000537The cutwidth of a graph. St000752The Grundy value for the game 'Couples are forever' on an integer partition. St000778The metric dimension of a graph. St001270The bandwidth of a graph. St001271The competition number of a graph. St001277The degeneracy of a graph. St001340The cardinality of a minimal non-edge isolating set of a graph. St001345The Hamming dimension of a graph. St001357The maximal degree of a regular spanning subgraph of a graph. St001358The largest degree of a regular subgraph of a graph. St001392The largest nonnegative integer which is not a part and is smaller than the largest part of the partition. St001512The minimum rank of a graph. St001613The binary logarithm of the size of the center of a lattice. St001615The number of join prime elements of a lattice. St001617The dimension of the space of valuations of a lattice. St001621The number of atoms of a lattice. St001622The number of join-irreducible elements of a lattice. St001623The number of doubly irreducible elements of a lattice. St001644The dimension of a graph. St001792The arboricity of a graph. St001918The degree of the cyclic sieving polynomial corresponding to an integer partition. St001949The rigidity index of a graph. St001962The proper pathwidth of a graph. St000093The cardinality of a maximal independent set of vertices of a graph. St000147The largest part of an integer partition. St000184The size of the centralizer of any permutation of given cycle type. St000258The burning number of a graph. St000273The domination number of a graph. St000287The number of connected components of a graph. St000299The number of nonisomorphic vertex-induced subtrees. St000345The number of refinements of a partition. St000384The maximal part of the shifted composition of an integer partition. St000452The number of distinct eigenvalues of a graph. St000453The number of distinct Laplacian eigenvalues of a graph. St000469The distinguishing number of a graph. St000482The (zero)-forcing number of a graph. St000544The cop number of a graph. St000550The number of modular elements of a lattice. St000551The number of left modular elements of a lattice. St000553The number of blocks of a graph. St000774The maximal multiplicity of a Laplacian eigenvalue in a graph. St000777The number of distinct eigenvalues of the distance Laplacian of a connected graph. St000784The maximum of the length and the largest part of the integer partition. St000786The maximal number of occurrences of a colour in a proper colouring of a graph. St000822The Hadwiger number of the graph. St000916The packing number of a graph. St000935The number of ordered refinements of an integer partition. St001093The detour number of a graph. St001116The game chromatic number of a graph. St001286The annihilation 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. 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. 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. St001384The number of boxes in the diagram of a partition that do not lie in the largest triangle it contains. St001389The number of partitions of the same length below the given integer partition. St001463The number of distinct columns in the nullspace of a graph. St001580The acyclic chromatic number of a graph. St001616The number of neutral elements in a lattice. St001642The Prague dimension of a graph. St001670The connected partition number of a graph. St001674The number of vertices of the largest induced star graph in the graph. St001720The minimal length of a chain of small intervals in a lattice. St001746The coalition number of a graph. St001820The size of the image of the pop stack sorting operator. St001828The Euler characteristic of a graph. St001829The common independence number of a graph. St001883The mutual visibility number of a graph. St001914The size of the orbit of an integer partition in Bulgarian solitaire. St001963The tree-depth of a graph. St000380Half of the maximal perimeter of a rectangle fitting into the diagram of an integer partition. St000474Dyson's crank of a partition. St000668The least common multiple of the parts of the partition. St001571The Cartan determinant of the integer partition. St001619The number of non-isomorphic sublattices of a lattice. St001626The number of maximal proper sublattices of a lattice. St001666The number of non-isomorphic subposets of a lattice which are lattices. St000012The area of a Dyck path. St000053The number of valleys of the 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. 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. St000377The dinv defect of an integer partition. St000394The sum of the heights of the peaks of a Dyck path minus the number of peaks. St000513The number of invariant subsets of size 2 when acting with a permutation of given cycle type. St000547The number of even non-empty partial sums of an integer partition. St000688The global dimension minus the dominant dimension of the LNakayama algebra associated to a Dyck path. St000741The Colin de Verdière graph invariant. St000743The number of entries in a standard Young tableau such that the next integer is a neighbour. St000970Number of peaks minus the dominant dimension of the corresponding LNakayama algebra. St000984The number of boxes below precisely one peak. St001067The number of simple modules of dominant dimension at least two in the corresponding Nakayama algebra. St001071The beta invariant of the graph. St001142The projective dimension of the socle of the regular module as a bimodule in the Nakayama algebra corresponding to the Dyck path. St001169Number of simple modules with projective dimension at least two in the corresponding Nakayama algebra. St001176The size of a partition minus its first part. 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 $eA$. 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. St001225The vector space dimension of the first extension group between J and itself when J is the Jacobson radical of the corresponding Nakayama algebra. St001252Half the sum of the even parts of a partition. 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. St001300The rank of the boundary operator in degree 1 of the chain complex of the order complex of the poset. St001349The number of different graphs obtained from the given graph by removing an edge. St001418Half of the global dimension of the stable Auslander algebra of the Nakayama algebra corresponding to the Dyck path. St001431Half of the Loewy length minus one of a modified stable Auslander algebra of the Nakayama algebra corresponding to the Dyck path. St001480The number of simple summands of the module J^2/J^3. St001502The global dimension minus the dominant dimension of magnitude 1 Nakayama algebras. St001506Half the projective dimension of the unique simple module with even projective dimension in a magnitude 1 Nakayama algebra. 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. St001553The number of indecomposable summands of the square of the Jacobson radical as a bimodule in the Nakayama algebra corresponding to the Dyck path. St001587Half of the largest even part of an integer partition. St001631The number of simple modules $S$ with $dim Ext^1(S,A)=1$ in the incidence algebra $A$ of the poset. St001714The number of subpartitions of an integer partition that do not dominate the conjugate subpartition. St001767The largest minimal number of arrows pointing to a cell in the Ferrers diagram in any assignment. St001783The number of odd automorphisms of a graph. St001812The biclique partition number of a graph. St001931The weak major index of an integer composition regarded as a word. St000010The length of the partition. St000011The number of touch points (or returns) of a Dyck path. St000015The number of peaks of a Dyck path. St000026The position of the first return of a Dyck path. St000032The number of elements smaller than the given Dyck path in the Tamari Order. St000097The order of the largest clique of the graph. St000098The chromatic number of a graph. St000172The Grundy number of a graph. St000189The number of elements in the poset. St000286The number of connected components of the complement of a graph. St000381The largest part of an integer composition. St000383The last part of an integer composition. St000507The number of ascents of a standard tableau. St000519The largest length of a factor maximising the subword complexity. St000645The sum of the areas of the rectangles formed by two consecutive peaks and the valley in between. St000676The number of odd rises of a Dyck path. St000684The global dimension of the LNakayama algebra associated to a Dyck path. St000686The finitistic dominant dimension of a Dyck path. St000722The number of different neighbourhoods in a graph. St000734The last entry in the first row of a standard tableau. St000808The number of up steps of the associated bargraph. St000907The number of maximal antichains of minimal length in a poset. St000911The number of maximal antichains of maximal size in a poset. St000922The minimal number such that all substrings of this length are unique. St000930The k-Gorenstein degree of the corresponding Nakayama algebra with linear quiver. St000952Gives the number of irreducible factors of the Coxeter polynomial of the Dyck path over the rational numbers. St001024Maximum of dominant dimensions of the simple modules in the Nakayama algebra corresponding to the Dyck path. St001029The size of the core of a graph. St001068Number of torsionless simple modules in the corresponding Nakayama algebra. St001108The 2-dynamic chromatic number of a graph. St001202Call a CNakayama algebra (a Nakayama algebra with a cyclic quiver) with Kupisch series $L=[c_0,c_1,...,c_{n−1}]$ such that $n=c_0 < c_i$ for all $i > 0$ a special CNakayama algebra. St001203We associate to 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 Dyck path as follows: St001250The number of parts of a partition that are not congruent 0 modulo 3. St001291The number of indecomposable summands of the tensor product of two copies of the dual of the Nakayama algebra associated to a Dyck path. St001302The number of minimally dominating sets of vertices of a graph. St001304The number of maximally independent sets of vertices of a graph. St001316The domatic number of a graph. St001436The index of a given binary word in the lex-order among all its cyclic shifts. St001462The number of factors of a standard tableaux under concatenation. St001486The number of corners of the ribbon associated with an integer composition. St001488The number of corners of a skew partition. St001494The Alon-Tarsi number of a graph. St001515The vector space dimension of the socle of the first syzygy module of the regular module (as a bimodule). St001530The depth of a Dyck path. St001581The achromatic number of a graph. St001655The general position number of a graph. St001656The monophonic position number of a graph. St001675The number of parts equal to the part in the reversed composition. St001717The largest size of an interval in a poset. St001733The number of weak left to right maxima of a Dyck path. St001785The number of ways to obtain a partition as the multiset of antidiagonal lengths of the Ferrers diagram of a partition. St001929The number of meanders with top half given by the noncrossing matching corresponding to the Dyck path. St001955The number of natural descents for set-valued two row standard Young tableaux. St000070The number of antichains in a poset. St000104The number of facets in the order polytope of this poset. St000151The number of facets in the chain polytope of the poset. St000393The number of strictly increasing runs in a binary word. St000969We 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 $c_{n-1}$. St001012Number of simple modules with projective dimension at most 2 in the Nakayama algebra corresponding to the Dyck path. St001020Sum of the codominant dimensions of the non-projective indecomposable injective modules of the Nakayama algebra corresponding to the Dyck path. St001028Number of simple modules with injective dimension equal to the dominant dimension in the Nakayama algebra corresponding to the Dyck path. St001034The area of the parallelogram polyomino associated with 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. St001170Number of indecomposable injective modules whose socle has projective dimension at most g-1 when g denotes the global dimension in the corresponding Nakayama algebra. St001179Number of indecomposable injective modules with projective dimension at most 2 in the corresponding Nakayama algebra. St001211The number of simple modules in the corresponding Nakayama algebra that have vanishing second Ext-group with the regular module. St001290The first natural number n such that the tensor product of n copies of D(A) is zero for the corresponding Nakayama algebra A. St001348The bounce of the parallelogram polyomino associated with the Dyck path. St001437The flex of a binary word. 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. St001505The number of elements generated by the Dyck path as a map in the full transformation monoid. St001664The number of non-isomorphic subposets of a poset. St001023Number of simple modules with projective dimension at most 3 in the Nakayama algebra corresponding to the Dyck path. St001065Number of indecomposable reflexive modules in the corresponding Nakayama algebra. St001190Number of simple modules with projective dimension at most 4 in the corresponding Nakayama algebra. St001650The order of Ringel's homological bijection associated to the linear Nakayama algebra corresponding to the Dyck path. St001232The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2. St000327The number of cover relations in a poset. St001637The number of (upper) dissectors of a poset. St001645The pebbling number of a connected graph. St001668The number of points of the poset minus the width of the poset. St000100The number of linear extensions of a poset. St000633The size of the automorphism group of a poset. St000640The rank of the largest boolean interval in a poset. St000910The number of maximal chains of minimal length in a poset. St001105The number of greedy linear extensions of a poset. St001106The number of supergreedy linear extensions of a poset. St001632The number of indecomposable injective modules $I$ with $dim Ext^1(I,A)=1$ for the incidence algebra A of a poset. St000680The Grundy value for Hackendot on posets. St000717The number of ordinal summands of a poset. St000848The balance constant multiplied with the number of linear extensions of a poset. St000849The number of 1/3-balanced pairs in a poset. St000850The number of 1/2-balanced pairs in a poset. St000906The length of the shortest maximal chain in a poset. St000643The size of the largest orbit of antichains under Panyushev complementation. St000456The monochromatic index of a connected graph. St000509The diagonal index (content) of a partition. St000698The number of 2-rim hooks removed from an integer partition to obtain its associated 2-core. St000939The number of characters of the symmetric group whose value on the partition is positive. St001281The normalized isoperimetric number of a graph. St001592The maximal number of simple paths between any two different vertices of a graph. St001604The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on polygons. St001630The global dimension of the incidence algebra of the lattice over the rational numbers. St000379The number of Hamiltonian cycles in a graph. St000512The number of invariant subsets of size 3 when acting with a permutation of given cycle type. St000515The number of invariant set partitions when acting with a permutation of given cycle type. St000708The product of the parts of an integer partition. St000933The number of multipartitions of sizes given by 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. 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. St001124The multiplicity of the standard representation in the Kronecker square corresponding to a partition. St001651The Frankl number of a lattice. St001704The size of the largest multi-subset-intersection of the deck of a graph with the deck of another graph. St001876The number of 2-regular simple modules in the incidence algebra of the lattice. St001877Number of indecomposable injective modules with projective dimension 2. St000455The second largest eigenvalue of a graph if it is integral. St000418The number of Dyck paths that are weakly below a Dyck path. St000444The length of the maximal rise of a Dyck path. St000476The sum of the semi-lengths of tunnels before a valley of a Dyck path. St000478Another weight of a partition according to Alladi. St000510The number of invariant oriented cycles 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. St000707The product of the factorials of the parts. St000744The length of the path to the largest entry in a standard Young tableau. 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. St000927The alternating sum of the coefficients of the character polynomial of an integer partition. St000932The number of occurrences of the pattern UDU in a Dyck path. St000934The 2-degree of an integer partition. St000937The number of positive values of the symmetric group character corresponding to the partition. St001128The exponens consonantiae of a partition. St001199The dominant dimension of $eAe$ for the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. St001499The number of indecomposable projective-injective modules of a magnitude 1 Nakayama algebra. St001531Number of partial orders contained in the poset determined by the Dyck path. St001959The product of the heights of the peaks of a Dyck path. St000421The number of Dyck paths that are weakly below a Dyck path, except for the path itself. St000442The maximal area to the right of an up step of a Dyck path. 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. St000656The number of cuts of a poset. St000658The number of rises of length 2 of a Dyck path. St000659The number of rises of length at least 2 of a Dyck path. 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. St000693The modular (standard) major index of a standard tableau. St000940The number of characters of the symmetric group whose value on the partition is zero. St000941The number of characters of the symmetric group whose value on the partition is even. St001031The height of the bicoloured Motzkin path associated with the Dyck path. St001035The convexity degree of the parallelogram polyomino associated with the Dyck path. St001039The maximal height of a column in the parallelogram polyomino associated with a Dyck path. St001139The number of occurrences of hills of size 2 in a Dyck path. 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 $eA$. St000477The weight of a partition according to Alladi. St000642The size of the smallest orbit of antichains under Panyushev complementation. St000981The length of the longest zigzag subpath. St000173The segment statistic of a semistandard tableau. St000282The size of the preimage of the map 'to poset' from Ordered trees to Posets. 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. St000635The number of strictly order preserving maps of a poset into itself. St000914The sum of the values of the Möbius function of a poset. St001890The maximum magnitude of the Möbius function of a poset. St000281The size of the preimage of the map 'to poset' from Binary trees to Posets. St001095The number of non-isomorphic posets with precisely one further covering relation. St000634The number of endomorphisms of a poset. St000639The number of relations in a poset. St000641The number of non-empty boolean intervals in a poset. St000112The sum of the entries reduced by the index of their row in a semistandard tableau. 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. St000771The largest multiplicity of a distance Laplacian eigenvalue in a connected graph. St000772The multiplicity of the largest distance Laplacian eigenvalue in a connected graph. 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. St000514The number of invariant simple graphs when acting with a permutation of given cycle type. 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. St000997The even-odd crank of an integer partition. St001878The projective dimension of the simple modules corresponding to the minimum of L in the incidence algebra of the lattice L. St000284The Plancherel distribution on integer partitions. St000681The Grundy value of Chomp on Ferrers diagrams. St000704The number of semistandard tableaux on a given integer partition with minimal maximal entry. St000706The product of the factorials of the multiplicities of an integer partition. St000714The number of semistandard Young tableau of given shape, with entries at most 2. St000813The number of zero-one matrices with weakly decreasing column sums and row sums given by the partition. St000901The cube of the number of standard Young tableaux with shape given by the partition. St000993The multiplicity of the largest part of an integer partition. St001060The distinguishing index of a graph. St001118The acyclic chromatic index of a graph. St001123The multiplicity of the dual of the standard representation in the Kronecker square corresponding to a partition. St001568The smallest positive integer that does not appear twice in the partition. St001570The minimal number of edges to add to make a graph Hamiltonian. 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. St001875The number of simple modules with projective dimension at most 1. St000264The girth of a graph, which is not a tree. St000567The sum of the products of all pairs of parts. St000928The sum of the coefficients of the character polynomial of an integer partition. St000929The constant term of the character polynomial of an integer partition. 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. St000699The toughness times the least common multiple of 1,. St000713The dimension of the irreducible representation of Sp(4) labelled by an integer partition. St000716The dimension of the irreducible representation of Sp(6) labelled by an integer partition. St000464The Schultz index of a connected graph. St001545The second Elser number of a connected graph. St001629The coefficient of the integer composition in the quasisymmetric expansion of the relabelling action of the symmetric group on cycles. 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. 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. St000460The hook length of the last cell along the main diagonal of an integer partition. St000618The number of self-evacuating tableaux of given shape. St000667The greatest common divisor of the parts of the partition. St000755The number of real roots of the characteristic polynomial of a linear recurrence associated with an integer partition. St000781The number of proper colouring schemes of a Ferrers diagram. St000870The product of the hook lengths of the diagonal cells in an integer partition. St001122The multiplicity of the sign representation in the Kronecker square corresponding to a partition. St001195The global dimension of the algebra $A/AfA$ of the corresponding Nakayama algebra $A$ with minimal left faithful projective-injective module $Af$. St001247The number of parts of a partition that are not congruent 2 modulo 3. St001249Sum of the odd parts of a partition. St001262The dimension of the maximal parabolic seaweed algebra corresponding to the 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. St001360The number of covering relations in Young's lattice below a partition. St001364The number of permutations whose cube equals a fixed permutation of given cycle type. St001378The product of the cohook lengths of the integer partition. St001380The number of monomer-dimer tilings of a Ferrers diagram. St001383The BG-rank of an integer partition. St001432The order dimension of the partition. St001442The number of standard Young tableaux whose major index is divisible by the size of a given integer partition. St001525The number of symmetric hooks on the diagonal of a partition. St001527The cyclic permutation representation number of an integer partition. St001529The number of monomials in the expansion of the nabla operator applied to the power-sum symmetric function indexed by the partition. St001561The value of the elementary symmetric function evaluated at 1. 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. St001593This is the number of standard Young tableaux of the given shifted shape. St001599The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on rooted trees. St001600The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on simple graphs. St001601The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on trees. St001602The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on endofunctions. 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. 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. St001610The number of coloured endofunctions 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. St001627The number of coloured connected graphs such that the multiplicities of colours are given by a partition. St001628The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on simple connected graphs. St001763The Hurwitz number of an integer partition. 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. St001913The number of preimages of an integer partition in Bulgarian solitaire. St001924The number of cells in an integer partition whose arm and leg length coincide. St001933The largest multiplicity of a part in an integer partition. 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. St001938The number of transitive monotone factorizations of genus zero of a permutation of given cycle type. 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. St001943The sum of the squares of the hook lengths of an integer partition. St000145The Dyson rank of a partition. 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. St000506The number of standard desarrangement tableaux of shape equal to the given partition. 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. St001175The size of a partition minus the hook length of the base cell. 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. 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. St001440The number of standard Young tableaux whose major index is congruent one modulo the size of a given integer partition. St001541The Gini index of an integer partition. St001586The number of odd parts smaller than the largest even part in an integer partition. St001657The number of twos in an integer partition. St001912The length of the preperiod in Bulgarian solitaire corresponding to an integer partition. St001961The sum of the greatest common divisors of all pairs of parts.