St001190Number of simple modules with projective dimension at most 4 in the corresponding Nakayama algebra. St001237The number of simple modules with injective dimension at most one or dominant dimension at least one. St001295Gives the vector space dimension of the homomorphism space between J^2 and J^2. St001508The degree of the standard monomial associated to a Dyck path relative to the diagonal boundary. St001955The number of natural descents for set-valued two row standard Young tableaux. St000011The number of touch points (or returns) of a Dyck path. St000014The number of parking functions supported by a Dyck path. St000015The number of peaks of a Dyck path. St000019The cardinality of the support of a permutation. St000022The number of fixed points of a permutation. St000031The number of cycles in the cycle decomposition of a permutation. St000050The depth or height of a binary tree. St000056The decomposition (or block) number of a permutation. St000058The order of a permutation. St000062The length of the longest increasing subsequence of the permutation. St000110The number of permutations less than or equal to a permutation in left weak order. St000144The pyramid weight of the Dyck path. St000153The number of adjacent cycles of a permutation. St000189The number of elements in the poset. St000203The number of external nodes of a binary tree. St000213The number of weak exceedances (also weak excedences) of a permutation. St000221The number of strong fixed points of a permutation. St000228The size of a partition. St000229Sum of the difference between the maximal and the minimal elements of the blocks plus the number of blocks of a set partition. St000236The number of cyclical small weak excedances. St000239The number of small weak excedances. St000240The number of indices that are not small excedances. St000241The number of cyclical small excedances. St000288The number of ones in a binary word. St000308The height of the tree associated to a permutation. St000314The number of left-to-right-maxima of a permutation. St000336The leg major index of a standard tableau. St000338The number of pixed points of a permutation. St000381The largest part of an integer composition. St000382The first part of an integer composition. St000383The last part of an integer composition. St000395The sum of the heights of the peaks of a Dyck path. St000445The number of rises of length 1 of a Dyck path. St000501The size of the first part in the decomposition of a permutation. St000505The biggest entry in the block containing the 1. St000528The height of a poset. St000617The number of global maxima of a Dyck path. St000657The smallest part of an integer composition. St000676The number of odd rises of a Dyck path. St000684The global dimension of the LNakayama algebra associated to a Dyck path. St000685The dominant dimension of the LNakayama algebra associated to a Dyck path. St000686The finitistic dominant dimension of a Dyck path. St000696The number of cycles in the breakpoint graph of a permutation. St000703The number of deficiencies of a permutation. St000725The smallest label of a leaf of the increasing binary tree associated to a permutation. St000740The last entry of a permutation. St000808The number of up steps of the associated bargraph. St000863The length of the first row of the shifted shape of a permutation. St000875The semilength of the longest Dyck word in the Catalan factorisation of a binary word. St000907The number of maximal antichains of minimal length in a poset. St000911The number of maximal antichains of maximal size in a poset. St000912The number of maximal antichains in a poset. St000930The k-Gorenstein degree of the corresponding Nakayama algebra with linear quiver. St000991The number of right-to-left minima of a permutation. St000994The number of cycle peaks and the number of cycle valleys of a permutation. St001018Sum of projective dimension of the indecomposable injective modules of 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. St001024Maximum of dominant dimensions of the simple modules in the Nakayama algebra corresponding to the Dyck path. St001038The minimal height of a column in the parallelogram polyomino associated with the Dyck path. St001039The maximal height of a column in the parallelogram polyomino associated with a Dyck path. St001068Number of torsionless simple modules in the corresponding Nakayama algebra. St001090The number of pop-stack-sorts needed to sort a permutation. St001135The projective dimension of the first simple module in the Nakayama algebra corresponding to the Dyck path. 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. St001183The maximum of $projdim(S)+injdim(S)$ over all simple modules in the Nakayama algebra corresponding to the Dyck path. St001201The grade of the simple module $S_0$ in the special CNakayama algebra corresponding to the Dyck path. St001202Call a CNakayama algebra (a Nakayama algebra with a cyclic quiver) with Kupisch series $L=[c_0,c_1,...,c_{n−1}]$ such that $n=c_0 < c_i$ for all $i > 0$ a special CNakayama algebra. 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: St001228The vector space dimension of the space of module homomorphisms between J and itself when J denotes the Jacobson radical of the corresponding Nakayama algebra. St001239The largest vector space dimension of the double dual of a simple module in the corresponding Nakayama algebra. St001254The vector space dimension of the first extension-group between A/soc(A) and J when A is the corresponding Nakayama algebra with Jacobson radical J. St001258Gives the maximum of injective plus projective dimension of an indecomposable module over the corresponding Nakayama algebra. St001268The size of the largest ordinal summand in the poset. St001291The number of indecomposable summands of the tensor product of two copies of the dual of the Nakayama algebra associated to a Dyck path. 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. St001343The dimension of the reduced incidence algebra of a poset. St001430The number of positive entries in a signed permutation. St001439The number of even weak deficiencies and of odd weak exceedences. St001461The number of topologically connected components of the chord diagram of a permutation. St001464The number of bases of the positroid corresponding to the permutation, with all fixed points counterclockwise. St001497The position of the largest weak excedence of a permutation. St001530The depth of a Dyck path. St001554The number of distinct nonempty subtrees of a binary tree. St001566The length of the longest arithmetic progression in a permutation. St001614The cyclic permutation representation number of a skew partition. St001622The number of join-irreducible elements of a lattice. St001636The number of indecomposable injective modules with projective dimension at most one in the incidence algebra of the poset. St001652The length of a longest interval of consecutive numbers. St001660The number of ways to place as many non-attacking rooks as possible on a skew Ferrers board. St001662The length of the longest factor of consecutive numbers in a permutation. St001672The restrained domination number of a graph. St001688The sum of the squares of the heights of the peaks of a Dyck path. St001717The largest size of an interval in a poset. St001733The number of weak left to right maxima of a Dyck path. St001778The largest greatest common divisor of an element and its image in a permutation. St001784The minimum of the smallest closer and the second element of the block containing 1 in a set partition. St001800The number of 3-Catalan paths having this Dyck path as first and last coordinate projections. St001929The number of meanders with top half given by the noncrossing matching corresponding to the Dyck path. St000004The major index of a permutation. St000005The bounce statistic of a Dyck path. St000006The dinv of a Dyck path. St000018The number of inversions of a permutation. St000028The number of stack-sorts needed to sort a permutation. St000029The depth of a permutation. St000030The sum of the descent differences of a permutations. St000041The number of nestings of a perfect matching. St000051The size of the left subtree of a binary tree. St000053The number of valleys of the Dyck path. St000057The Shynar inversion number of a standard tableau. St000070The number of antichains in a poset. St000076The rank of the alternating sign matrix in the alternating sign matrix poset. St000080The rank of the poset. St000104The number of facets in the order polytope of this poset. St000120The number of left tunnels of a Dyck path. St000133The "bounce" of a permutation. St000151The number of facets in the chain polytope of the poset. St000155The number of exceedances (also excedences) of a permutation. St000161The sum of the sizes of the right subtrees of a binary tree. St000209Maximum difference of elements in cycles. St000210Minimum over maximum difference of elements in cycles. St000224The sorting index of a permutation. St000234The number of global ascents of a permutation. St000237The number of small exceedances. St000245The number of ascents of a permutation. St000246The number of non-inversions of a permutation. St000304The load of a permutation. St000306The bounce count of a Dyck path. St000331The number of upper interactions of a Dyck path. St000334The maz index, the major index of a permutation after replacing fixed points by zeros. St000339The maf index of a permutation. St000441The number of successions of a permutation. St000446The disorder of a permutation. St000645The sum of the areas of the rectangles formed by two consecutive peaks and the valley in between. St000651The maximal size of a rise in a permutation. St000672The number of minimal elements in Bruhat order not less than the permutation. St000954Number of times the corresponding LNakayama algebra has $Ext^i(D(A),A)=0$ for $i>0$. 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 $c_{n−1}$. 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 $c_{n-1}$. St000996The number of exclusive left-to-right maxima of a permutation. St000998Number of indecomposable projective modules with injective dimension smaller than or equal to the dominant dimension in the Nakayama algebra corresponding to the Dyck path. St001012Number of simple modules with projective dimension at most 2 in the Nakayama algebra corresponding to the Dyck path. St001023Number of simple modules with projective dimension at most 3 in the Nakayama algebra corresponding to the Dyck path. St001027Number of simple modules with projective dimension equal to injective dimension in the Nakayama algebra corresponding to the Dyck path. St001028Number of simple modules with injective dimension equal to the dominant dimension in the Nakayama algebra corresponding to the Dyck path. St001032The number of horizontal steps in the bicoloured Motzkin path associated with the Dyck path. St001033The normalized area of the parallelogram polyomino associated with the Dyck path. St001065Number of indecomposable reflexive modules in the corresponding Nakayama algebra. St001067The number of simple modules of dominant dimension at least two in the corresponding Nakayama algebra. St001096The size of the overlap set of a permutation. St001142The projective dimension of the socle of the regular module as a bimodule in the Nakayama algebra corresponding to the Dyck path. St001161The major index north count of a Dyck path. 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. St001169Number of simple modules with projective dimension at least two in the corresponding Nakayama algebra. St001179Number of indecomposable injective modules with projective dimension at most 2 in the corresponding Nakayama algebra. St001185The number of indecomposable injective modules of grade at least 2 in the corresponding Nakayama algebra. St001192The maximal dimension of $Ext_A^2(S,A)$ for a simple module $S$ over the corresponding Nakayama algebra $A$. 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 $eA$. St001215Let X be the direct sum of all simple modules of the corresponding Nakayama algebra. St001216The number of indecomposable injective modules in the corresponding Nakayama algebra that have non-vanishing second Ext-group with the regular module. 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. St001227The vector space dimension of the first extension group between the socle of the regular module and the Jacobson radical of the corresponding Nakayama algebra. St001232The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2. St001240The number of indecomposable modules e_i J^2 that have injective dimension at most one in the corresponding Nakayama algebra St001245The cyclic maximal difference between two consecutive entries of a permutation. St001274The number of indecomposable injective modules with projective dimension equal to two. St001278The number of indecomposable modules that are fixed by $\tau \Omega^1$ composed with its inverse in the corresponding Nakayama algebra. St001290The first natural number n such that the tensor product of n copies of D(A) is zero for the corresponding Nakayama algebra A. St001294The maximal torsionfree index of a simple non-projective module in the corresponding Nakayama algebra. St001296The maximal torsionfree index of an indecomposable non-projective module in the corresponding Nakayama algebra. St001298The number of repeated entries in the Lehmer code of a permutation. St001300The rank of the boundary operator in degree 1 of the chain complex of the order complex of the poset. St001332The number of steps on the non-negative side of the walk associated with the permutation. St001397Number of pairs of incomparable elements in a finite poset. St001405The number of bonds in a permutation. St001504The sum of all indegrees of vertices with indegree at least two in the resolution quiver of a Nakayama algebra corresponding to the Dyck path. St001505The number of elements generated by the Dyck path as a map in the full transformation monoid. St001506Half the projective dimension of the unique simple module with even projective dimension in a magnitude 1 Nakayama algebra. St001509The degree of the standard monomial associated to a Dyck path relative to the trivial lower boundary. St001558The number of transpositions that are smaller or equal to a permutation in Bruhat order. St001579The number of cyclically simple transpositions decreasing the number of cyclic descents needed to sort a permutation. St001631The number of simple modules $S$ with $dim Ext^1(S,A)=1$ in the incidence algebra $A$ of the poset. St001640The number of ascent tops in the permutation such that all smaller elements appear before. St001641The number of ascent tops in the flattened set partition such that all smaller elements appear before. St001650The order of Ringel's homological bijection associated to the linear Nakayama algebra corresponding to the Dyck path. St001658The total number of rook placements on a Ferrers board. St001664The number of non-isomorphic subposets of a poset. St001726The number of visible inversions of a permutation. St001759The Rajchgot index of a permutation. St001782The order of rowmotion on the set of order ideals of a poset. St001958The degree of the polynomial interpolating the values of a permutation. St000967The value p(1) for the Coxeterpolynomial p of the corresponding LNakayama algebra. St001218Smallest index k greater than or equal to one such that the Coxeter matrix C of the corresponding Nakayama algebra has C^k=1. St000007The number of saliances of the permutation. St000010The length of the partition. St000013The height of a Dyck path. St000025The number of initial rises of a Dyck path. St000048The multinomial of the parts of a partition. St000054The first entry of the permutation. St000059The inversion number of a standard tableau as defined by Haglund and Stevens. St000063The number of linear extensions of a certain poset defined for an integer partition. St000066The column of the unique '1' in the first row of the alternating sign matrix. St000081The number of edges of a graph. St000084The number of subtrees. St000085The number of linear extensions of the tree. St000086The number of subgraphs. St000087The number of induced subgraphs. St000093The cardinality of a maximal independent set of vertices of a graph. St000105The number of blocks in the set partition. St000108The number of partitions contained in the given partition. St000117The number of centered tunnels of a Dyck path. St000141The maximum drop size of a permutation. St000147The largest part of an integer partition. St000148The number of odd parts of a partition. St000157The number of descents of a standard tableau. St000160The multiplicity of the smallest part of a partition. St000164The number of short pairs. St000166The depth minus 1 of an ordered tree. St000167The number of leaves of an ordered tree. St000171The degree of the graph. St000184The size of the centralizer of any permutation of given cycle type. St000207Number of integral Gelfand-Tsetlin polytopes with prescribed top row and integer composition weight. St000215The number of adjacencies of a permutation, zero appended. St000231Sum of the maximal elements of the blocks of a set partition. St000258The burning number of a graph. St000271The chromatic index of a graph. St000273The domination number of a graph. St000287The number of connected components of a graph. St000291The number of descents of a binary word. St000293The number of inversions of a binary word. St000299The number of nonisomorphic vertex-induced subtrees. St000309The number of vertices with even degree. St000315The number of isolated vertices of a graph. St000318The number of addable cells of the Ferrers diagram of an integer partition. St000325The width of the tree associated to a permutation. St000328The maximum number of child nodes in a tree. St000335The difference of lower and upper interactions. St000337The lec statistic, the sum of the inversion numbers of the hook factors of a permutation. St000374The number of exclusive right-to-left minima of a permutation. St000384The maximal part of the shifted composition of an integer partition. St000385The number of vertices with out-degree 1 in a binary tree. St000389The number of runs of ones of odd length in a binary word. St000390The number of runs of ones in a binary word. St000392The length of the longest run of ones in a binary word. St000393The number of strictly increasing runs in a binary word. St000400The path length of an ordered tree. St000414The binary logarithm of the number of binary trees with the same underlying unordered tree. St000420The number of Dyck paths that are weakly above a Dyck path. St000443The number of long tunnels of a Dyck path. St000444The length of the maximal rise of a Dyck path. St000451The length of the longest pattern of the form k 1 2. St000452The number of distinct eigenvalues of a graph. St000453The number of distinct Laplacian eigenvalues 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. St000468The Hosoya index of a graph. St000469The distinguishing number of a graph. St000470The number of runs in a permutation. St000475The number of parts equal to 1 in a partition. St000476The sum of the semi-lengths of tunnels before a valley of a Dyck path. St000479The Ramsey number of a graph. St000482The (zero)-forcing number of a graph. St000503The maximal difference between two elements in a common block. St000507The number of ascents of a standard tableau. St000529The number of permutations whose descent word is the given binary word. St000531The leading coefficient of the rook polynomial of an integer partition. St000532The total number of rook placements on a Ferrers board. St000542The number of left-to-right-minima of a permutation. St000543The size of the conjugacy class of a binary word. St000544The cop number of a graph. St000547The number of even non-empty partial sums of an integer partition. St000548The number of different non-empty partial sums of an integer partition. St000553The number of blocks of a graph. St000626The minimal period of a binary word. St000627The exponent of a binary word. St000636The hull number of a graph. St000638The number of up-down runs of a permutation. St000653The last descent of a permutation. St000655The length of the minimal rise of a Dyck path. St000667The greatest common divisor of the parts of the partition. St000675The number of centered multitunnels of a Dyck path. St000678The number of up steps after the last double rise of a Dyck path. St000698The number of 2-rim hooks removed from an integer partition to obtain its associated 2-core. St000700The protection number of an ordered tree. St000702The number of weak deficiencies of a permutation. St000721The sum of the partition sizes in the oscillating tableau corresponding to a perfect matching. St000723The maximal cardinality of a set of vertices with the same neighbourhood in a graph. St000728The dimension of a set partition. St000733The row containing the largest entry of a standard tableau. St000734The last entry in the first row of a standard tableau. St000738The first entry in the last row of a standard tableau. St000743The number of entries in a standard Young tableau such that the next integer is a neighbour. St000746The number of pairs with odd minimum in a perfect matching. St000757The length of the longest weakly inreasing subsequence of parts of an integer composition. St000759The smallest missing part in an integer partition. St000765The number of weak records in an integer composition. 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. 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. St000835The minimal difference in size when partitioning the integer partition into two subpartitions. St000839The largest opener of a set partition. St000843The decomposition number of a perfect matching. St000867The sum of the hook lengths in the first row of an integer partition. St000870The product of the hook lengths of the diagonal cells in an integer partition. St000874The position of the last double rise in a Dyck path. St000876The number of factors in the Catalan decomposition of a binary word. St000883The number of longest increasing subsequences of a permutation. St000885The number of critical steps in the Catalan decomposition of a binary word. St000895The number of ones on the main diagonal of an alternating sign matrix. 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. St000917The open packing number of a graph. St000918The 2-limited packing number of a graph. St000924The number of topologically connected components of a perfect matching. St000926The clique-coclique number of a graph. St000971The smallest closer of a set partition. St000974The length of the trunk of an ordered tree. St000975The length of the boundary minus the length of the trunk of an ordered tree. St000982The length of the longest constant subword. St000984The number of boxes below precisely one peak. St000986The multiplicity of the eigenvalue zero of the adjacency matrix of the graph. St000987The number of positive eigenvalues of the Laplacian matrix of the graph. St000989The number of final rises of a permutation. St000992The alternating sum of the parts of an integer partition. St000999Number of indecomposable projective module with injective dimension equal to the global dimension in the Nakayama algebra corresponding to the Dyck path. St001006Number of simple modules with projective dimension equal to the global dimension of the Nakayama algebra corresponding to the Dyck path. St001007Number of simple modules with projective dimension 1 in the Nakayama algebra corresponding to the Dyck path. St001008Number of indecomposable injective modules with projective dimension 1 in the Nakayama algebra corresponding to the Dyck path. St001009Number of indecomposable injective modules with projective dimension g when g is the global dimension of the Nakayama algebra corresponding to the Dyck path. St001013Number of indecomposable injective modules with codominant dimension equal to the global dimension in the Nakayama algebra corresponding to the Dyck path. St001014Number of indecomposable injective modules with codominant dimension equal to the dominant dimension of the Nakayama algebra corresponding to the Dyck path. St001015Number of indecomposable injective modules with codominant dimension equal to one in the Nakayama algebra corresponding to the Dyck path. St001016Number of indecomposable injective modules with codominant dimension at most 1 in the Nakayama algebra corresponding to the Dyck path. St001017Number of indecomposable injective modules with projective dimension equal to the codominant dimension in the Nakayama algebra corresponding to the Dyck path. St001019Sum of the projective dimensions of the simple modules in the Nakayama algebra corresponding to the Dyck path. St001048The number of leaves in the subtree containing 1 in the decreasing labelled binary unordered tree associated with the perfect matching. St001050The number of terminal closers of a set partition. St001051The depth of the label 1 in the decreasing labelled unordered tree associated with the set partition. St001052The length of the exterior of a permutation. St001055The Grundy value for the game of removing cells of a row in an integer partition. St001058The breadth of the ordered tree. St001070The absolute value of the derivative of the chromatic polynomial of the graph at 1. 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. St001102The number of words with multiplicities of the letters given by the composition, avoiding the consecutive pattern 132. St001103The number of words with multiplicities of the letters given by the partition, avoiding the consecutive pattern 123. St001118The acyclic chromatic index of a graph. St001126Number of simple module that are 1-regular in the corresponding Nakayama algebra. St001127The sum of the squares of the parts of a partition. St001176The size of a partition minus its first part. St001184Number of indecomposable injective modules with grade at least 1 in the corresponding Nakayama algebra. St001187The number of simple modules with grade at least one in the corresponding Nakayama algebra. 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 $g$. St001210Gives the maximal vector space dimension of the first Ext-group between an indecomposable module X and the regular module A, when A is the Nakayama algebra corresponding to the Dyck path. St001224Let X be the direct sum of all simple modules of the corresponding Nakayama algebra. St001235The global dimension of the corresponding Comp-Nakayama algebra. St001236The dominant dimension of the corresponding Comp-Nakayama algebra. St001241The number of non-zero radicals of the indecomposable projective modules that have injective dimension and projective dimension at most one. St001247The number of parts of a partition that are not congruent 2 modulo 3. St001249Sum of the odd parts of a partition. St001250The number of parts of a partition that are not congruent 0 modulo 3. St001252Half the sum of the even parts of a partition. St001267The length of the Lyndon factorization of the binary word. St001286The annihilation number of a graph. St001297The number of indecomposable non-injective projective modules minus the number of indecomposable non-injective projective modules that have reflexive Auslander-Reiten sequences in the corresponding Nakayama algebra. St001312Number of parabolic noncrossing partitions indexed by the composition. St001315The dissociation number of a graph. St001322The size of a minimal independent dominating set in a graph. St001337The upper domination number of a graph. St001338The upper irredundance number of a graph. St001339The irredundance number of a graph. St001342The number of vertices in the center of a graph. St001345The Hamming dimension of a graph. St001360The number of covering relations in Young's lattice below a partition. St001363The Euler characteristic of a graph according to Knill. St001365The number of lattice paths of the same length weakly above the path given by a binary word. St001366The maximal multiplicity of a degree of a vertex of a graph. St001368The number of vertices of maximal degree in a graph. St001372The length of a longest cyclic run of ones of a binary word. St001373The logarithm of the number of winning configurations of the lights out game on a graph. St001382The number of boxes in the diagram of a partition that do not lie in its Durfee square. St001387Number of standard Young tableaux of the skew shape tracing the border of the given partition. St001389The number of partitions of the same length below the given integer partition. St001390The number of bumps occurring when Schensted-inserting the letter 1 of a permutation. St001400The total number of Littlewood-Richardson tableaux of given shape. St001418Half of the global dimension of the stable Auslander algebra of the Nakayama algebra corresponding to the Dyck path. St001437The flex of a binary word. St001441The number of non-empty connected induced subgraphs of a graph. St001462The number of factors of a standard tableaux under concatenation. St001463The number of distinct columns in the nullspace of a graph. St001479The number of bridges of a graph. St001481The minimal height of a peak of a Dyck path. St001486The number of corners of the ribbon associated with an integer composition. St001499The number of indecomposable projective-injective modules of a magnitude 1 Nakayama algebra. St001527The cyclic permutation representation number of an integer partition. St001571The Cartan determinant of the integer partition. St001654The monophonic hull number of a graph. St001655The general position number of a graph. St001656The monophonic position number of a graph. St001659The number of ways to place as many non-attacking rooks as possible on a Ferrers board. St001674The number of vertices of the largest induced star graph in the graph. St001675The number of parts equal to the part in the reversed composition. St001691The number of kings in a 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. St001779The order of promotion on the set of linear extensions of a poset. St001780The order of promotion on the set of standard tableaux of given shape. St001786The number of total orderings of the north steps of a Dyck path such that steps after the k-th east step are not among the first k positions in the order. St001806The upper middle entry of a permutation. St001808The box weight or horizontal decoration of a Dyck path. St001809The index of the step at the first peak of maximal height in a Dyck path. St001813The product of the sizes of the principal order filters in a poset. St001814The number of partitions interlacing the given partition. St001816Eigenvalues of the top-to-random operator acting on a simple module. St001826The maximal number of leaves on a vertex of a graph. St001828The Euler characteristic 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. St001910The height of the middle non-run of a Dyck path. St001917The order of toric promotion on the set of labellings of a graph. St001933The largest multiplicity of a part in an integer partition. St000002The number of occurrences of the pattern 123 in a permutation. St000008The major index of the composition. St000009The charge of a standard tableau. St000021The number of descents of a permutation. St000024The number of double up and double down steps of a Dyck path. St000027The major index of a Dyck path. St000042The number of crossings of a perfect matching. St000052The number of valleys of a Dyck path not on the x-axis. St000094The depth of an ordered tree. St000145The Dyson rank of a partition. St000154The sum of the descent bottoms of a permutation. St000156The Denert index of a permutation. St000168The number of internal nodes of an ordered tree. St000169The cocharge of a standard tableau. St000211The rank of the set partition. St000214The number of adjacencies of a permutation. St000233The number of nestings of a set partition. St000238The number of indices that are not small weak excedances. St000259The diameter of a connected graph. St000292The number of ascents of a binary word. St000305The inverse major index of a permutation. St000313The number of degree 2 vertices of a graph. St000316The number of non-left-to-right-maxima of a permutation. St000319The spin of an integer partition. St000320The dinv adjustment of an integer partition. St000330The (standard) major index of a standard tableau. St000332The positive inversions of an alternating sign matrix. St000340The number of non-final maximal constant sub-paths of length greater than one. St000365The number of double ascents of a permutation. St000369The dinv deficit of a Dyck path. St000372The number of mid points of increasing subsequences of length 3 in a permutation. St000373The number of weak exceedences of a permutation that are also mid-points of a decreasing subsequence of length $3$. St000377The dinv defect of an integer partition. St000378The diagonal inversion number of an integer partition. St000380Half of the maximal perimeter of a rectangle fitting into the diagram of an integer partition. St000410The tree factorial of an ordered tree. St000419The number of Dyck paths that are weakly above the Dyck path, except for the path itself. St000428The number of occurrences of the pattern 123 or of the pattern 213 in a permutation. St000439The position of the first down step of a Dyck path. St000442The maximal area to the right of an up step of a Dyck path. St000461The rix statistic of a permutation. St000488The number of cycles of a permutation of length at most 2. St000489The number of cycles of a permutation of length at most 3. St000496The rcs statistic of a set partition. St000519The largest length of a factor maximising the subword complexity. St000521The number of distinct subtrees of an ordered tree. St000533The minimum of the number of parts and the size of the first part of an integer partition. St000546The number of global descents of a permutation. St000625The sum of the minimal distances to a greater element. St000648The number of 2-excedences of a permutation. St000654The first descent of a permutation. St000662The staircase size of the code of a permutation. St000692Babson and Steingrímsson's statistic of a permutation. St000718The largest Laplacian eigenvalue of a graph if it is integral. St000724The label of the leaf of the path following the smaller label in the increasing binary tree associated to a permutation. St000727The largest label of a leaf in the binary search tree associated with the permutation. St000778The metric dimension of a graph. St000783The side length of the largest staircase partition fitting into a partition. St000825The sum of the major and the inverse major index of a permutation. St000837The number of ascents of distance 2 of a permutation. St000840The number of closers smaller than the largest opener in a perfect matching. St000845The maximal number of elements covered by an element in a poset. St000846The maximal number of elements covering an element of a poset. St000864The number of circled entries of the shifted recording tableau of a permutation. St000868The aid statistic in the sense of Shareshian-Wachs. St000873The aix statistic of a permutation. St000887The maximal number of nonzero entries on a diagonal of a permutation matrix. St000915The Ore degree of a graph. St000921The number of internal inversions of a binary word. St000923The minimal number with no two order isomorphic substrings of this length in a permutation. St000932The number of occurrences of the pattern UDU in a Dyck path. St000947The major index east count of a Dyck path. St000961The shifted major index of a permutation. St000979Half of MacMahon's equal index of a Dyck path. St001074The number of inversions of the cyclic embedding of a permutation. St001079The minimal length of a factorization of a permutation using the permutations (12)(34). St001082The number of boxed occurrences of 123 in a permutation. St001084The number of occurrences of the vincular pattern |1-23 in a permutation. St001087The number of occurrences of the vincular pattern |12-3 in a permutation. St001091The number of parts in an integer partition whose next smaller part has the same size. St001094The depth index of a set partition. 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. St001115The number of even descents of a permutation. 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. St001130The number of two successive successions in a permutation. St001153The number of blocks with even minimum in a set partition. St001172The number of 1-rises at odd height of a Dyck path. St001180Number of indecomposable injective modules with projective dimension at most 1. St001189The number of simple modules with dominant and codominant dimension equal to zero in the Nakayama algebra corresponding to the Dyck path. St001194The injective dimension of $A/AfA$ in the corresponding Nakayama algebra $A$ when $Af$ is the minimal faithful projective-injective left $A$-module St001211The number of simple modules in the corresponding Nakayama algebra that have vanishing second Ext-group with the regular module. St001213The number of indecomposable modules in the corresponding Nakayama algebra that have vanishing first Ext-group with the regular module. St001226The number of integers i such that the radical of the i-th indecomposable projective module has vanishing first extension group with the Jacobson radical J in the corresponding Nakayama algebra. St001233The number of indecomposable 2-dimensional modules with projective dimension one. St001259The vector space dimension of the double dual of D(A) in 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. St001279The sum of the parts of an integer partition that are at least two. St001287The number of primes obtained by multiplying preimage and image of a permutation and subtracting one. St001323The independence gap of a graph. St001340The cardinality of a minimal non-edge isolating set of a graph. St001384The number of boxes in the diagram of a partition that do not lie in the largest triangle it contains. St001391The disjunction number of a graph. St001392The largest nonnegative integer which is not a part and is smaller than the largest part of the partition. St001428The number of B-inversions of a signed permutation. St001436The index of a given binary word in the lex-order among all its cyclic shifts. St001484The number of singletons of an integer partition. St001489The maximum of the number of descents and the number of inverse descents. 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. St001512The minimum rank of a graph. St001541The Gini index of an integer partition. St001584The area statistic between a Dyck path and its bounce path. St001649The length of a longest trail in a graph. St001671Haglund's hag of a permutation. St001682The number of distinct positions of the pattern letter 1 in occurrences of 123 in a permutation. St001697The shifted natural comajor index of a standard Young tableau. St001714The number of subpartitions of an integer partition that do not dominate the conjugate subpartition. St001718The number of non-empty open intervals in a poset. St001721The degree of a binary word. St001723The differential of a graph. St001724The 2-packing differential of a graph. St001777The number of weak descents in an integer composition. St001798The difference of the number of edges in a graph and the number of edges in the complement of the Turán graph. St001827The number of two-component spanning forests of a graph. St001869The maximum cut size of a graph. St001907The number of Bastidas - Hohlweg - Saliola excedances of a signed permutation. St001918The degree of the cyclic sieving polynomial corresponding to an integer partition. St001925The minimal number of zeros in a row of an alternating sign matrix. St001949The rigidity index of a graph. St000438The position of the last up step in a Dyck path. St000520The number of patterns in a permutation. St000806The semiperimeter of the associated bargraph. St000826The stopping time of the decimal representation of the binary word for the 3x+1 problem. St000060The greater neighbor of the maximum. St001480The number of simple summands of the module J^2/J^3. St000061The number of nodes on the left branch of a binary tree. St000064The number of one-box pattern of a permutation. St000082The number of elements smaller than a binary tree in Tamari order. St000280The size of the preimage of the map 'to labelling permutation' from Parking functions to Permutations. St000471The sum of the ascent tops of a permutation. St000485The length of the longest cycle of a permutation. St000487The length of the shortest cycle of a permutation. St000656The number of cuts of a poset. St000673The number of non-fixed points of a permutation. St000674The number of hills of a Dyck path. St000680The Grundy value for Hackendot on posets. St000717The number of ordinal summands of a poset. St000844The size of the largest block in the direct sum decomposition of a permutation. St000906The length of the shortest maximal chain in a poset. St001005The number of indices for a permutation that are either left-to-right maxima or right-to-left minima but not both. St001346The number of parking functions that give the same permutation. St000216The absolute length of a permutation. St000530The number of permutations with the same descent word as the given permutation. St000619The number of cyclic descents of a permutation. St000642The size of the smallest orbit of antichains under Panyushev complementation. St000643The size of the largest orbit of antichains under Panyushev complementation. St000652The maximal difference between successive positions of a permutation. St000695The number of blocks in the first part of the atomic decomposition of a set partition. St000729The minimal arc length of a set partition. St000730The maximal arc length of a set partition. St000794The mak of a permutation. St000809The reduced reflection length of the permutation. St000888The maximal sum of entries on a diagonal of an alternating sign matrix. St000892The maximal number of nonzero entries on a diagonal of an alternating sign matrix. St000925The number of topologically connected components of a set partition. St000946The sum of the skew hook positions in a Dyck path. St000956The maximal displacement of a permutation. St000957The number of Bruhat lower covers of a permutation. St000988The orbit size of a permutation under Foata's bijection. St000990The first ascent of a permutation. St001076The minimal length of a factorization of a permutation into transpositions that are cyclic shifts of (12). St001077The prefix exchange distance of a permutation. St001199The dominant dimension of $eAe$ for the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. St001246The maximal difference between two consecutive entries of a permutation. St001498The normalised height of a Nakayama algebra with magnitude 1. St001959The product of the heights of the peaks of a Dyck path. St000083The number of left oriented leafs of a binary tree except the first one. St000247The number of singleton blocks of a set partition. St000354The number of recoils of a permutation. St000376The bounce deficit of a Dyck path. St000434The number of occurrences of the pattern 213 or of the pattern 312 in a permutation. St000437The number of occurrences of the pattern 312 or of the pattern 321 in a permutation. St000491The number of inversions of a set partition. St000497The lcb statistic of a set partition. St000538The number of even inversions of a permutation. St000539The number of odd inversions of a permutation. St000541The number of indices greater than or equal to 2 of a permutation such that all smaller indices appear to its right. St000555The number of occurrences of the pattern {{1,3},{2}} in a set partition. St000572The dimension exponent of a set partition. St000581The number of occurrences of the pattern {{1,3},{2}} such that 1 is minimal, 2 is maximal. St000582The number of occurrences of the pattern {{1,3},{2}} such that 1 is minimal, 3 is maximal, (1,3) are consecutive in a block. St000585The number of occurrences of the pattern {{1,3},{2}} such that 2 is maximal, (1,3) are consecutive in a block. St000594The number of occurrences of the pattern {{1,3},{2}} such that 1,2 are minimal, (1,3) are consecutive in a block. St000600The number of occurrences of the pattern {{1,3},{2}} such that 1 is minimal, (1,3) are consecutive in a block. St000602The number of occurrences of the pattern {{1,3},{2}} such that 1 is minimal. St000610The number of occurrences of the pattern {{1,3},{2}} such that 2 is maximal. St000613The number of occurrences of the pattern {{1,3},{2}} such that 2 is minimal, 3 is maximal, (1,3) are consecutive in a block. St000711The number of big exceedences of a permutation. St000795The mad of a permutation. St000799The number of occurrences of the vincular pattern |213 in a permutation. St000800The number of occurrences of the vincular pattern |231 in a permutation. St000829The Ulam distance of a permutation to the identity permutation. St000831The number of indices that are either descents or recoils. St000866The number of admissible inversions of a permutation in the sense of Shareshian-Wachs. St001035The convexity degree of the parallelogram polyomino associated with the Dyck path. St001061The number of indices that are both descents and recoils of a permutation. St000100The number of linear extensions of a poset. St000248The number of anti-singletons of a set partition. St000249The number of singletons (St000247) plus the number of antisingletons (St000248) of a set partition. St000250The number of blocks (St000105) plus the number of antisingletons (St000248) of a set partition. St000294The number of distinct factors of a binary word. St000326The position of the first one in a binary word after appending a 1 at the end. St000477The weight of a partition according to Alladi. St000504The cardinality of the first block of a set partition. St000518The number of distinct subsequences in a binary word. St000668The least common multiple of the parts of the partition. 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. St000823The number of unsplittable factors of the set partition. St000890The number of nonzero entries in an alternating sign matrix. St000894The trace of an alternating sign matrix. St000981The length of the longest zigzag subpath. St000993The multiplicity of the largest part of an integer partition. St001062The maximal size of a block of a set partition. St001075The minimal size of a block of a set partition. St000197The number of entries equal to positive one in the alternating sign matrix. St000296The length of the symmetric border of a binary word. St000297The number of leading ones in a binary word. St000391The sum of the positions of the ones in a binary word. St000472The sum of the ascent bottoms of a permutation. St000490The intertwining number of a set partition. St000492The rob statistic of a set partition. St000493The los statistic of a set partition. St000498The lcs statistic of a set partition. St000499The rcb statistic of a set partition. St000502The number of successions of a set partitions. 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. St000564The number of occurrences of the pattern {{1},{2}} in a set partition. St000567The sum of the products of all pairs of parts. St000577The number of occurrences of the pattern {{1},{2}} such that 1 is a maximal element. St000578The number of occurrences of the pattern {{1},{2}} such that 1 is a singleton. St000579The number of occurrences of the pattern {{1},{2}} such that 2 is a maximal element. St000639The number of relations in a poset. St000641The number of non-empty boolean intervals in a poset. St000681The Grundy value of Chomp on Ferrers diagrams. St000693The modular (standard) major index of a standard tableau. St000704The number of semistandard tableaux on a given integer partition with minimal maximal entry. St000714The number of semistandard Young tableau of given shape, with entries at most 2. St000744The length of the path to the largest entry in a standard Young tableau. St000796The stat' of a permutation. St000797The stat`` of a permutation. St000798The makl of a permutation. St000813The number of zero-one matrices with weakly decreasing column sums and row sums given by the partition. St000833The comajor index of a permutation. St000877The depth of the binary word interpreted as a path. St000878The number of ones minus the number of zeros of a binary word. St000886The number of permutations with the same antidiagonal sums. St000898The number of maximal entries in the last diagonal of the monotone triangle. St000910The number of maximal chains of minimal length in a poset. St000914The sum of the values of the Möbius function of a poset. St000922The minimal number such that all substrings of this length are unique. St000983The length of the longest alternating subword. St001080The minimal length of a factorization of a permutation using the transposition (12) and the cycle (1,. St001081The number of minimal length factorizations of a permutation into star transpositions. St001128The exponens consonantiae of a partition. St001220The width of a permutation. St001313The number of Dyck paths above the lattice path given by a binary word. St001371The length of the longest Yamanouchi prefix of a binary word. St001415The length of the longest palindromic prefix of a binary word. St001416The length of a longest palindromic factor of a binary word. St001417The length of a longest palindromic subword of a binary word. St001419The length of the longest palindromic factor beginning with a one of a binary word. St001500The global dimension of magnitude 1 Nakayama algebras. St001884The number of borders of a binary word. St001914The size of the orbit of an integer partition in Bulgarian solitaire. St000225Difference between largest and smallest parts in a partition. St000290The major index of a binary word. St000295The length of the border of a binary word. St000432The number of occurrences of the pattern 231 or of the pattern 312 in a permutation. St000435The number of occurrences of the pattern 213 or of the pattern 231 in a permutation. St000436The number of occurrences of the pattern 231 or of the pattern 321 in a permutation. St000462The major index minus the number of excedences of a permutation. St000494The number of inversions of distance at most 3 of a permutation. St000495The number of inversions of distance at most 2 of a permutation. St000554The number of occurrences of the pattern {{1,2},{3}} in a set partition. St000556The number of occurrences of the pattern {{1},{2,3}} in a set partition. St000586The number of occurrences of the pattern {{1},{2,3}} such that 2 is minimal. St000589The number of occurrences of the pattern {{1},{2,3}} such that 1 is maximal, (2,3) are consecutive in a block. St000590The number of occurrences of the pattern {{1},{2,3}} such that 2 is minimal, 1 is maximal, (2,3) are consecutive in a block. St000595The number of occurrences of the pattern {{1},{2,3}} such that 1 is minimal. St000597The number of occurrences of the pattern {{1},{2,3}} such that 2 is minimal, (2,3) are consecutive in a block. St000598The number of occurrences of the pattern {{1},{2,3}} such that 1,2 are minimal, 3 is maximal, (2,3) are consecutive in a block. St000599The number of occurrences of the pattern {{1},{2,3}} such that (2,3) are consecutive in a block. St000601The number of occurrences of the pattern {{1},{2,3}} such that 1,2 are minimal, (2,3) are consecutive in a block. St000605The number of occurrences of the pattern {{1},{2,3}} such that 3 is maximal, (2,3) are consecutive in a block. St000606The number of occurrences of the pattern {{1},{2,3}} such that 1,3 are maximal, (2,3) are consecutive in a block. St000607The number of occurrences of the pattern {{1},{2,3}} such that 2 is minimal, 3 is maximal, (2,3) are consecutive in a block. St000609The number of occurrences of the pattern {{1},{2,3}} such that 1,2 are minimal. St000611The number of occurrences of the pattern {{1},{2,3}} such that 1 is maximal. St000612The number of occurrences of the pattern {{1},{2,3}} such that 1 is minimal, (2,3) are consecutive in a block. St000614The number of occurrences of the pattern {{1},{2,3}} such that 1 is minimal, 3 is maximal, (2,3) are consecutive in a block. St000620The number of standard tableaux of shape equal to the given partition such that the minimal cyclic descent is odd. St000646The number of big ascents of a permutation. St000682The Grundy value of Welter's game on a binary word. St000691The number of changes of a binary word. St000710The number of big deficiencies of a permutation. St000732The number of double deficiencies of a permutation. St000747A variant of the major index of a set partition. St000801The number of occurrences of the vincular pattern |312 in a permutation. St000802The number of occurrences of the vincular pattern |321 in a permutation. St000803The number of occurrences of the vincular pattern |132 in a permutation. St000836The number of descents of distance 2 of a permutation. St000931The number of occurrences of the pattern UUU in a Dyck path. St001078The minimal number of occurrences of (12) in a factorization of a permutation into transpositions (12) and cycles (1,. St001280The number of parts of an integer partition that are at least two. St001388The number of non-attacking neighbors of a permutation. St001485The modular major index of a binary word. St001502The global dimension minus the dominant dimension of magnitude 1 Nakayama algebras. St001552The number of inversions between excedances and fixed points of a permutation. St001684The reduced word complexity of a permutation. St001880The number of 2-Gorenstein indecomposable injective modules in the incidence algebra of the lattice. St001879The number of indecomposable summands of the top of the first syzygy of the dual of the regular module in the incidence algebra of the lattice. St001432The order dimension of the partition. St000474Dyson's crank of a partition. St000949Gives the number of generalised tilting modules of the corresponding LNakayama algebra. St001182Number of indecomposable injective modules with codominant dimension at least two in the corresponding Nakayama algebra. St001255The vector space dimension of the double dual of A/J when A is the corresponding Nakayama algebra with Jacobson radical J. St001570The minimal number of edges to add to make a graph Hamiltonian. St000045The number of linear extensions of a binary tree. St001003The number of indecomposable modules with projective dimension at most 1 in the Nakayama algebra corresponding to the Dyck path. St001060The distinguishing index of a graph. St001785The number of ways to obtain a partition as the multiset of antidiagonal lengths of the Ferrers diagram of a partition. St000219The number of occurrences of the pattern 231 in a permutation. St000456The monochromatic index of a connected graph. St000509The diagonal index (content) of a partition. St000689The maximal n such that the minimal generator-cogenerator module in the LNakayama algebra of a Dyck path is n-rigid. St000832The number of permutations obtained by reversing blocks of three consecutive numbers. St000937The number of positive values of the symmetric group character corresponding to the partition. St001066The number of simple reflexive modules in the corresponding Nakayama algebra. St001124The multiplicity of the standard representation in the Kronecker square corresponding to a partition. St001238The number of simple modules S such that the Auslander-Reiten translate of S is isomorphic to the Nakayama functor applied to the second syzygy of S. St001355Number of non-empty prefixes of a binary word that contain equally many 0's and 1's. St001420Half the length of a longest factor which is its own reverse-complement of a binary word. St001421Half the length of a longest factor which is its own reverse-complement and begins with a one of a binary word. St001483The number of simple module modules that appear in the socle of the regular module but have no nontrivial selfextensions with the regular module. St001514The dimension of the top of the Auslander-Reiten translate of the regular modules as a bimodule. St001515The vector space dimension of the socle of the first syzygy module of the regular module (as a bimodule). St001948The number of augmented double ascents of a permutation. St000159The number of distinct parts of the integer partition. St000549The number of odd partial sums of an integer partition. St000677The standardized bi-alternating inversion number of a permutation. St000697The number of 3-rim hooks removed from an integer partition to obtain its associated 3-core. St000970Number of peaks minus the dominant dimension of the corresponding LNakayama algebra. St001036The number of inner corners of the parallelogram polyomino associated with the Dyck path. St001037The number of inner corners of the upper path of the parallelogram polyomino associated with the Dyck path. St001163The number of simple modules with dominant dimension at least three in the corresponding Nakayama algebra. St001167The number of simple modules that appear as the top of an indecomposable non-projective modules that is reflexive in the corresponding Nakayama algebra. St001219Number of simple modules S in the corresponding Nakayama algebra such that the Auslander-Reiten sequence ending at S has the property that all modules in the exact sequence are reflexive. St001253The number of non-projective indecomposable reflexive modules in the corresponding Nakayama algebra. St001414Half the length of the longest odd length palindromic prefix of a binary word. St001424The number of distinct squares in a binary word. St001557The number of inversions of the second entry of a permutation. St001811The Castelnuovo-Mumford regularity of a permutation. St001960The number of descents of a permutation minus one if its first entry is not one. St001123The multiplicity of the dual of the standard representation in the Kronecker square corresponding to a 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 $eA$. 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. St001604The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on polygons. St000512The number of invariant subsets of size 3 when acting with a permutation of given cycle type. 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. St000284The Plancherel distribution on integer partitions. St000514The number of invariant simple graphs when acting with a permutation of given cycle type. St000901The cube of the number of standard Young tableaux with shape given by the partition. St000515The number of invariant set partitions when acting with a permutation of given cycle type. 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. St000707The product of the factorials of the parts. 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. 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. 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. St000706The product of the factorials of the multiplicities of an integer partition. St000938The number of zeros of the symmetric group character corresponding to the partition. St000939The number of characters of the symmetric group whose value on the partition is positive. 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. St000997The even-odd crank of an integer partition. St001097The coefficient of the monomial symmetric function indexed by the partition in the formal group law for linear orders. 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. St001568The smallest positive integer that does not appear twice in the partition. St001603The number of colourings of a polygon such that the multiplicities of a colour are given by a partition. St001605The number of colourings of a cycle such that the multiplicities of colours are given by a partition. St000478Another weight of a partition according to Alladi. St000510The number of invariant oriented cycles when acting with a permutation of given cycle type. St000928The sum of the coefficients of the character polynomial of an integer partition. St000929The constant term of the character polynomial of an integer partition. St000934The 2-degree of an integer partition. St000713The dimension of the irreducible representation of Sp(4) labelled by an integer partition. St000927The alternating sum of the coefficients of the character polynomial of an integer partition. St000716The dimension of the irreducible representation of Sp(6) labelled by an integer partition. St001615The number of join prime elements of a lattice. St001617The dimension of the space of valuations of a lattice. St001136The largest label with larger sister in the leaf labelled binary unordered tree associated with the perfect matching. St001553The number of indecomposable summands of the square of the Jacobson radical as a bimodule in the Nakayama algebra corresponding to the Dyck path. St000134The size of the orbit of an alternating sign matrix under gyration. St001045The number of leaves in the subtree not containing one in the decreasing labelled binary unordered tree associated with the perfect matching. St001132The number of leaves in the subtree whose sister has label 1 in the decreasing labelled binary unordered tree associated with the perfect matching. St001526The Loewy length of the Auslander-Reiten translate of the regular module as a bimodule of the Nakayama algebra corresponding to the Dyck path. St001134The largest label in the subtree rooted at the sister of 1 in the leaf labelled binary unordered tree associated with the perfect matching. St001152The number of pairs with even minimum in a perfect matching. St001468The smallest fixpoint of a permutation. St000199The column of the unique '1' in the last row of the alternating sign matrix. St000200The row of the unique '1' in the last column of the alternating sign matrix. St000670The reversal length of a permutation. St000780The size of the orbit under rotation of a perfect matching. St000882The number of connected components of short braid edges in the graph of braid moves of a permutation. St000945The number of matchings in the dihedral orbit of a perfect matching. St001041The depth of the label 1 in the decreasing labelled binary unordered tree associated with the perfect matching. St001131The number of trivial trees on the path to label one in the decreasing labelled binary unordered tree associated with the perfect matching. St001429The number of negative entries in a signed permutation. St001488The number of corners of a skew partition. St001555The order of a signed permutation. St001760The number of prefix or suffix reversals needed to sort a permutation. St001863The number of weak excedances of a signed permutation. St001889The size of the connectivity set of a signed permutation. St000034The maximum defect over any reduced expression for a permutation and any subexpression. St000111The sum of the descent tops (or Genocchi descents) of a permutation. St000119The number of occurrences of the pattern 321 in a permutation. St000123The difference in Coxeter length of a permutation and its image under the Simion-Schmidt map. St000217The number of occurrences of the pattern 312 in a permutation. St000222The number of alignments in the permutation. St000223The number of nestings in the permutation. St000235The number of indices that are not cyclical small weak excedances. St000317The cycle descent number of a permutation. St000358The number of occurrences of the pattern 31-2. St000367The number of simsun double descents of a permutation. St000371The number of mid points of decreasing subsequences of length 3 in a permutation. St000423The number of occurrences of the pattern 123 or of the pattern 132 in a permutation. St000424The number of occurrences of the pattern 132 or of the pattern 231 in a permutation. St000426The number of occurrences of the pattern 132 or of the pattern 312 in a permutation. St000427The number of occurrences of the pattern 123 or of the pattern 231 in a permutation. St000430The number of occurrences of the pattern 123 or of the pattern 312 in a permutation. St000431The number of occurrences of the pattern 213 or of the pattern 321 in a permutation. St000433The number of occurrences of the pattern 132 or of the pattern 321 in a permutation. St000457The number of occurrences of one of the patterns 132, 213 or 321 in a permutation. St000483The number of times a permutation switches from increasing to decreasing or decreasing to increasing. St000647The number of big descents of a permutation. St000719The number of alignments in a perfect matching. St000787The number of flips required to make a perfect matching noncrossing. St001010Number of indecomposable injective modules with projective dimension g-1 when g is the global dimension of the Nakayama algebra corresponding to the Dyck path. St001021Sum of the differences between projective and codominant dimension of the non-projective indecomposable injective modules in the Nakayama algebra corresponding to the Dyck path. St001040The depth of the decreasing labelled binary unordered tree associated with the perfect matching. St001089Number of indecomposable projective non-injective modules minus the number of indecomposable projective non-injective modules with dominant dimension equal to the injective dimension in the corresponding Nakayama algebra. 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. St001229The vector space dimension of the first extension group between the Jacobson radical J and J^2. St001263The index of the maximal parabolic seaweed algebra associated with the composition. St001379The number of inversions plus the major index of a permutation. St001402The number of separators in a permutation. St001411The number of patterns 321 or 3412 in a permutation. St001524The degree of symmetry of a binary word. St001727The number of invisible inversions of a permutation. St001742The difference of the maximal and the minimal degree in a graph. St001744The number of occurrences of the arrow pattern 1-2 with an arrow from 1 to 2 in a permutation. St001772The number of occurrences of the signed pattern 12 in a signed permutation. St001810The number of fixed points of a permutation smaller than its largest moved point. St001834The number of non-isomorphic minors of a graph. St001911A descent variant minus the number of inversions. St001473The absolute value of the sum of all entries of the Coxeter matrix of the corresponding LNakayama algebra. St001872The number of indecomposable injective modules with even projective dimension in the corresponding Nakayama algebra. St001431Half of the Loewy length minus one of a modified stable Auslander algebra of the Nakayama algebra corresponding to the Dyck path. St000327The number of cover relations in a poset. St001637The number of (upper) dissectors of a poset. St001668The number of points of the poset minus the width of the poset. St000896The number of zeros on the main diagonal of an alternating sign matrix. St001491The number of indecomposable projective-injective modules in the algebra corresponding to a subset. 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 $eA$. St001927Sparre Andersen's number of positives of a signed permutation. St001165Number of simple modules with even projective dimension in the corresponding Nakayama algebra. St001207The Lowey length of the algebra $A/T$ when $T$ is the 1-tilting module corresponding to the permutation in the Auslander algebra of $K[x]/(x^n)$. St001583The projective dimension of the simple module corresponding to the point in the poset of the symmetric group under bruhat order. St001804The minimal height of the rectangular inner shape in a cylindrical tableau associated to a tableau. 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. St001212The number of simple modules in the corresponding Nakayama algebra that have non-zero second Ext-group with the regular module. St001244The number of simple modules of projective dimension one that are not 1-regular for the Nakayama algebra associated to a Dyck path. St001507The sum of projective dimension of simple modules with even projective dimension divided by 2 in the LNakayama algebra corresponding to Dyck paths. St001873For a Nakayama algebra corresponding to a Dyck path, we define the matrix C with entries the Hom-spaces between $e_i J$ and $e_j J$ (the radical of the indecomposable projective modules). St001817The number of flag weak exceedances of a signed permutation. St001892The flag excedance statistic of a signed permutation. St001629The coefficient of the integer composition in the quasisymmetric expansion of the relabelling action of the symmetric group on cycles. St001894The depth of a signed permutation. St001882The number of occurrences of a type-B 231 pattern in a signed permutation. St000035The number of left outer peaks of a permutation. St000742The number of big ascents of a permutation after prepending zero. St001693The excess length of a longest path consisting of elements and blocks of a set partition. St000356The number of occurrences of the pattern 13-2. St000834The number of right outer peaks of a permutation. St000884The number of isolated descents of a permutation. St001434The number of negative sum pairs of a signed permutation. St000044The number of vertices of the unicellular map given by a perfect matching. St000135The number of lucky cars of the parking function. St000186The sum of the first row in a Gelfand-Tsetlin pattern. St000201The number of leaf nodes in a binary tree. St000522The number of 1-protected nodes of a rooted tree. St000820The number of compositions obtained by rotating the composition. St000942The number of critical left to right maxima of the parking functions. St001000Number of indecomposable modules with projective dimension equal to the global dimension in the Nakayama algebra corresponding to the Dyck path. St001030Half the number of non-boundary horizontal edges in the fully packed loop corresponding to the alternating sign matrix. St001413Half the length of the longest even length palindromic prefix of a binary word. St001427The number of descents of a signed permutation. St001770The number of facets of a certain subword complex associated with the signed permutation. St001773The number of minimal elements in Bruhat order not less than the signed permutation. St001855The number of signed permutations less than or equal to a signed permutation in left weak order. St001903The number of fixed points of a parking function. St001904The length of the initial strictly increasing segment of a parking function. St001937The size of the center of a parking function. St000017The number of inversions of a standard tableau. St000136The dinv of a parking function. St000194The number of primary dinversion pairs of a labelled dyck path corresponding to a parking function. St000352The Elizalde-Pak rank of a permutation. St001086The number of occurrences of the consecutive pattern 132 in a permutation. St001209The pmaj statistic of a parking function. St001314The number of tilting modules of arbitrary projective dimension that have no simple modules as a direct summand in the corresponding Nakayama algebra. St001712The number of natural descents of a standard Young tableau. St001769The reflection length of a signed permutation. St001821The sorting index of a signed permutation. St001861The number of Bruhat lower covers of a permutation. St001864The number of excedances of a signed permutation. St001912The length of the preperiod in Bulgarian solitaire corresponding to an integer partition. St001935The number of ascents in a parking function. St001621The number of atoms of a lattice. St000628The balance of a binary word. St000753The Grundy value for the game of Kayles on a binary word. St001105The number of greedy linear extensions of a poset. St001106The number of supergreedy linear extensions of a poset. St001875The number of simple modules with projective dimension at most 1. St000848The balance constant multiplied with the number of linear extensions of a poset. St000849The number of 1/3-balanced pairs in a poset. St001582The grades of the simple modules corresponding to the points in the poset of the symmetric group under the Bruhat order. St001926Sparre Andersen's position of the maximum of a signed permutation. St000208Number of integral Gelfand-Tsetlin polytopes with prescribed top row and integer partition weight. 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. St001645The pebbling number of a connected graph.