St000697The number of 3-rim hooks removed from an integer partition to obtain its associated 3-core. St000870The product of the hook lengths of the diagonal cells in an integer partition. 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. St001380The number of monomer-dimer tilings of a Ferrers diagram. 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. St001023Number of simple modules with projective dimension at most 3 in the Nakayama algebra corresponding to the Dyck path. St001190Number of simple modules with projective dimension at most 4 in the corresponding Nakayama algebra. St001240The number of indecomposable modules e_i J^2 that have injective dimension at most one in the corresponding Nakayama algebra St001650The order of Ringel's homological bijection associated to the linear Nakayama algebra corresponding to the Dyck path. 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. St000053The number of valleys of the Dyck path. St000080The rank of the poset. St000306The bounce count of a Dyck path. St000327The number of cover relations in a poset. St000331The number of upper interactions of a Dyck path. St000476The sum of the semi-lengths of tunnels before a valley of a Dyck path. St000645The sum of the areas of the rectangles formed by two consecutive peaks and the valley in between. St000672The number of minimal elements in Bruhat order not less than the permutation. St000675The number of centered multitunnels of a Dyck path. St000689The maximal n such that the minimal generator-cogenerator module in the LNakayama algebra of a Dyck path is n-rigid. St000921The number of internal inversions of a binary word. St000932The number of occurrences of the pattern UDU in a Dyck path. St000954Number of times the corresponding LNakayama algebra has $Ext^i(D(A),A)=0$ for $i>0$. St001066The number of simple reflexive modules in the corresponding Nakayama algebra. St001067The number of simple modules of dominant dimension at least two in the corresponding Nakayama algebra. 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. St001197The global dimension of $eAe$ for the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. St001199The dominant 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. 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. 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. St001245The cyclic maximal difference between two consecutive entries of a permutation. 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. 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. St001483The number of simple module modules that appear in the socle of the regular module but have no nontrivial selfextensions with the regular module. St001499The number of indecomposable projective-injective modules of a magnitude 1 Nakayama algebra. St001503The largest distance of a vertex to a vertex in a cycle in the resolution quiver of the corresponding Nakayama algebra. 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. 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). St001637The number of (upper) dissectors of a poset. St001641The number of ascent tops in the flattened set partition such that all smaller elements appear before. St001668The number of points of the poset minus the width of the poset. St001723The differential of a graph. St001724The 2-packing differential of a graph. 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). St001925The minimal number of zeros in a row of an alternating sign matrix. St001955The number of natural descents for set-valued two row standard Young tableaux. St000011The number of touch points (or returns) of a Dyck path. St000015The number of peaks of a Dyck path. St000018The number of inversions of a permutation. St000019The cardinality of the support of a permutation. St000029The depth of a permutation. St000117The number of centered tunnels of a Dyck path. St000171The degree of the graph. St000189The number of elements in the poset. St000197The number of entries equal to positive one in the alternating sign matrix. St000209Maximum difference of elements in cycles. St000210Minimum over maximum difference of elements in cycles. St000216The absolute length of a permutation. St000229Sum of the difference between the maximal and the minimal elements of the blocks plus the number of blocks of a set partition. St000288The number of ones in a binary word. St000293The number of inversions of a binary word. St000336The leg major index of a standard tableau. St000389The number of runs of ones of odd length in a binary word. St000393The number of strictly increasing runs in a binary word. St000394The sum of the heights of the peaks of a Dyck path minus the number of peaks. St000423The number of occurrences of the pattern 123 or of the pattern 132 in a permutation. St000428The number of occurrences of the pattern 123 or of the pattern 213 in a permutation. St000445The number of rises of length 1 of a Dyck path. St000458The number of permutations obtained by switching adjacencies or successions. St000494The number of inversions of distance at most 3 of a permutation. St000528The height of a poset. St000617The number of global maxima of a Dyck path. St000636The hull number of a graph. St000674The number of hills of a Dyck path. St000676The number of odd rises of a Dyck path. St000678The number of up steps after the last double rise of a Dyck path. St000680The Grundy value for Hackendot on posets. 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. St000717The number of ordinal summands of a poset. St000744The length of the path to the largest entry in a standard Young tableau. St000809The reduced reflection length of the permutation. St000875The semilength of the longest Dyck word in the Catalan factorisation of a binary word. St000876The number of factors in the Catalan decomposition of a binary word. St000885The number of critical steps in the Catalan decomposition of a binary word. St000890The number of nonzero entries in an alternating sign matrix. St000906The length of the shortest maximal chain in a poset. St000912The number of maximal antichains in a poset. St000922The minimal number such that all substrings of this length are unique. St000923The minimal number with no two order isomorphic substrings of this length in a permutation. St000924The number of topologically connected components of a perfect matching. St000930The k-Gorenstein degree of the corresponding Nakayama algebra with linear quiver. St000944The 3-degree of an integer partition. St000957The number of Bruhat lower covers of a permutation. St000987The number of positive eigenvalues of the Laplacian matrix of the graph. St001004The number of indices that are either left-to-right maxima or right-to-left minima. St001017Number of indecomposable injective modules with projective dimension equal to the codominant dimension in the Nakayama algebra corresponding to the Dyck path. St001022Number of simple modules with projective dimension 3 in the Nakayama algebra corresponding to the Dyck path. St001024Maximum of dominant dimensions of the simple modules in the Nakayama algebra corresponding to the Dyck path. St001032The number of horizontal steps in the bicoloured Motzkin path associated with the Dyck path. St001034The area of the parallelogram polyomino associated with the Dyck path. St001038The minimal height of a column in the parallelogram polyomino associated with the Dyck path. St001039The maximal height of a column in the parallelogram polyomino associated with a Dyck path. St001068Number of torsionless simple modules in the corresponding Nakayama algebra. St001076The minimal length of a factorization of a permutation into transpositions that are cyclic shifts of (12). St001077The prefix exchange distance of a permutation. St001113Number of indecomposable projective non-injective modules with reflexive Auslander-Reiten sequences in the corresponding Nakayama algebra. St001135The projective dimension of the first simple module in the Nakayama algebra corresponding to the Dyck path. St001137Number of simple modules that are 3-regular in the corresponding Nakayama algebra. St001163The number of simple modules with dominant dimension at least three in the corresponding Nakayama algebra. St001167The number of simple modules that appear as the top of an indecomposable non-projective modules that is reflexive 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. St001180Number of indecomposable injective modules with projective dimension at most 1. St001181Number of indecomposable injective modules with grade at least 3 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. St001186Number of simple modules with grade at least 3 in the corresponding Nakayama algebra. 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 $eA$. 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: St001211The number of simple modules in the corresponding Nakayama algebra that have vanishing second Ext-group with the regular module. 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. 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. St001246The maximal difference between two consecutive entries of a permutation. St001253The number of non-projective indecomposable reflexive modules 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. St001266The largest vector space dimension of an indecomposable non-projective module that is reflexive in the corresponding Nakayama algebra. St001267The length of the Lyndon factorization of the binary word. St001287The number of primes obtained by multiplying preimage and image of a permutation and subtracting one. St001291The number of indecomposable summands of the tensor product of two copies of the dual of the Nakayama algebra associated to a Dyck path. St001342The number of vertices in the center of a graph. St001343The dimension of the reduced incidence algebra of a poset. St001348The bounce of the parallelogram polyomino associated with the Dyck path. St001416The length of a longest palindromic factor of a binary word. St001417The length of a longest palindromic subword of a binary word. St001437The flex of a binary word. St001480The number of simple summands of the module J^2/J^3. 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. St001523The degree of symmetry of a Dyck path. St001530The depth of a Dyck path. 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. St001636The number of indecomposable injective modules with projective dimension at most one in the incidence algebra of the poset. St001654The monophonic hull number of a graph. St001655The general position number of a graph. St001656The monophonic position number of a graph. St001688The sum of the squares of the heights of the peaks of a Dyck path. St001718The number of non-empty open intervals in a poset. St001733The number of weak left to right maxima of a Dyck path. St001910The height of the middle non-run of a Dyck path. St001956The comajor index for set-valued two-row standard Young tableaux. St001958The degree of the polynomial interpolating the values of a permutation. St000026The position of the first return of a Dyck path. St000044The number of vertices of the unicellular map given by a perfect matching. St000058The order of a permutation. St000485The length of the longest cycle of a permutation. St000487The length of the shortest cycle of a permutation. St000501The size of the first part in the decomposition of a permutation. St000643The size of the largest orbit of antichains under Panyushev complementation. St000673The number of non-fixed points of a permutation. St000718The largest Laplacian eigenvalue of a graph if it is integral. St000844The size of the largest block in the direct sum decomposition of a permutation. St000949Gives the number of generalised tilting modules of the corresponding LNakayama algebra. 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 $c_{n-1}$. St001005The number of indices for a permutation that are either left-to-right maxima or right-to-left minima but not both. St001012Number of simple modules with projective dimension at most 2 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. St001110The 3-dynamic chromatic number of a graph. 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. St001179Number of indecomposable injective modules with projective dimension at most 2 in the corresponding Nakayama algebra. St001182Number of indecomposable injective modules with codominant dimension at least two in the corresponding Nakayama algebra. St001237The number of simple modules with injective dimension at most one or dominant dimension at least one. St001255The vector space dimension of the double dual of A/J when A is the corresponding Nakayama algebra with Jacobson radical J. St001290The first natural number n such that the tensor product of n copies of D(A) is zero for the corresponding Nakayama algebra A. St001505The number of elements generated by the Dyck path as a map in the full transformation monoid. St001725The harmonious chromatic number of a graph. St001746The coalition number of a graph. St001782The order of rowmotion on the set of order ideals of a poset. St001800The number of 3-Catalan paths having this Dyck path as first and last coordinate projections. St001003The number of indecomposable modules with projective dimension at most 1 in the Nakayama algebra corresponding to the Dyck path. St001065Number of indecomposable reflexive modules in the corresponding Nakayama algebra. St001468The smallest fixpoint of a permutation. St001643The Frobenius dimension of the Nakayama algebra corresponding to the Dyck path. St001213The number of indecomposable modules in the corresponding Nakayama algebra that have vanishing first Ext-group with the regular module. St000001The number of reduced words for a permutation. St000017The number of inversions of a standard tableau. St000024The number of double up and double down steps of a Dyck path. St000028The number of stack-sorts needed to sort a permutation. St000036The evaluation at 1 of the Kazhdan-Lusztig polynomial with parameters given by the identity and the permutation. St000060The greater neighbor of the maximum. St000062The length of the longest increasing subsequence of the permutation. St000078The number of alternating sign matrices whose left key is the permutation. St000079The number of alternating sign matrices for a given Dyck path. St000081The number of edges of a graph. St000083The number of left oriented leafs of a binary tree except the first one. St000092The number of outer peaks of a permutation. St000093The cardinality of a maximal independent set of vertices of a graph. St000099The number of valleys of a permutation, including the boundary. St000133The "bounce" of a permutation. St000141The maximum drop size of a permutation. St000160The multiplicity of the smallest part of a partition. St000168The number of internal nodes of an ordered tree. St000245The number of ascents of a permutation. St000255The number of reduced Kogan faces with the permutation as type. St000259The diameter of a connected graph. St000271The chromatic index of a graph. St000276The size of the preimage of the map 'to graph' from Ordered trees to Graphs. St000296The length of the symmetric border of a binary word. St000307The number of rowmotion orbits of a poset. St000308The height of the tree associated to a permutation. St000316The number of non-left-to-right-maxima of a permutation. St000329The number of evenly positioned ascents of the Dyck path, with the initial position equal to 1. St000337The lec statistic, the sum of the inversion numbers of the hook factors of a permutation. St000338The number of pixed points of a permutation. St000358The number of occurrences of the pattern 31-2. St000385The number of vertices with out-degree 1 in a binary tree. St000388The number of orbits of vertices of a graph under automorphisms. St000402Half the size of the symmetry class of a permutation. St000414The binary logarithm of the number of binary trees with the same underlying unordered tree. St000425The number of occurrences of the pattern 132 or of the pattern 213 in a permutation. St000426The number of occurrences of the pattern 132 or of the pattern 312 in a permutation. St000432The number of occurrences of the pattern 231 or of the pattern 312 in a permutation. St000442The maximal area to the right of an up step of a Dyck path. St000457The number of occurrences of one of the patterns 132, 213 or 321 in a permutation. St000513The number of invariant subsets of size 2 when acting with a permutation of given cycle type. St000530The number of permutations with the same descent word as the given permutation. St000531The leading coefficient of the rook polynomial of an integer partition. St000538The number of even inversions of a permutation. St000539The number of odd inversions of a permutation. St000547The number of even non-empty partial sums of an integer partition. St000553The number of blocks of a graph. St000619The number of cyclic descents of a permutation. St000624The normalized sum of the minimal distances to a greater element. St000627The exponent of a binary word. St000631The number of distinct palindromic decompositions of a binary word. St000669The number of permutations obtained by switching ascents or descents of size 2. St000670The reversal length of a permutation. St000682The Grundy value of Welter's game on a binary word. St000706The product of the factorials of the multiplicities of an integer partition. St000723The maximal cardinality of a set of vertices with the same neighbourhood in a graph. St000741The Colin de Verdière graph invariant. St000743The number of entries in a standard Young tableau such that the next integer is a neighbour. St000786The maximal number of occurrences of a colour in a proper colouring of a graph. St000829The Ulam distance of a permutation to the identity permutation. St000832The number of permutations obtained by reversing blocks of three consecutive numbers. St000836The number of descents of distance 2 of a permutation. St000848The balance constant multiplied with the number of linear extensions of a poset. St000862The number of parts of the shifted shape of a permutation. St000880The number of connected components of long braid edges in the graph of braid moves of a permutation. St000887The maximal number of nonzero entries on a diagonal of a permutation matrix. St000920The logarithmic height of a Dyck path. St000937The number of positive values of the symmetric group character corresponding to the partition. St000956The maximal displacement of a permutation. St000982The length of the longest constant subword. St000989The number of final rises of a permutation. St000999Number of indecomposable projective module with injective dimension equal to the global dimension 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. St001027Number of simple modules with projective dimension equal to injective dimension in the Nakayama algebra corresponding to the Dyck path. St001052The length of the exterior of a permutation. St001056The Grundy value for the game of deleting vertices of a graph until it has no edges. St001057The Grundy value of the game of creating an independent set in a graph. St001096The size of the overlap set of a permutation. St001111The weak 2-dynamic chromatic number of a graph. St001112The 3-weak dynamic number of a graph. St001117The game chromatic index of a graph. St001118The acyclic chromatic index of a graph. St001119The length of a shortest maximal path in a graph. St001120The length of a longest path in a graph. St001160The number of proper blocks (or intervals) of a permutations. St001176The size of a partition minus its first part. St001192The maximal dimension of $Ext_A^2(S,A)$ for a simple module $S$ over the corresponding Nakayama algebra $A$. St001207The Lowey length of the algebra $A/T$ when $T$ is the 1-tilting module corresponding to the permutation in the Auslander algebra of $K[x]/(x^n)$. 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. St001220The width of a permutation. St001273The projective dimension of the first term in an injective coresolution of the regular module. St001274The number of indecomposable injective modules with projective dimension equal to two. St001282The number of graphs with the same chromatic polynomial. St001286The annihilation number of a graph. St001298The number of repeated entries in the Lehmer code of a permutation. St001332The number of steps on the non-negative side of the walk associated with the permutation. St001337The upper domination number of a graph. St001338The upper irredundance number of a graph. St001345The Hamming dimension of a graph. St001352The number of internal nodes in the modular decomposition of a graph. St001372The length of a longest cyclic run of ones of a binary word. St001391The disjunction number of a graph. St001405The number of bonds in a permutation. St001415The length of the longest palindromic prefix of a binary word. St001418Half of the global dimension of the stable Auslander algebra of the Nakayama algebra corresponding to the Dyck path. St001424The number of distinct squares in a binary word. St001431Half of the Loewy length minus one of a modified stable Auslander algebra of the Nakayama algebra corresponding to the Dyck path. St001436The index of a given binary word in the lex-order among all its cyclic shifts. St001479The number of bridges of a graph. St001481The minimal height of a peak of a Dyck path. St001489The maximum of the number of descents and the number of inverse descents. St001508The degree of the standard monomial associated to a Dyck path relative to the diagonal boundary. St001512The minimum rank of a graph. St001517The length of a longest pair of twins in a permutation. St001553The number of indecomposable summands of the square of the Jacobson radical as a bimodule in the Nakayama algebra corresponding to the Dyck path. St001569The maximal modular displacement of a permutation. St001571The Cartan determinant of the integer partition. St001601The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on trees. St001603The number of colourings of a polygon such that the multiplicities of a colour are given by a partition. St001606The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on set partitions. St001623The number of doubly irreducible elements of a lattice. St001630The global dimension of the incidence algebra of the lattice over the rational numbers. St001640The number of ascent tops in the permutation such that all smaller elements appear before. St001642The Prague dimension of a graph. St001649The length of a longest trail in a graph. St001652The length of a longest interval of consecutive numbers. St001659The number of ways to place as many non-attacking rooks as possible on a Ferrers board. St001662The length of the longest factor of consecutive numbers in a permutation. St001667The maximal size of a pair of weak twins for a permutation. St001716The 1-improper chromatic number of a graph. St001726The number of visible inversions of a permutation. St001727The number of invisible inversions of a permutation. St001734The lettericity of a graph. St001740The number of graphs with the same symmetric edge polytope as the given graph. St001741The largest integer such that all patterns of this size are contained in the permutation. St001744The number of occurrences of the arrow pattern 1-2 with an arrow from 1 to 2 in a permutation. St001758The number of orbits of promotion on a graph. St001765The number of connected components of the friends and strangers graph. St001774The degree of the minimal polynomial of the smallest eigenvalue of a graph. St001775The degree of the minimal polynomial of the largest eigenvalue of a graph. St001778The largest greatest common divisor of an element and its image in a permutation. St001801Half the number of preimage-image pairs of different parity in a permutation. St001826The maximal number of leaves on a vertex of a graph. St001827The number of two-component spanning forests of a graph. St001869The maximum cut size of a graph. St001884The number of borders of a binary word. St001917The order of toric promotion on the set of labellings of a graph. St001929The number of meanders with top half given by the noncrossing matching corresponding to the Dyck path. St001933The largest multiplicity of a part in an integer partition. St001951The number of factors in the disjoint direct product decomposition of the automorphism group of a graph. St000002The number of occurrences of the pattern 123 in a permutation. St000004The major index of a permutation. St000013The height of a Dyck path. St000021The number of descents of a permutation. St000023The number of inner peaks of a permutation. St000030The sum of the descent differences of a permutations. St000031The number of cycles in the cycle decomposition of a permutation. St000050The depth or height of a binary tree. St000051The size of the left subtree of a binary tree. St000052The number of valleys of a Dyck path not on the x-axis. St000064The number of one-box pattern of a permutation. St000067The inversion number of the alternating sign matrix. St000086The number of subgraphs. St000105The number of blocks in the set partition. St000118The number of occurrences of the contiguous pattern [.,[.,[.,.]]] in a binary tree. St000148The number of odd parts of a partition. St000149The number of cells of the partition whose leg is zero and arm is odd. St000150The floored half-sum of the multiplicities of a partition. St000155The number of exceedances (also excedences) of a permutation. St000156The Denert index of a permutation. St000162The number of nontrivial cycles in the cycle decomposition of a permutation. St000186The sum of the first row in a Gelfand-Tsetlin pattern. St000199The column of the unique '1' in the last row of the alternating sign matrix. St000211The rank of the set partition. St000213The number of weak exceedances (also weak excedences) of a permutation. St000220The number of occurrences of the pattern 132 in a permutation. St000222The number of alignments in the permutation. St000235The number of indices that are not cyclical small weak excedances. St000236The number of cyclical small weak excedances. St000240The number of indices that are not small excedances. St000242The number of indices that are not cyclical small weak excedances. St000246The number of non-inversions of a permutation. St000249The number of singletons (St000247) plus the number of antisingletons (St000248) of a set partition. St000251The number of nonsingleton blocks of a set partition. St000256The number of parts from which one can substract 2 and still get an integer partition. St000257The number of distinct parts of a partition that occur at least twice. St000290The major index of a binary word. St000292The number of ascents of a binary word. St000294The number of distinct factors of a binary word. St000295The length of the border of a binary word. St000299The number of nonisomorphic vertex-induced subtrees. St000309The number of vertices with even degree. St000313The number of degree 2 vertices of a graph. St000314The number of left-to-right-maxima of a permutation. St000332The positive inversions of an alternating sign matrix. St000333The dez statistic, the number of descents of a permutation after replacing fixed points by zeros. St000334The maz index, the major index of a permutation after replacing fixed points by zeros. St000339The maf index of a permutation. St000345The number of refinements of a partition. St000353The number of inner valleys of a permutation. St000354The number of recoils of a permutation. St000356The number of occurrences of the pattern 13-2. St000365The number of double ascents of a permutation. St000372The number of mid points of increasing subsequences of length 3 in a permutation. St000374The number of exclusive right-to-left minima of a permutation. St000381The largest part of an integer composition. St000382The first part of an integer composition. St000383The last part of an integer composition. St000384The maximal part of the shifted composition of an integer partition. St000427The number of occurrences of the pattern 123 or of the pattern 231 in a permutation. St000429The number of occurrences of the pattern 123 or of the pattern 321 in a permutation. St000431The number of occurrences of the pattern 213 or of the pattern 321 in a permutation. St000434The number of occurrences of the pattern 213 or of the pattern 312 in a permutation. St000436The number of occurrences of the pattern 231 or of the pattern 321 in a permutation. St000437The number of occurrences of the pattern 312 or of the pattern 321 in a permutation. St000441The number of successions of a permutation. St000443The number of long tunnels of a Dyck path. St000448The number of pairs of vertices of a graph with distance 2. 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. St000461The rix statistic of a permutation. St000468The Hosoya index of a graph. St000479The Ramsey number of a graph. St000483The number of times a permutation switches from increasing to decreasing or decreasing to increasing. St000484The sum of St000483 over all subsequences of length at least three. St000488The number of cycles of a permutation of length at most 2. St000489The number of cycles of a permutation of length at most 3. St000503The maximal difference between two elements in a common block. St000518The number of distinct subsequences in a binary word. St000529The number of permutations whose descent word is the given binary word. St000543The size of the conjugacy class of a binary word. St000552The number of cut vertices of a graph. St000558The number of occurrences of the pattern {{1,2}} in a set partition. St000564The number of occurrences of the pattern {{1},{2}} in a set partition. St000620The number of standard tableaux of shape equal to the given partition such that the minimal cyclic descent is odd. St000622The number of occurrences of the patterns 2143 or 4231 in a permutation. St000625The sum of the minimal distances to a greater element. St000626The minimal period of a binary word. St000648The number of 2-excedences of a permutation. St000649The number of 3-excedences of a permutation. St000651The maximal size of a rise in a permutation. St000653The last descent of a permutation. St000654The first descent of a permutation. St000657The smallest part of an integer composition. St000665The number of rafts of a permutation. St000677The standardized bi-alternating inversion number of a permutation. St000688The global dimension minus the dominant dimension of the LNakayama algebra associated to a Dyck path. St000696The number of cycles in the breakpoint graph of a permutation. St000702The number of weak deficiencies of a permutation. St000703The number of deficiencies of a permutation. St000710The number of big deficiencies of a permutation. St000711The number of big exceedences of a permutation. St000719The number of alignments in a perfect matching. St000724The label of the leaf of the path following the smaller label in the increasing binary tree associated to a permutation. St000725The smallest label of a leaf of the increasing binary tree associated to a permutation. St000733The row containing the largest entry of a standard tableau. St000746The number of pairs with odd minimum in a perfect matching. St000753The Grundy value for the game of Kayles on a binary word. St000777The number of distinct eigenvalues of the distance Laplacian of a connected graph. St000779The tier of a permutation. St000794The mak of a permutation. St000795The mad of a permutation. St000798The makl of a permutation. St000801The number of occurrences of the vincular pattern |312 in a permutation. St000808The number of up steps of the associated bargraph. St000815The number of semistandard Young tableaux of partition weight of given shape. St000831The number of indices that are either descents or recoils. St000833The comajor index of a permutation. St000837The number of ascents of distance 2 of a permutation. St000863The length of the first row of the shifted shape of a permutation. St000873The aix statistic of a permutation. St000881The number of short braid edges in the graph of braid moves of a permutation. St000883The number of longest increasing subsequences of a permutation. St000888The maximal sum of entries on a diagonal of an alternating sign matrix. St000891The number of distinct diagonal sums of a permutation matrix. St000892The maximal number of nonzero entries on a diagonal of an alternating sign matrix. St000907The number of maximal antichains of minimal length in a poset. St000911The number of maximal antichains of maximal size in a poset. St000915The Ore degree of a graph. St000917The open packing number of a graph. St000918The 2-limited packing number of a graph. St000925The number of topologically connected components of a set partition. St000935The number of ordered refinements of an integer partition. St000941The number of characters of the symmetric group whose value on the partition is even. St000961The shifted major index of a permutation. St000963The 2-shifted major index of a permutation. St000970Number of peaks minus the dominant dimension of the corresponding LNakayama algebra. St000975The length of the boundary minus the length of the trunk of an ordered tree. St000986The multiplicity of the eigenvalue zero of the adjacency matrix of the graph. St000988The orbit size of a permutation under Foata's bijection. St000991The number of right-to-left minima of a permutation. St000994The number of cycle peaks and the number of cycle valleys of a permutation. St000996The number of exclusive left-to-right maxima of a permutation. St001007Number of simple modules with projective dimension 1 in the Nakayama algebra corresponding to the Dyck path. St001010Number of indecomposable injective modules with projective dimension g-1 when g is the global dimension of the Nakayama algebra corresponding to the Dyck path. 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. 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. St001033The normalized area of the parallelogram polyomino associated with the Dyck path. St001035The convexity degree of the parallelogram polyomino associated with the Dyck path. St001074The number of inversions of the cyclic embedding of a permutation. St001078The minimal number of occurrences of (12) in a factorization of a permutation into transpositions (12) and cycles (1,. St001082The number of boxed occurrences of 123 in a permutation. St001083The number of boxed occurrences of 132 in a permutation. St001089Number of indecomposable projective non-injective modules minus the number of indecomposable projective non-injective modules with dominant dimension equal to the injective dimension in the corresponding Nakayama algebra. St001090The number of pop-stack-sorts needed to sort a permutation. St001091The number of parts in an integer partition whose next smaller part has the same size. St001093The detour number of a graph. 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. St001108The 2-dynamic chromatic number of a graph. St001114The number of odd descents of a permutation. St001161The major index north count of a Dyck path. 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. St001174The Gorenstein dimension of the algebra $A/I$ when $I$ is the tilting module corresponding to the permutation in the Auslander algebra of $K[x]/(x^n)$. St001187The number of simple modules with grade at least one in the corresponding Nakayama algebra. St001221The number of simple modules in the corresponding LNakayama algebra that have 2 dimensional second Extension group with the regular module. St001224Let X be the direct sum of all simple modules of the corresponding Nakayama algebra. St001229The vector space dimension of the first extension group between the Jacobson radical J and J^2. St001239The largest vector space dimension of the double dual of a simple module in the corresponding Nakayama algebra. St001247The number of parts of a partition that are not congruent 2 modulo 3. St001263The index of the maximal parabolic seaweed algebra associated with the composition. St001269The sum of the minimum of the number of exceedances and deficiencies in each cycle of a permutation. 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. St001308The number of induced paths on three vertices in a graph. St001313The number of Dyck paths above the lattice path given by a binary word. St001315The dissociation 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. St001323The independence gap of a graph. St001347The number of pairs of vertices of a graph having the same neighbourhood. St001350Half of the Albertson index of a graph. St001371The length of the longest Yamanouchi prefix of a binary word. St001384The number of boxes in the diagram of a partition that do not lie in the largest triangle it contains. St001388The number of non-attacking neighbors of a permutation. St001389The number of partitions of the same length below the given integer partition. St001397Number of pairs of incomparable elements in a finite poset. St001403The number of vertical separators in a permutation. St001413Half the length of the longest even length palindromic prefix of a binary word. St001414Half the length of the longest odd length palindromic prefix of a binary word. St001419The length of the longest palindromic factor beginning with a one of a binary word. 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. St001428The number of B-inversions of a signed permutation. St001430The number of positive entries in a signed permutation. St001442The number of standard Young tableaux whose major index is divisible by the size of a given integer partition. St001461The number of topologically connected components of the chord diagram of a permutation. St001469The holeyness of a permutation. St001470The cyclic holeyness of a permutation. St001485The modular major index of a binary word. St001497The position of the largest weak excedence of a permutation. St001500The global dimension of magnitude 1 Nakayama algebras. St001511The minimal number of transpositions needed to sort a permutation in either direction. St001520The number of strict 3-descents. St001521Half the total irregularity of a graph. St001524The degree of symmetry of a binary word. St001526The Loewy length of the Auslander-Reiten translate of the regular module as a bimodule of the Nakayama algebra corresponding to the Dyck path. St001533The largest coefficient of the Poincare polynomial of the poset cone. St001554The number of distinct nonempty subtrees of a binary tree. St001556The number of inversions of the third entry of a permutation. St001559The number of transpositions that are smaller or equal to a permutation in Bruhat order while not being inversions. St001565The number of arithmetic progressions of length 2 in a permutation. St001566The length of the longest arithmetic progression in a permutation. St001574The minimal number of edges to add or remove to make a graph regular. St001576The minimal number of edges to add or remove to make a graph vertex transitive. St001583The projective dimension of the simple module corresponding to the point in the poset of the symmetric group under bruhat order. St001615The number of join prime elements of a lattice. St001617The dimension of the space of valuations of a lattice. St001622The number of join-irreducible elements of a lattice. St001639The number of alternating subsets such that applying the permutation does not yield an alternating subset. St001646The number of edges that can be added without increasing the maximal degree of a graph. St001665The number of pure excedances of a permutation. St001672The restrained domination number of a graph. St001674The number of vertices of the largest induced star graph in the graph. St001682The number of distinct positions of the pattern letter 1 in occurrences of 123 in a permutation. St001683The number of distinct positions of the pattern letter 3 in occurrences of 132 in a permutation. St001685The number of distinct positions of the pattern letter 1 in occurrences of 132 in a permutation. St001689The number of celebrities in a graph. St001691The number of kings in a graph. St001692The number of vertices with higher degree than the average degree in a graph. St001704The size of the largest multi-subset-intersection of the deck of a graph with the deck of another 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. St001729The number of visible descents of a permutation. St001738The minimal order of a graph which is not an induced subgraph of the given graph. St001742The difference of the maximal and the minimal degree in a graph. St001745The number of occurrences of the arrow pattern 13 with an arrow from 1 to 2 in a permutation. St001757The number of orbits of toric promotion on a graph. St001759The Rajchgot index of a permutation. St001764The number of non-convex subsets of vertices in a graph. St001767The largest minimal number of arrows pointing to a cell in the Ferrers diagram in any assignment. St001769The reflection length of a signed permutation. St001773The number of minimal elements in Bruhat order not less than the signed permutation. St001798The difference of the number of edges in a graph and the number of edges in the complement of the Turán graph. St001799The number of proper separations of a graph. St001811The Castelnuovo-Mumford regularity of a permutation. St001856The number of edges in the reduced word graph of a permutation. St001861The number of Bruhat lower covers of a permutation. St001874Lusztig's a-function for the symmetric group. St001894The depth of a signed permutation. St001911A descent variant minus the number of inversions. St001926Sparre Andersen's position of the maximum of a signed permutation. St001927Sparre Andersen's number of positives of a signed permutation. St001928The number of non-overlapping descents in a permutation. St001930The weak major index of a binary word. St000054The first entry of the permutation. St000111The sum of the descent tops (or Genocchi descents) of a permutation. St000167The number of leaves of an ordered tree. St000325The width of the tree associated to a permutation. St000351The determinant of the adjacency matrix of a graph. St000380Half of the maximal perimeter of a rectangle fitting into the diagram of an integer partition. St000455The second largest eigenvalue of a graph if it is integral. St000470The number of runs in a permutation. St000505The biggest entry in the block containing the 1. St000520The number of patterns in a permutation. St000727The largest label of a leaf in the binary search tree associated with the permutation. St000740The last entry of a permutation. St000820The number of compositions obtained by rotating the composition. St000896The number of zeros on the main diagonal of an alternating sign matrix. 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. St001268The size of the largest ordinal summand in the poset. St001383The BG-rank of an integer partition. St001473The absolute value of the sum of all entries of the Coxeter matrix of the corresponding LNakayama algebra. St001519The pinnacle sum of a permutation. St001555The order of a signed permutation. St001814The number of partitions interlacing the given partition. St001838The number of nonempty primitive factors of a binary word. St001872The number of indecomposable injective modules with even projective dimension in the corresponding Nakayama algebra. St001875The number of simple modules with projective dimension at most 1. St001957The number of Hasse diagrams with a given underlying undirected graph. St000867The sum of the hook lengths in the first row of an integer partition. St001134The largest label in the subtree rooted at the sister of 1 in the leaf labelled binary unordered tree associated with the perfect matching. 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. St000656The number of cuts of a poset. St000939The number of characters of the symmetric group whose value on the partition is positive. St000782The indicator function of whether a given perfect matching is an L & P matching. St001605The number of colourings of a cycle such that the multiplicities of colours are given by a partition. St000219The number of occurrences of the pattern 231 in a permutation. St001195The global dimension of the algebra $A/AfA$ of the corresponding Nakayama algebra $A$ with minimal left faithful projective-injective module $Af$. 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. St000418The number of Dyck paths that are weakly below a Dyck path. St000444The length of the maximal rise of a Dyck path. St000817The sum of the entries in the column specified by the composition of the change of basis matrix from dual immaculate quasisymmetric functions to monomial quasisymmetric functions. 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. St001060The distinguishing index of a graph. St001346The number of parking functions that give the same permutation. 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. St000045The number of linear extensions of a binary tree. St000699The toughness times the least common multiple of 1,. St001570The minimal number of edges to add to make a graph Hamiltonian. St001582The grades of the simple modules corresponding to the points in the poset of the symmetric group under the Bruhat order. St001629The coefficient of the integer composition in the quasisymmetric expansion of the relabelling action of the symmetric group on cycles. St001651The Frankl number of a lattice. St001604The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on polygons. St001964The interval resolution global dimension of a poset. St001171The vector space dimension of $Ext_A^1(I_o,A)$ when $I_o$ is the tilting module corresponding to the permutation $o$ in the Auslander algebra $A$ of $K[x]/(x^n)$. 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.