St000870The product of the hook lengths of the diagonal cells in an integer partition. St001020Sum of the codominant dimensions of the non-projective indecomposable injective modules of the Nakayama algebra corresponding to the Dyck path. St001342The number of vertices in the center of a graph. St001746The coalition number of a graph. 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. St000171The degree of the graph. St000921The number of internal inversions of a binary word. St001004The number of indices that are either left-to-right maxima or right-to-left minima. St001119The length of a shortest maximal path in a graph. St001120The length of a longest path in a graph. St001332The number of steps on the non-negative side of the walk associated with the permutation. St001641The number of ascent tops in the flattened set partition such that all smaller elements appear before. St000026The position of the first return of a Dyck path. St000293The number of inversions of a binary word. St000394The sum of the heights of the peaks of a Dyck path minus the number of peaks. St000548The number of different non-empty partial sums of an integer partition. St000722The number of different neighbourhoods in a graph. St000734The last entry in the first row of a standard tableau. St001034The area of the parallelogram polyomino associated with the Dyck path. St001348The bounce of the parallelogram polyomino associated with the Dyck path. St001554The number of distinct nonempty subtrees of a binary tree. St001672The restrained domination number of 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. St001012Number of simple modules with projective dimension at most 2 in the Nakayama algebra corresponding to the Dyck path. St001643The Frobenius dimension of the Nakayama algebra corresponding to the Dyck path. 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. St001869The maximum cut size of a graph. St000806The semiperimeter of the associated bargraph. St000189The number of elements in the poset. St000385The number of vertices with out-degree 1 in a binary tree. St000393The number of strictly increasing runs in a binary word. St000414The binary logarithm of the number of binary trees with the same underlying unordered tree. St000476The sum of the semi-lengths of tunnels before a valley of a Dyck path. St001267The length of the Lyndon factorization of the binary word. St001371The length of the longest Yamanouchi prefix of a binary word. St001430The number of positive entries in a signed permutation. St001437The flex of a binary word. St001636The number of indecomposable injective modules with projective dimension at most one in the incidence algebra of the poset. St001279The sum of the parts of an integer partition that are at least two. St001645The pebbling number of a connected graph. St000454The largest eigenvalue of a graph if it is integral. St001330The hat guessing number of a graph. St001622The number of join-irreducible elements of a lattice. St000725The smallest label of a leaf of the increasing binary tree associated to a permutation. St000724The label of the leaf of the path following the smaller label in the increasing binary tree associated to a permutation. St000271The chromatic index of a graph. St000777The number of distinct eigenvalues of the distance Laplacian of a connected graph. St001300The rank of the boundary operator in degree 1 of the chain complex of the order complex of the poset. St000019The cardinality of the support of a permutation. St000625The sum of the minimal distances to a greater element. St001074The number of inversions of the cyclic embedding of a permutation. St001974The rank of the alternating sign matrix. St001925The minimal number of zeros in a row of an alternating sign matrix. St000890The number of nonzero entries in an alternating sign matrix. St000050The depth or height of a binary tree. St000141The maximum drop size of a permutation. St000054The first entry of the permutation. St000288The number of ones in a binary word. St000336The leg major index of a standard tableau. St000875The semilength of the longest Dyck word in the Catalan factorisation of a binary word. St001875The number of simple modules with projective dimension at most 1. St000505The biggest entry in the block containing the 1. St000503The maximal difference between two elements in a common block. St001245The cyclic maximal difference between two consecutive entries of a permutation. St001958The degree of the polynomial interpolating the values of a permutation. St000863The length of the first row of the shifted shape of a permutation. St001827The number of two-component spanning forests of a graph. St000167The number of leaves of an ordered tree. St000052The number of valleys of a Dyck path not on the x-axis. 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. St001311The cyclomatic number of a graph. St001317The minimal number of occurrences of the forest-pattern in a linear ordering of the vertices of the graph. St001328The minimal number of occurrences of the bipartite-pattern in a linear ordering of the vertices of the graph. St001341The number of edges in the center of a graph. St001391The disjunction number of a graph. St001723The differential of a graph. St001724The 2-packing differential of a graph. St000144The pyramid weight of the Dyck path. St000553The number of blocks of a graph. St000632The jump number of the poset. St001018Sum of projective dimension of the indecomposable injective modules of the Nakayama algebra corresponding to the Dyck path. St001291The number of indecomposable summands of the tensor product of two copies of the dual of the Nakayama algebra associated to a Dyck path. St000068The number of minimal elements in a poset. St000071The number of maximal chains in a poset. St000312The number of leaves in a graph. St000527The width of the poset. St000718The largest Laplacian eigenvalue of a graph if it is integral. 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. St000209Maximum difference of elements in cycles. St000316The number of non-left-to-right-maxima of a permutation. St000362The size of a minimal vertex cover of a graph. St000448The number of pairs of vertices of a graph with distance 2. St001646The number of edges that can be added without increasing the maximal degree of a graph. St000028The number of stack-sorts needed to sort a permutation. St000031The number of cycles in the cycle decomposition 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. St000337The lec statistic, the sum of the inversion numbers of the hook factors of a permutation. St000363The number of minimal vertex covers of a graph. St000374The number of exclusive right-to-left minima of a permutation. St000501The size of the first part in the decomposition of a permutation. St000703The number of deficiencies of a permutation. St000733The row containing the largest entry of a standard tableau. 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. St001052The length of the exterior of a permutation. St001096The size of the overlap set of a permutation. St001118The acyclic chromatic index of a graph. 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. St001258Gives the maximum of injective plus projective dimension of an indecomposable module over the corresponding Nakayama algebra. St001725The harmonious chromatic number of a graph. St000010The length of the partition. St000058The order of a permutation. St000451The length of the longest pattern of the form k 1 2. St001023Number of simple modules with projective dimension at most 3 in the Nakayama algebra corresponding to the Dyck path. St001179Number of indecomposable injective modules with projective dimension at most 2 in the corresponding Nakayama algebra. 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. 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. St000060The greater neighbor of the maximum. St000197The number of entries equal to positive one in the alternating sign matrix. St000653The last descent of a permutation. St000956The maximal displacement of a permutation. St001480The number of simple summands of the module J^2/J^3. St000844The size of the largest block in the direct sum decomposition of a permutation. St001615The number of join prime elements of a lattice. St001617The dimension of the space of valuations of a lattice. St001570The minimal number of edges to add to make a graph Hamiltonian. St000528The height of a poset. St001917The order of toric promotion on the set of labellings of a 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. St000672The number of minimal elements in Bruhat order not less than the permutation. St000018The number of inversions of a permutation. St000924The number of topologically connected components of a perfect matching. St000906The length of the shortest maximal chain in a poset. St000643The size of the largest orbit of antichains under Panyushev complementation. St001232The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2. St001268The size of the largest ordinal summand in the poset. St000080The rank of the poset. St000912The number of maximal antichains in a poset. St000727The largest label of a leaf in the binary search tree associated with the permutation. St000740The last entry of a permutation. St001497The position of the largest weak excedence of a permutation. St001778The largest greatest common divisor of an element and its image in a permutation. St000095The number of triangles of a graph. St000450The number of edges minus the number of vertices plus 2 of a graph. St000673The number of non-fixed points of a permutation. St001468The smallest fixpoint of a permutation. St001706The number of closed sets in a graph. St001742The difference of the maximal and the minimal degree in a graph. St000029The depth of a permutation. St000051The size of the left subtree of a binary tree. St000067The inversion number of the alternating sign matrix. St000210Minimum over maximum difference of elements in cycles. St000216The absolute length of a permutation. St000547The number of even non-empty partial sums of an integer partition. St000809The reduced reflection length of the permutation. St000957The number of Bruhat lower covers 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. St001117The game chromatic index of a graph. St001225The vector space dimension of the first extension group between J and itself when J is the Jacobson radical of the corresponding Nakayama algebra. St001304The number of maximally independent sets of vertices of a graph. St001429The number of negative entries in a signed permutation. 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. St001963The tree-depth of a graph. St000235The number of indices that are not cyclical small weak excedances. St000240The number of indices that are not small excedances. St000384The maximal part of the shifted composition of an integer partition. St000485The length of the longest cycle of a permutation. St000487The length of the shortest cycle of a permutation. St000549The number of odd partial sums of an integer partition. St000784The maximum of the length and the largest part of the integer partition. St001005The number of indices for a permutation that are either left-to-right maxima or right-to-left minima but not both. St000380Half of the maximal perimeter of a rectangle fitting into the diagram of an integer partition. St000456The monochromatic index of a connected graph. St001065Number of indecomposable reflexive modules 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. St000327The number of cover relations in a poset. St001927Sparre Andersen's number of positives of a signed permutation. St000918The 2-limited packing number of a graph. St001315The dissociation number of a graph. St000260The radius of a connected graph. St000535The rank-width of a graph. St001644The dimension of a graph. St000201The number of leaf nodes in a binary tree. St001434The number of negative sum pairs of a signed permutation. St001882The number of occurrences of a type-B 231 pattern in a signed 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. St001637The number of (upper) dissectors of a poset. St001668The number of points of the poset minus the width of the poset. St001817The number of flag weak exceedances of a signed permutation. St001892The flag excedance statistic of a signed permutation. St000680The Grundy value for Hackendot on posets. St000717The number of ordinal summands of a poset. St001704The size of the largest multi-subset-intersection of the deck of a graph with the deck of another graph. St000245The number of ascents of a permutation. St000834The number of right outer peaks of a permutation. St000035The number of left outer peaks of a permutation. St000742The number of big ascents of a permutation after prepending zero. St000884The number of isolated descents of a permutation. St001861The number of Bruhat lower covers of a permutation. St000135The number of lucky cars of the parking function. St000744The length of the path to the largest entry in a standard Young tableau. St000044The number of vertices of the unicellular map given by a perfect matching. St000017The number of inversions of a standard tableau. St000919The number of maximal left branches of a binary tree. St001613The binary logarithm of the size of the center of a lattice. 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. St000568The hook number of a binary tree. St000691The number of changes of a binary word. St001214The aft of an integer partition. St001420Half the length of a longest factor which is its own reverse-complement of a binary word. St001515The vector space dimension of the socle of the first syzygy module of the regular module (as a bimodule). 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. St001134The largest label in the subtree rooted at the sister of 1 in the leaf labelled binary unordered tree associated with the perfect matching. St001207The Lowey length of the algebra $A/T$ when $T$ is the 1-tilting module corresponding to the permutation in the Auslander algebra of $K[x]/(x^n)$. St000741The Colin de Verdière graph invariant. St001555The order of a signed permutation.