St001267The length of the Lyndon factorization of the binary word. St001437The flex of a binary word. St001654The monophonic hull number of a graph. St001655The general position number of a graph. St001656The monophonic position 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. St000385The number of vertices with out-degree 1 in a binary tree. 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. St000921The number of internal inversions of a binary word. St001641The number of ascent tops in the flattened set partition such that all smaller elements appear before. St001955The number of natural descents for set-valued two row standard Young tableaux. St000203The number of external nodes of a binary tree. 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. St000725The smallest label of a leaf of the increasing binary tree associated to a permutation. 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. St001004The number of indices that are either left-to-right maxima or right-to-left minima. St001034The area of the parallelogram polyomino associated with the Dyck path. St001211The number of simple modules in the corresponding Nakayama algebra that have vanishing second Ext-group with the regular module. St001348The bounce of the parallelogram polyomino associated with the Dyck path. St001523The degree of symmetry of a Dyck path. St001554The number of distinct nonempty subtrees of a binary tree. 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. St000081The number of edges of a graph. St000259The diameter of a connected graph. St000288The number of ones in a binary word. St000296The length of the symmetric border of a binary word. St000553The number of blocks of a graph. St000627The exponent of a binary word. St000645The sum of the areas of the rectangles formed by two consecutive peaks and the valley in between. St000681The Grundy value of Chomp on Ferrers diagrams. St000778The metric dimension of a graph. St000922The minimal number such that all substrings of this length are unique. St000982The length of the longest constant subword. St000987The number of positive eigenvalues of the Laplacian matrix of the graph. St001119The length of a shortest maximal path in a graph. St001120The length of a longest path in a graph. St001176The size of a partition minus its first part. St001332The number of steps on the non-negative side of the walk associated with the permutation. St001371The length of the longest Yamanouchi prefix of a binary word. St001372The length of a longest cyclic run of ones of a binary word. St001384The number of boxes in the diagram of a partition that do not lie in the largest triangle it contains. 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. St001479The number of bridges of a graph. St001512The minimum rank of a graph. St001631The number of simple modules $S$ with $dim Ext^1(S,A)=1$ in the incidence algebra $A$ of the poset. 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. St001884The number of borders of a binary word. St001917The order of toric promotion on the set of labellings of a graph. St001949The rigidity index of a graph. St000018The number of inversions of a permutation. St000019The cardinality of the support of a permutation. St000141The maximum drop size of a permutation. St000246The number of non-inversions of a permutation. St000290The major index of a binary word. St000294The number of distinct factors of a binary word. St000295The length of the border of a binary word. St000313The number of degree 2 vertices of a graph. 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. St000448The number of pairs of vertices of a graph with distance 2. St000452The number of distinct eigenvalues of a graph. St000453The number of distinct Laplacian eigenvalues of a graph. St000469The distinguishing number of a graph. St000507The number of ascents of a standard tableau. St000518The number of distinct subsequences in a binary word. St000519The largest length of a factor maximising the subword complexity. St000528The height of a poset. St000531The leading coefficient of the rook polynomial of an integer partition. St000543The size of the conjugacy class of a binary word. St000548The number of different non-empty partial sums of an integer partition. St000552The number of cut vertices of a graph. St000626The minimal period of a binary word. St000657The smallest part of an integer composition. St000734The last entry in the first row of a standard tableau. 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. St000808The number of up steps of the associated bargraph. St000878The number of ones minus the number of zeros 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. St000926The clique-coclique number of a graph. St000975The length of the boundary minus the length of the trunk of an ordered tree. St001084The number of occurrences of the vincular pattern |1-23 in a permutation. St001093The detour number of a graph. St001308The number of induced paths on three vertices in a graph. St001318The number of vertices of the largest induced subforest with the same number of connected components of a graph. St001321The number of vertices of the largest induced subforest of a graph. St001342The number of vertices in the center of a graph. St001343The dimension of the reduced incidence algebra of a poset. St001360The number of covering relations in Young's lattice below a partition. St001368The number of vertices of maximal degree in a graph. St001485The modular major index of a binary word. St001492The number of simple modules that do not appear in the socle of the regular module or have no nontrivial selfextensions with the regular module in the corresponding Nakayama algebra. St001521Half the total irregularity of a graph. St001659The number of ways to place as many non-attacking rooks as possible on a Ferrers board. St001672The restrained domination number of a graph. St001692The number of vertices with higher degree than the average degree 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. St001880The number of 2-Gorenstein indecomposable injective modules in the incidence algebra of the lattice. St000054The first entry of the permutation. St000063The number of linear extensions of a certain poset defined for an integer partition. St000070The number of antichains in a poset. St000108The number of partitions contained in the given partition. St000380Half of the maximal perimeter of a rectangle fitting into the diagram of an integer partition. St000447The number of pairs of vertices of a graph with distance 3. St000532The total number of rook placements on a Ferrers board. St001306The number of induced paths on four vertices in a graph. St001400The total number of Littlewood-Richardson tableaux of given shape. St000867The sum of the hook lengths in the first row of an integer partition. St001636The number of indecomposable injective modules with projective dimension at most one in the incidence algebra of the poset. St000007The number of saliances of the permutation. St000245The number of ascents of a permutation. St000662The staircase size of the code of a permutation. St000672The number of minimal elements in Bruhat order not less than the permutation. St000724The label of the leaf of the path following the smaller label in the increasing binary tree associated to a permutation. St000837The number of ascents of distance 2 of a permutation. St000371The number of mid points of decreasing subsequences of length 3 in a permutation. St001245The cyclic maximal difference between two consecutive entries of a permutation. St001300The rank of the boundary operator in degree 1 of the chain complex of the order complex of the poset. St000503The maximal difference between two elements in a common block. St000696The number of cycles in the breakpoint graph of a permutation. St000728The dimension of a set partition. St001087The number of occurrences of the vincular pattern |12-3 in a permutation. St001090The number of pop-stack-sorts needed to sort a permutation. St001759The Rajchgot index of a permutation. St000505The biggest entry in the block containing the 1. St000771The largest multiplicity of a distance Laplacian eigenvalue in a connected graph. St000772The multiplicity of the largest distance Laplacian eigenvalue in a connected graph. St000010The length of the partition. St000336The leg major index of a standard tableau. St000875The semilength of the longest Dyck word in the Catalan factorisation of a binary word. St001645The pebbling number of a connected graph. St000050The depth or height of a binary tree. St000727The largest label of a leaf in the binary search tree associated with the permutation. St000863The length of the first row of the shifted shape of a permutation. St000653The last descent of a permutation. St001958The degree of the polynomial interpolating the values of a permutation. St000625The sum of the minimal distances to a greater element. St001074The number of inversions of the cyclic embedding of a permutation. St001298The number of repeated entries in the Lehmer code of a permutation. St001366The maximal multiplicity of a degree of a vertex of a graph. St001430The number of positive entries in a signed permutation. St001844The maximal degree of a generator of the invariant ring of the automorphism group of a graph. St001018Sum of projective dimension of the indecomposable injective modules 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. St000144The pyramid weight of the Dyck path. St001237The number of simple modules with injective dimension at most one or dominant dimension at least one. 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. St000060The greater neighbor of the maximum. 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. St001723The differential of a graph. St001724The 2-packing differential of a graph. St000171The degree of the graph. St000189The number of elements in the poset. St000229Sum of the difference between the maximal and the minimal elements of the blocks plus the number of blocks of a set partition. St001291The number of indecomposable summands of the tensor product of two copies of the dual of the Nakayama algebra associated to a Dyck path. St000026The position of the first return of a Dyck path. St000058The order of a permutation. St000718The largest Laplacian eigenvalue of a graph if it is integral. 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. St001746The coalition number of a graph. St000030The sum of the descent differences of a permutations. St000080The rank of the poset. St000209Maximum difference of elements in cycles. St000276The size of the preimage of the map 'to graph' from Ordered trees to Graphs. St000304The load of a permutation. St000308The height of the tree associated to a permutation. St000325The width of the tree associated to a permutation. St000470The number of runs in a permutation. St000619The number of cyclic descents of a permutation. St001032The number of horizontal steps in the bicoloured Motzkin path associated with the Dyck path. St001246The maximal difference between two consecutive entries of a permutation. St001391The disjunction number of a graph. St001516The number of cyclic bonds of a permutation. St001566The length of the longest arithmetic progression in a permutation. St001649The length of a longest trail in a graph. St001827The number of two-component spanning forests of a graph. St001869The maximum cut size of a graph. St000021The number of descents of a permutation. St000028The number of stack-sorts needed to sort a permutation. St000031The number of cycles in the cycle decomposition of a permutation. St000087The number of induced subgraphs. St000240The number of indices that are not small excedances. St000242The number of indices that are not cyclical small weak excedances. St000299The number of nonisomorphic vertex-induced subtrees. St000309The number of vertices with even degree. St000316The number of non-left-to-right-maxima of a permutation. St000337The lec statistic, the sum of the inversion numbers of the hook factors of a permutation. St000354The number of recoils of a permutation. St000374The number of exclusive right-to-left minima of a permutation. St000482The (zero)-forcing number of a graph. St000501The size of the first part in the decomposition of a permutation. St000656The number of cuts of a poset. St000680The Grundy value for Hackendot on posets. St000703The number of deficiencies of a permutation. St000717The number of ordinal summands of a poset. St000733The row containing the largest entry of a standard tableau. St000829The Ulam distance of a permutation to the identity permutation. St000844The size of the largest block in the direct sum decomposition of a permutation. St000906The length of the shortest maximal chain in a poset. 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. 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. St001489The maximum of the number of descents and the number of inverse descents. St001509The degree of the standard monomial associated to a Dyck path relative to the trivial lower boundary. St001622The number of join-irreducible elements of a lattice. St001717The largest size of an interval in a poset. St000104The number of facets in the order polytope of this poset. St000151The number of facets in the chain polytope of the poset. St000167The number of leaves of an ordered tree. St000451The length of the longest pattern of the form k 1 2. St000642The size of the smallest orbit of antichains under Panyushev complementation. St000643The size of the largest orbit of antichains under Panyushev complementation. St000915The Ore degree of a graph. St000961The shifted major index of a permutation. St001065Number of indecomposable reflexive modules in the corresponding Nakayama algebra. St001664The number of non-isomorphic subposets of a poset. St001782The order of rowmotion on the set of order ideals of a poset. 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. St001925The minimal number of zeros in a row of an alternating sign matrix. St000365The number of double ascents of a permutation. St000372The number of mid points of increasing subsequences of length 3 in a permutation. St000530The number of permutations with the same descent word as the given permutation. St000654The first descent of a permutation. St000794The mak of a permutation. St000890The number of nonzero entries in an alternating sign matrix. St000923The minimal number with no two order isomorphic substrings of this length in a permutation. St001497The position of the largest weak excedence of a permutation. St001682The number of distinct positions of the pattern letter 1 in occurrences of 123 in a permutation. St001519The pinnacle sum of a permutation. St000924The number of topologically connected components of a perfect matching. St000883The number of longest increasing subsequences of a permutation. St001345The Hamming dimension of a graph. St001725The harmonious chromatic number of a graph. St001615The number of join prime elements of a lattice. St001617The dimension of the space of valuations of a lattice. St001180Number of indecomposable injective modules with projective dimension at most 1. St000356The number of occurrences of the pattern 13-2. St000719The number of alignments in a perfect matching. St000740The last entry of a permutation. St001778The largest greatest common divisor of an element and its image in a permutation. St000327The number of cover relations in a poset. St001515The vector space dimension of the socle of the first syzygy module of the regular module (as a bimodule). St000029The depth of a permutation. St000197The number of entries equal to positive one in the alternating sign matrix. St000210Minimum over maximum difference of elements in cycles. St000216The absolute length of a permutation. 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. St001480The number of simple summands of the module J^2/J^3. St001511The minimal number of transpositions needed to sort a permutation in either direction. 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. St000485The length of the longest cycle of a permutation. St000487The length of the shortest cycle of a permutation. St000673The number of non-fixed points of a permutation. St001005The number of indices for a permutation that are either left-to-right maxima or right-to-left minima but not both. St001468The smallest fixpoint of a permutation. St000022The number of fixed points of a permutation. St000034The maximum defect over any reduced expression for a permutation and any subexpression. St000062The length of the longest increasing subsequence of the permutation. St000064The number of one-box pattern of a permutation. St000083The number of left oriented leafs of a binary tree except the first one. 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. St000153The number of adjacent cycles of a permutation. St000222The number of alignments in the permutation. St000223The number of nestings in the permutation. St000239The number of small weak excedances. St000338The number of pixed points of a permutation. St000339The maf index of a permutation. St000373The number of weak exceedences of a permutation that are also mid-points of a decreasing subsequence of length $3$. 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. St000463The number of admissible inversions of a permutation. St000538The number of even inversions of a permutation. St000802The number of occurrences of the vincular pattern |321 in a permutation. St000866The number of admissible inversions of a permutation in the sense of Shareshian-Wachs. St000887The maximal number of nonzero entries on a diagonal of a permutation matrix. St000956The maximal displacement of a permutation. St001411The number of patterns 321 or 3412 in a permutation. St001514The dimension of the top of the Auslander-Reiten translate of the regular modules as a bimodule. St001552The number of inversions between excedances and fixed points of a permutation. St001637The number of (upper) dissectors of a poset. St001652The length of a longest interval of consecutive numbers. St001662The length of the longest factor of consecutive numbers in a permutation. St001668The number of points of the poset minus the width of the poset. St001727The number of invisible inversions of a permutation. St001810The number of fixed points of a permutation smaller than its largest moved point. St000004The major index of a permutation. St000051The size of the left subtree of a binary tree. St000067The inversion number of the alternating sign matrix. St000134The size of the orbit of an alternating sign matrix under gyration. St000156The Denert index of a permutation. St000213The number of weak exceedances (also weak excedences) of a permutation. St000224The sorting index of a permutation. St000226The convexity of a permutation. St000235The number of indices that are not cyclical small weak excedances. St000236The number of cyclical small weak excedances. St000314The number of left-to-right-maxima of a permutation. St000332The positive inversions of an alternating sign matrix. St000334The maz index, the major index of a permutation after replacing fixed points by zeros. St000358The number of occurrences of the pattern 31-2. St000359The number of occurrences of the pattern 23-1. St000441The number of successions of a permutation. St000462The major index minus the number of excedences 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. St000539The number of odd inversions of a permutation. St000702The number of weak deficiencies of a permutation. St000726The normalized sum of the leaf labels of the increasing binary tree associated to a permutation. St000795The mad of a permutation. St000831The number of indices that are either descents or recoils. 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. St001220The width of a permutation. St001225The vector space dimension of the first extension group between J and itself when J is the Jacobson radical of the corresponding Nakayama algebra. St001278The number of indecomposable modules that are fixed by $\tau \Omega^1$ composed with its inverse in the corresponding Nakayama algebra. St001397Number of pairs of incomparable elements in a finite poset. St001405The number of bonds in a permutation. St001428The number of B-inversions of a signed permutation. St001461The number of topologically connected components of the chord diagram of a permutation. St001533The largest coefficient of the Poincare polynomial of the poset cone. St001557The number of inversions of the second entry of a permutation. St001683The number of distinct positions of the pattern letter 3 in occurrences of 132 in a permutation. St001726The number of visible inversions of a permutation. St001744The number of occurrences of the arrow pattern 1-2 with an arrow from 1 to 2 in a permutation. St001960The number of descents of a permutation minus one if its first entry is not one. St000111The sum of the descent tops (or Genocchi descents) of a permutation. St000305The inverse major index of a permutation. St000446The disorder of a permutation. St000796The stat' of a permutation. St000797The stat`` of a permutation. St000798The makl of a permutation. St000833The comajor index of a permutation. St000868The aid statistic in the sense of Shareshian-Wachs. St001040The depth of the decreasing labelled binary unordered tree associated with the perfect matching. St001082The number of boxed occurrences of 123 in a permutation. St001130The number of two successive successions in a permutation. St001134The largest label in the subtree rooted at the sister of 1 in the leaf labelled binary unordered tree associated with the perfect matching. St001268The size of the largest ordinal summand in the poset. St001556The number of inversions of the third entry of a permutation. St001715The number of non-records in a permutation. St001255The vector space dimension of the double dual of A/J when A is the corresponding Nakayama algebra with Jacobson radical J. St000329The number of evenly positioned ascents of the Dyck path, with the initial position equal to 1. St001875The number of simple modules with projective dimension at most 1. St000744The length of the path to the largest entry in a standard Young tableau. 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. St000044The number of vertices of the unicellular map given by a perfect matching. St000017The number of inversions of a standard tableau. St001207The Lowey length of the algebra $A/T$ when $T$ is the 1-tilting module corresponding to the permutation in the Auslander algebra of $K[x]/(x^n)$. St001420Half the length of a longest factor which is its own reverse-complement of a binary word. St001424The number of distinct squares in a binary word. St001948The number of augmented double ascents 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. St000882The number of connected components of short braid edges in the graph of braid moves of a permutation. St000898The number of maximal entries in the last diagonal of the monotone triangle. St001421Half the length of a longest factor which is its own reverse-complement and begins with a one of a binary word. St001520The number of strict 3-descents. St001927Sparre Andersen's number of positives of a signed permutation. St000820The number of compositions obtained by rotating the composition. St000896The number of zeros on the main diagonal of an alternating sign matrix. St001555The order of a signed permutation. St001232The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2. St000522The number of 1-protected nodes of a rooted tree. St001583The projective dimension of the simple module corresponding to the point in the poset of the symmetric group under bruhat order. St000521The number of distinct subtrees of an ordered tree. St000527The width of the poset. St001118The acyclic chromatic index of a graph. St001060The distinguishing index of a graph. St000973The length of the boundary of an ordered tree. St000782The indicator function of whether a given perfect matching is an L & P matching. St001722The number of minimal chains with small intervals between a binary word and the top element. St000084The number of subtrees. St000092The number of outer peaks of a permutation. St000099The number of valleys of a permutation, including the boundary. St000133The "bounce" of a permutation. St000168The number of internal nodes of an ordered tree. St000298The order dimension or Dushnik-Miller dimension of a poset. St000328The maximum number of child nodes in a tree. St000504The cardinality of the first block of a set partition. St000542The number of left-to-right-minima of a permutation. St000624The normalized sum of the minimal distances to a greater element. St000640The rank of the largest boolean interval in a poset. St000823The number of unsplittable factors of the set partition. St000836The number of descents of distance 2 of a permutation. St000845The maximal number of elements covered by an element in a poset. St000846The maximal number of elements covering an element of a poset. St000848The balance constant multiplied with the number of linear extensions of a poset. St000849The number of 1/3-balanced pairs in a poset. St000989The number of final rises of a permutation. St001062The maximal size of a block of a set partition. St001075The minimal size of a block of a set partition. St001235The global dimension of the corresponding Comp-Nakayama algebra. St001390The number of bumps occurring when Schensted-inserting the letter 1 of a permutation. St001491The number of indecomposable projective-injective modules in the algebra corresponding to a subset. St001632The number of indecomposable injective modules $I$ with $dim Ext^1(I,A)=1$ for the incidence algebra A of a poset. St001633The number of simple modules with projective dimension two in the incidence algebra of the poset. St001640The number of ascent tops in the permutation such that all smaller elements appear before. St001741The largest integer such that all patterns of this size are contained in the permutation. St000023The number of inner peaks of a permutation. St000056The decomposition (or block) number of a permutation. St000068The number of minimal elements in a poset. St000105The number of blocks in the set partition. St000154The sum of the descent bottoms of a permutation. St000155The number of exceedances (also excedences) of a permutation. St000162The number of nontrivial cycles in the cycle decomposition of a permutation. St000166The depth minus 1 of an ordered tree. St000211The rank of the set partition. St000251The number of nonsingleton blocks of a set partition. St000253The crossing number of a set partition. St000333The dez statistic, the number of descents of a permutation after replacing fixed points by zeros. St000353The number of inner valleys of a permutation. St000461The rix statistic of a permutation. St000495The number of inversions of distance at most 2 of a permutation. St000526The number of posets with combinatorially isomorphic order polytopes. St000541The number of indices greater than or equal to 2 of a permutation such that all smaller indices appear to its right. St000558The number of occurrences of the pattern {{1,2}} in a set partition. St000570The Edelman-Greene number of a permutation. St000595The number of occurrences of the pattern {{1},{2,3}} such that 1 is minimal. 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. St000601The number of occurrences of the pattern {{1},{2,3}} such that 1,2 are minimal, (2,3) are consecutive in a block. St000609The number of occurrences of the pattern {{1},{2,3}} such that 1,2 are minimal. 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. St000638The number of up-down runs of a permutation. St000694The number of affine bounded permutations that project to a given permutation. St000729The minimal arc length of a set partition. St000864The number of circled entries of the shifted recording tableau of a permutation. St000872The number of very big descents of a permutation. St000873The aix statistic of a permutation. St000886The number of permutations with the same antidiagonal sums. St000908The length of the shortest maximal antichain in a poset. St000914The sum of the values of the Möbius function of a poset. St000925The number of topologically connected components of a set partition. St000962The 3-shifted major index of a permutation. St000963The 2-shifted major index of a permutation. St000990The first ascent of a permutation. St000991The number of right-to-left minima of a permutation. St001114The number of odd descents of a permutation. St001162The minimum jump of a permutation. St001174The Gorenstein dimension of the algebra $A/I$ when $I$ is the tilting module corresponding to the permutation in the Auslander algebra of $K[x]/(x^n)$. St001195The global dimension of the algebra $A/AfA$ of the corresponding Nakayama algebra $A$ with minimal left faithful projective-injective module $Af$. St001208The number of connected components of the quiver of $A/T$ when $T$ is the 1-tilting module corresponding to the permutation in the Auslander algebra $A$ of $K[x]/(x^n)$. St001269The sum of the minimum of the number of exceedances and deficiencies in each cycle of a permutation. St001344The neighbouring number of a permutation. St001355Number of non-empty prefixes of a binary word that contain equally many 0's and 1's. St001359The number of permutations in the equivalence class of a permutation obtained by taking inverses of cycles. St001431Half of the Loewy length minus one of a modified stable Auslander algebra of the Nakayama algebra corresponding to the Dyck path. St001462The number of factors of a standard tableaux under concatenation. St001470The cyclic holeyness of a permutation. St001517The length of a longest pair of twins in a permutation. St001532The leading coefficient of the Poincare polynomial of the poset cone. St001553The number of indecomposable summands of the square of the Jacobson radical as a bimodule in the Nakayama algebra corresponding to the Dyck path. St001582The grades of the simple modules corresponding to the points in the poset of the symmetric group under the Bruhat order. St001665The number of pure excedances of a permutation. St001667The maximal size of a pair of weak twins for a permutation. St001729The number of visible descents of a permutation. St001731The factorization defect of a permutation. St001737The number of descents of type 2 in a permutation. St001745The number of occurrences of the arrow pattern 13 with an arrow from 1 to 2 in a permutation. St001769The reflection length of a signed permutation. St001772The number of occurrences of the signed pattern 12 in a signed permutation. St001773The number of minimal elements in Bruhat order not less than the signed permutation. St001801Half the number of preimage-image pairs of different parity in a permutation. St001805The maximal overlap of a cylindrical tableau associated with a semistandard tableau. St001806The upper middle entry of a permutation. St001859The number of factors of the Stanley symmetric function associated with a permutation. St001860The number of factors of the Stanley symmetric function associated with a signed permutation. St001861The number of Bruhat lower covers of a permutation. St001874Lusztig's a-function for the symmetric group. St001889The size of the connectivity set of a signed permutation. St001894The depth of a signed permutation. St001896The number of right descents of a signed permutations. St001926Sparre Andersen's position of the maximum of a signed permutation. St001928The number of non-overlapping descents in a permutation. St000039The number of crossings of a permutation. St000094The depth of an ordered tree. St000116The major index of a semistandard tableau obtained by standardizing. St000217The number of occurrences of the pattern 312 in a permutation. St000219The number of occurrences of the pattern 231 in a permutation. St000221The number of strong fixed points of a permutation. St000234The number of global ascents of a permutation. St000247The number of singleton blocks of a set partition. St000279The size of the preimage of the map 'cycle-as-one-line notation' from Permutations to Permutations. St000281The size of the preimage of the map 'to poset' from Binary trees to Posets. St000282The size of the preimage of the map 'to poset' from Ordered trees to Posets. St000317The cycle descent number of a permutation. St000355The number of occurrences of the pattern 21-3. St000360The number of occurrences of the pattern 32-1. St000367The number of simsun double descents of a permutation. St000375The number of non weak exceedences of a permutation that are mid-points of a decreasing subsequence of length $3$. St000406The number of occurrences of the pattern 3241 in a permutation. St000407The number of occurrences of the pattern 2143 in a permutation. St000432The number of occurrences of the pattern 231 or of the pattern 312 in a permutation. St000486The number of cycles of length at least 3 of a permutation. St000500Eigenvalues of the random-to-random operator acting on the regular representation. St000516The number of stretching pairs of a permutation. St000559The number of occurrences of the pattern {{1,3},{2,4}} in a set partition. St000561The number of occurrences of the pattern {{1,2,3}} in a set partition. St000562The number of internal points of a set partition. St000563The number of overlapping pairs of blocks of a set partition. St000573The number of occurrences of the pattern {{1},{2}} such that 1 is a singleton and 2 a maximal element. St000575The number of occurrences of the pattern {{1},{2}} such that 1 is a maximal element and 2 a singleton. St000578The number of occurrences of the pattern {{1},{2}} such that 1 is a singleton. St000622The number of occurrences of the patterns 2143 or 4231 in a permutation. St000623The number of occurrences of the pattern 52341 in a permutation. St000664The number of right ropes of a permutation. St000666The number of right tethers of a permutation. St000732The number of double deficiencies of a permutation. St000750The number of occurrences of the pattern 4213 in a permutation. St000751The number of occurrences of either of the pattern 2143 or 2143 in a permutation. St000779The tier of a permutation. St000800The number of occurrences of the vincular pattern |231 in a permutation. St000801The number of occurrences of the vincular pattern |312 in a permutation. St001059Number of occurrences of the patterns 41352,42351,51342,52341 in a permutation. St001287The number of primes obtained by multiplying preimage and image of a permutation and subtracting one. St001301The first Betti number of the order complex associated with the poset. St001381The fertility of a permutation. St001396Number of triples of incomparable elements in a finite poset. St001398Number of subsets of size 3 of elements in a poset that form a "v". St001402The number of separators in a permutation. St001403The number of vertical separators in a permutation. St001439The number of even weak deficiencies and of odd weak exceedences. St001466The number of transpositions swapping cyclically adjacent numbers in a permutation. St001513The number of nested exceedences of a permutation. St001537The number of cyclic crossings of a permutation. St001549The number of restricted non-inversions between exceedances. St001550The number of inversions between exceedances where the greater exceedance is linked. St001551The number of restricted non-inversions between exceedances where the rightmost exceedance is linked. St001559The number of transpositions that are smaller or equal to a permutation in Bruhat order while not being inversions. St001661Half the permanent of the Identity matrix plus the permutation matrix associated to the permutation. St001663The number of occurrences of the Hertzsprung pattern 132 in a permutation. St001705The number of occurrences of the pattern 2413 in a permutation. St001728The number of invisible descents of a permutation. St001730The number of times the path corresponding to a binary word crosses the base line. St001771The number of occurrences of the signed pattern 1-2 in a signed permutation. St001781The interlacing number of a set partition. St001847The number of occurrences of the pattern 1432 in a permutation. St001851The number of Hecke atoms of a signed permutation. St001857The number of edges in the reduced word graph of a signed permutation. St001866The nesting alignments of a signed permutation. St001867The number of alignments of type EN of a signed permutation. St001870The number of positive entries followed by a negative entry in a signed permutation. St001895The oddness of a signed permutation. St001906Half of the difference between the total displacement and the number of inversions and the reflection length of a permutation. St000037The sign of a permutation. St001472The permanent of the Coxeter matrix of the poset. St001634The trace of the Coxeter matrix of the incidence algebra of a poset. St001718The number of non-empty open intervals in a poset. St000493The los statistic of a set partition. St000494The number of inversions of distance at most 3 of a permutation. St000677The standardized bi-alternating inversion number of a permutation. St000756The sum of the positions of the left to right maxima of a permutation. St000824The sum of the number of descents and the number of recoils of a permutation. St001535The number of cyclic alignments of a permutation. St001536The number of cyclic misalignments of a permutation. St001807The lower middle entry of a permutation. St001436The index of a given binary word in the lex-order among all its cyclic shifts. St001721The degree of a binary word. St000557The number of occurrences of the pattern {{1},{2},{3}} in a set partition. St001464The number of bases of the positroid corresponding to the permutation, with all fixed points counterclockwise. 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 $K[x]/(x^n)$. St001671Haglund's hag of a permutation. St001858The number of covering elements of a signed permutation in absolute order. St001865The number of alignments of a signed permutation. St000564The number of occurrences of the pattern {{1},{2}} in a set partition. St001412Number of minimal entries in the Bruhat order matrix of a permutation. St000690The size of the conjugacy class of a permutation. St000016The number of attacking pairs of a standard tableau. St001168The vector space dimension of the tilting module corresponding to the permutation in the Auslander algebra of $K[x]/(x^n)$. St001852The size of the conjugacy class of the signed permutation. St001081The number of minimal length factorizations of a permutation into star transpositions. St000280The size of the preimage of the map 'to labelling permutation' from Parking functions to Permutations. St001885The number of binary words with the same proper border set. St000324The shape of the tree associated to a permutation. St001528The number of permutations such that the product with the permutation has the same number of fixed points.