St000725The smallest label of a leaf of the increasing binary tree associated to a permutation. St000863The length of the first row of the shifted shape of a permutation. St000907The number of maximal antichains of minimal length in a poset. St000975The length of the boundary minus the length of the trunk of an ordered tree. St001183The maximum of $projdim(S)+injdim(S)$ over all simple modules in the Nakayama algebra corresponding to the Dyck path. St001245The cyclic maximal difference between two consecutive entries of a permutation. St001246The maximal difference between two consecutive entries of a permutation. St001258Gives the maximum of injective plus projective dimension of an indecomposable module over the corresponding Nakayama algebra. St001554The number of distinct nonempty subtrees of a binary tree. St000672The number of minimal elements in Bruhat order not less than the permutation. St001958The degree of the polynomial interpolating the values of a permutation. St000011The number of touch points (or returns) of a Dyck path. St000015The number of peaks of a Dyck path. St000054The first entry of the permutation. St000094The depth of an ordered tree. St000216The absolute length of a permutation. St000235The number of indices that are not cyclical small weak excedances. St000240The number of indices that are not small excedances. St000299The number of nonisomorphic vertex-induced subtrees. St000326The position of the first one in a binary word after appending a 1 at the end. St000380Half of the maximal perimeter of a rectangle fitting into the diagram of an integer partition. St000459The hook length of the base cell of a partition. St000501The size of the first part in the decomposition of a permutation. St000521The number of distinct subtrees of an ordered tree. St000676The number of odd rises of a Dyck path. St000724The label of the leaf of the path following the smaller label in the increasing binary tree associated to a permutation. St000727The largest label of a leaf in the binary search tree associated with the permutation. St000740The last entry of a permutation. St000844The size of the largest block in the direct sum decomposition of a permutation. St000870The product of the hook lengths of the diagonal cells in an integer partition. St001040The depth of the decreasing labelled binary unordered tree associated with the perfect matching. St001065Number of indecomposable reflexive modules in the corresponding Nakayama algebra. St001068Number of torsionless simple modules in the corresponding Nakayama algebra. St001170Number of indecomposable injective modules whose socle has projective dimension at most g-1 when g denotes the global dimension in the corresponding Nakayama algebra. St001180Number of indecomposable injective modules with projective dimension at most 1. 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. St001291The number of indecomposable summands of the tensor product of two copies of the dual of the Nakayama algebra associated to a Dyck path. St001318The number of vertices of the largest induced subforest with the same number of connected components of a graph. St001321The number of vertices of the largest induced subforest of a graph. 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. St000003The number of standard Young tableaux of the partition. St000019The cardinality of the support of a permutation. St000031The number of cycles in the cycle decomposition of a permutation. St000053The number of valleys of the Dyck path. St000056The decomposition (or block) number of a permutation. St000060The greater neighbor of the maximum. St000062The length of the longest increasing subsequence of the permutation. St000075The orbit size of a standard tableau under promotion. St000088The row sums of the character table of the symmetric group. St000141The maximum drop size of a permutation. St000153The number of adjacent cycles of a permutation. St000166The depth minus 1 of an ordered tree. St000203The number of external nodes of a binary tree. St000209Maximum difference of elements in cycles. St000210Minimum over maximum difference of elements in cycles. St000213The number of weak exceedances (also weak excedences) of a permutation. St000236The number of cyclical small weak excedances. St000239The number of small weak excedances. St000306The bounce count of a Dyck path. St000308The height of the tree associated to a permutation. St000309The number of vertices with even degree. St000314The number of left-to-right-maxima of a permutation. St000315The number of isolated vertices of a graph. St000316The number of non-left-to-right-maxima of a permutation. St000331The number of upper interactions of a Dyck path. St000337The lec statistic, the sum of the inversion numbers of the hook factors of a permutation. St000345The number of refinements of a partition. 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. St000392The length of the longest run of ones in a binary word. St000393The number of strictly increasing runs in a binary word. St000469The distinguishing number of a graph. St000489The number of cycles of a permutation of length at most 3. St000522The number of 1-protected nodes of a rooted tree. St000528The height of a poset. St000531The leading coefficient of the rook polynomial of an integer partition. St000626The minimal period of a binary word. St000628The balance of a binary word. St000636The hull number of a graph. St000653The last descent of a permutation. St000702The number of weak deficiencies of a permutation. St000723The maximal cardinality of a set of vertices with the same neighbourhood in a graph. St000776The maximal multiplicity of an eigenvalue in a graph. St000780The size of the orbit under rotation of a perfect matching. St000806The semiperimeter of the associated bargraph. St000808The number of up steps of the associated bargraph. St000831The number of indices that are either descents or recoils. St000835The minimal difference in size when partitioning the integer partition into two subpartitions. St000877The depth of the binary word interpreted as a path. St000883The number of longest increasing subsequences of a permutation. St000911The number of maximal antichains of maximal size in a poset. St000912The number of maximal antichains in a poset. St000935The number of ordered refinements of an integer partition. St000945The number of matchings in the dihedral orbit of a perfect matching. St000956The maximal displacement of a permutation. St000982The length of the longest constant subword. 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. St000992The alternating sum of the parts of an integer partition. St001023Number of simple modules with projective dimension at most 3 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. St001055The Grundy value for the game of removing cells of a row in an integer partition. St001090The number of pop-stack-sorts needed to sort a permutation. St001114The number of odd descents of a permutation. St001142The projective dimension of the socle of the regular module as a bimodule in the Nakayama algebra corresponding to the Dyck path. 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 $eA$. St001207The Lowey length of the algebra $A/T$ when $T$ is the 1-tilting module corresponding to the permutation in the Auslander algebra of $K[x]/(x^n)$. St001225The vector space dimension of the first extension group between J and itself when J is the Jacobson radical of the corresponding Nakayama algebra. St001267The length of the Lyndon factorization of the binary word. St001269The sum of the minimum of the number of exceedances and deficiencies in each cycle of a permutation. St001278The number of indecomposable modules that are fixed by $\tau \Omega^1$ composed with its inverse in the corresponding Nakayama algebra. St001290The first natural number n such that the tensor product of n copies of D(A) is zero for the corresponding Nakayama algebra A. St001332The number of steps on the non-negative side of the walk associated with the permutation. St001343The dimension of the reduced incidence algebra of a poset. St001355Number of non-empty prefixes of a binary word that contain equally many 0's and 1's. St001366The maximal multiplicity of a degree of a vertex of a graph. St001368The number of vertices of maximal degree in a graph. St001372The length of a longest cyclic run of ones of a binary word. St001389The number of partitions of the same length below the given integer partition. St001415The length of the longest palindromic prefix of a binary word. St001437The flex of a binary word. St001461The number of topologically connected components of the chord diagram of a permutation. St001486The number of corners of the ribbon associated with an integer composition. St001497The position of the largest weak excedence of a permutation. St001499The number of indecomposable projective-injective modules of a magnitude 1 Nakayama algebra. St001504The sum of all indegrees of vertices with indegree at least two in the resolution quiver of a Nakayama algebra corresponding to the Dyck path. St001505The number of elements generated by the Dyck path as a map in the full transformation monoid. St001506Half the projective dimension of the unique simple module with even projective dimension in a magnitude 1 Nakayama algebra. St001508The degree of the standard monomial associated to a Dyck path relative to the diagonal boundary. St001509The degree of the standard monomial associated to a Dyck path relative to the trivial lower boundary. 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). St001566The length of the longest arithmetic progression in a permutation. St001571The Cartan determinant of the integer partition. St001606The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on set partitions. St001654The monophonic hull number of a graph. St001655The general position number of a graph. St001656The monophonic position number of a graph. St001659The number of ways to place as many non-attacking rooks as possible on a Ferrers board. St001667The maximal size of a pair of weak twins for a permutation. St001672The restrained domination number of a graph. St001691The number of kings in a graph. St001717The largest size of an interval in a poset. St001726The number of visible inversions of a permutation. St001746The coalition number of a graph. St001757The number of orbits of toric promotion on a graph. St001773The number of minimal elements in Bruhat order not less than the signed permutation. St001780The order of promotion on the set of standard tableaux of given shape. St001844The maximal degree of a generator of the invariant ring of the automorphism group of a graph. St001917The order of toric promotion on the set of labellings of a graph. St001928The number of non-overlapping descents in a permutation. St001955The number of natural descents for set-valued two row standard Young tableaux. St000022The number of fixed points of a permutation. St000029The depth of a permutation. St000030The sum of the descent differences of a permutations. St000034The maximum defect over any reduced expression for a permutation and any subexpression. St000080The rank of the poset. St000145The Dyson rank of a partition. St000222The number of alignments in the permutation. St000224The sorting index of a permutation. St000234The number of global ascents of a permutation. St000245The number of ascents of a permutation. St000291The number of descents of a binary word. St000293The number of inversions of a binary word. St000338The number of pixed points of a permutation. St000372The number of mid points of increasing subsequences of length 3 in a permutation. St000620The number of standard tableaux of shape equal to the given partition such that the minimal cyclic descent is odd. St000829The Ulam distance of a permutation to the identity permutation. St000837The number of ascents 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. St000875The semilength of the longest Dyck word in the Catalan factorisation of a binary word. St000957The number of Bruhat lower covers of a permutation. St001096The size of the overlap set of a permutation. St001176The size of a partition minus its first part. St001298The number of repeated entries in the Lehmer code of a permutation. St001384The number of boxes in the diagram of a partition that do not lie in the largest triangle it contains. St001405The number of bonds in a permutation. 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. St001424The number of distinct squares in a binary word. St001436The index of a given binary word in the lex-order among all its cyclic shifts. St001469The holeyness of a permutation. St001489The maximum of the number of descents and the number of inverse descents. St001569The maximal modular displacement of a permutation. St001601The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on trees. St001668The number of points of the poset minus the width of the poset. St001727The number of invisible inversions of a permutation. St000007The number of saliances of the permutation. St000013The height of a Dyck path. St000025The number of initial rises of a Dyck path. St000026The position of the first return of a Dyck path. St000058The order of a permutation. St000064The number of one-box pattern of a permutation. St000066The column of the unique '1' in the first row of the alternating sign matrix. St000111The sum of the descent tops (or Genocchi descents) of a permutation. St000184The size of the centralizer of any permutation of given cycle type. St000193The row of the unique '1' in the first column of the alternating sign matrix. St000199The column of the unique '1' in the last row of the alternating sign matrix. St000200The row of the unique '1' in the last column of the alternating sign matrix. St000211The rank of the set partition. St000250The number of blocks (St000105) plus the number of antisingletons (St000248) of a set partition. St000325The width of the tree associated to a permutation. St000395The sum of the heights of the peaks of a Dyck path. St000443The number of long tunnels of a Dyck path. St000444The length of the maximal rise of a Dyck path. St000452The number of distinct eigenvalues of a graph. St000453The number of distinct Laplacian eigenvalues of a graph. St000470The number of runs in a permutation. St000485The length of the longest cycle of a permutation. St000488The number of cycles of a permutation of length at most 2. St000505The biggest entry in the block containing the 1. St000519The largest length of a factor maximising the subword complexity. St000542The number of left-to-right-minima of a permutation. St000548The number of different non-empty partial sums of an integer partition. St000642The size of the smallest orbit of antichains under Panyushev complementation. St000654The first descent of a permutation. St000673The number of non-fixed points of a permutation. St000675The number of centered multitunnels 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. St000686The finitistic dominant dimension of a Dyck path. St000708The product of the parts of an integer partition. St000717The number of ordinal summands of a poset. St000726The normalized sum of the leaf labels of the increasing binary tree associated to a permutation. St000734The last entry in the first row of a standard tableau. St000738The first entry in the last row of a standard tableau. St000743The number of entries in a standard Young tableau such that the next integer is a neighbour. St000777The number of distinct eigenvalues of the distance Laplacian of a connected graph. St000839The largest opener of a set partition. St000876The number of factors in the Catalan decomposition of a binary word. St000906The length of the shortest maximal chain in a poset. St000917The open packing number of a graph. St000918The 2-limited packing number of a graph. 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. 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 $c_{n-1}$. St000971The smallest closer of a set partition. St000973The length of the boundary of an ordered tree. St000999Number of indecomposable projective module with injective dimension equal to the global dimension in the Nakayama algebra corresponding to the Dyck path. St001007Number of simple modules with projective dimension 1 in the Nakayama algebra corresponding to the Dyck path. St001009Number of indecomposable injective modules with projective dimension g 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. St001018Sum of projective dimension of the indecomposable injective modules of the Nakayama algebra corresponding to the Dyck path. St001020Sum of the codominant dimensions of the non-projective indecomposable injective modules of the Nakayama algebra corresponding to the Dyck path. St001024Maximum of dominant dimensions of the simple modules in the Nakayama algebra corresponding to the Dyck path. St001088Number of indecomposable projective non-injective modules with dominant dimension equal to the injective dimension in the corresponding Nakayama algebra. St001093The detour number of a graph. St001110The 3-dynamic chromatic number of a graph. St001134The largest label in the subtree rooted at the sister of 1 in the leaf labelled binary unordered tree associated with the perfect matching. St001135The projective dimension of the first simple module in the Nakayama algebra corresponding to the Dyck path. St001166Number of indecomposable projective non-injective modules with dominant dimension equal to the global dimension plus the number of indecomposable projective injective modules in the corresponding Nakayama algebra. St001184Number of indecomposable injective modules with grade at least 1 in the corresponding Nakayama algebra. St001187The number of simple modules with grade at least one in the corresponding Nakayama algebra. St001201The grade of the simple module $S_0$ in the special CNakayama algebra corresponding to the Dyck path. St001210Gives the maximal vector space dimension of the first Ext-group between an indecomposable module X and the regular module A, when A is the Nakayama algebra corresponding to the Dyck path. St001224Let X be the direct sum of all simple modules of the corresponding Nakayama algebra. St001241The number of non-zero radicals of the indecomposable projective modules that have injective dimension and projective dimension at most one. St001279The sum of the parts of an integer partition that are at least two. 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. St001315The dissociation number of a graph. St001345The Hamming dimension of a graph. St001373The logarithm of the number of winning configurations of the lights out game on a graph. St001390The number of bumps occurring when Schensted-inserting the letter 1 of a permutation. St001391The disjunction number of a graph. St001416The length of a longest palindromic factor of a binary word. St001419The length of the longest palindromic factor beginning with a one of a binary word. St001439The number of even weak deficiencies and of odd weak exceedences. St001463The number of distinct columns in the nullspace of a graph. St001464The number of bases of the positroid corresponding to the permutation, with all fixed points counterclockwise. St001481The minimal height of a peak of a Dyck path. St001526The Loewy length of the Auslander-Reiten translate of the regular module as a bimodule of the Nakayama algebra corresponding to the Dyck path. St001530The depth of a Dyck path. St001581The achromatic number of a graph. St001619The number of non-isomorphic sublattices of a lattice. St001626The number of maximal proper sublattices of a lattice. St001636The number of indecomposable injective modules with projective dimension at most one in the incidence algebra of the poset. St001666The number of non-isomorphic subposets of a lattice which are lattices. St001670The connected partition number of a graph. St001720The minimal length of a chain of small intervals in a lattice. St001725The harmonious chromatic number of a graph. St001778The largest greatest common divisor of an element and its image in a permutation. St001784The minimum of the smallest closer and the second element of the block containing 1 in a set partition. St001809The index of the step at the first peak of maximal height in a Dyck path. St001927Sparre Andersen's number of positives of a signed permutation. St000010The length of the partition. St000012The area of a Dyck path. St000021The number of descents of a permutation. St000024The number of double up and double down steps of a Dyck path. St000028The number of stack-sorts needed to sort a permutation. St000047The number of standard immaculate tableaux of a given shape. St000051The size of the left subtree of a binary tree. St000063The number of linear extensions of a certain poset defined for an integer partition. St000071The number of maximal chains in a poset. St000078The number of alternating sign matrices whose left key is the permutation. St000089The absolute variation of a composition. 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. St000105The number of blocks in the set partition. St000108The number of partitions contained in the given partition. St000110The number of permutations less than or equal to a permutation in left weak order. St000133The "bounce" of a permutation. St000134The size of the orbit of an alternating sign matrix under gyration. St000147The largest part of an integer partition. St000148The number of odd parts of a partition. St000155The number of exceedances (also excedences) of a permutation. St000156The Denert index of a permutation. St000160The multiplicity of the smallest part of a partition. St000162The number of nontrivial cycles in the cycle decomposition of a permutation. St000163The size of the orbit of the set partition under rotation. St000171The degree of the graph. St000172The Grundy number of a graph. St000208Number of integral Gelfand-Tsetlin polytopes with prescribed top row and integer partition weight. St000238The number of indices that are not small weak excedances. St000255The number of reduced Kogan faces with the permutation as type. St000258The burning number of a graph. St000259The diameter of a connected graph. St000271The chromatic index of a graph. St000273The domination number of a graph. St000276The size of the preimage of the map 'to graph' from Ordered trees to Graphs. St000278The size of the preimage of the map 'to partition' from Integer compositions to Integer partitions. St000287The number of connected components of a graph. St000297The number of leading ones in a binary word. St000321The number of integer partitions of n that are dominated by an integer partition. St000329The number of evenly positioned ascents of the Dyck path, with the initial position equal to 1. St000333The dez statistic, the number of descents of a permutation after replacing fixed points by zeros. St000339The maf index of a permutation. St000346The number of coarsenings of a partition. St000354The number of recoils of a permutation. St000362The size of a minimal vertex cover of a graph. St000363The number of minimal vertex covers of a graph. St000374The number of exclusive right-to-left minima of a permutation. St000387The matching number of a graph. St000390The number of runs of ones in a binary word. St000394The sum of the heights of the peaks of a Dyck path minus the number of peaks. St000414The binary logarithm of the number of binary trees with the same underlying unordered tree. St000439The position of the first down step of a Dyck path. St000442The maximal area to the right of an up step of a Dyck path. St000451The length of the longest pattern of the form k 1 2. St000475The number of parts equal to 1 in a partition. St000476The sum of the semi-lengths of tunnels before a valley of a Dyck path. St000482The (zero)-forcing number of a graph. St000495The number of inversions of distance at most 2 of a permutation. St000503The maximal difference between two elements in a common block. St000507The number of ascents of a standard tableau. St000532The total number of rook placements on a Ferrers board. St000533The minimum of the number of parts and the size of the first part of an integer partition. St000539The number of odd inversions of a permutation. St000541The number of indices greater than or equal to 2 of a permutation such that all smaller indices appear to its right. St000544The cop number of a graph. St000546The number of global descents of a permutation. St000550The number of modular elements of a lattice. St000551The number of left modular elements of a lattice. St000553The number of blocks of a graph. St000568The hook number of a binary tree. St000617The number of global maxima of a Dyck path. St000619The number of cyclic descents of a permutation. St000638The number of up-down runs of a permutation. St000643The size of the largest orbit of antichains under Panyushev complementation. St000645The sum of the areas of the rectangles formed by two consecutive peaks and the valley in between. St000651The maximal size of a rise in a permutation. St000652The maximal difference between successive positions of a permutation. St000662The staircase size of the code of a permutation. St000670The reversal length of a permutation. St000681The Grundy value of Chomp on Ferrers diagrams. St000692Babson and Steingrímsson's statistic of a permutation. St000695The number of blocks in the first part of the atomic decomposition of a set partition. St000703The number of deficiencies of a permutation. St000729The minimal arc length of a set partition. St000730The maximal arc length of a set partition. St000742The number of big ascents of a permutation after prepending zero. St000757The length of the longest weakly inreasing subsequence of parts of an integer composition. St000765The number of weak records in an integer composition. St000774The maximal multiplicity of a Laplacian eigenvalue in a graph. St000783The side length of the largest staircase partition fitting into a partition. St000784The maximum of the length and the largest part of the integer partition. St000786The maximal number of occurrences of a colour in a proper colouring of a graph. St000793The length of the longest partition in the vacillating tableau corresponding to a set partition. St000797The stat`` of a permutation. St000809The reduced reflection length of the permutation. St000833The comajor index of a permutation. St000840The number of closers smaller than the largest opener in a perfect matching. St000849The number of 1/3-balanced pairs in a poset. St000864The number of circled entries of the shifted recording tableau of a permutation. St000868The aid statistic in the sense of Shareshian-Wachs. St000874The position of the last double rise in a Dyck path. St000887The maximal number of nonzero entries on a diagonal of a permutation matrix. St000891The number of distinct diagonal sums of a permutation matrix. St000899The maximal number of repetitions of an integer composition. St000904The maximal number of repetitions of an integer composition. St000909The number of maximal chains of maximal size in a poset. St000910The number of maximal chains of minimal length in a poset. St000915The Ore degree of a graph. St000916The packing number of a graph. St000930The k-Gorenstein degree of the corresponding Nakayama algebra with linear quiver. St000937The number of positive values of the symmetric group character corresponding to the partition. St000942The number of critical left to right maxima of the parking functions. St000983The length of the longest alternating subword. St000984The number of boxes below precisely one peak. St000985The number of positive eigenvalues of the adjacency matrix of the graph. 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. St001017Number of indecomposable injective modules with projective dimension equal to the codominant dimension in the Nakayama algebra corresponding to the Dyck path. St001027Number of simple modules with projective dimension equal to injective dimension in the Nakayama algebra corresponding to the Dyck path. St001030Half the number of non-boundary horizontal edges in the fully packed loop corresponding to the alternating sign matrix. St001039The maximal height of a column in the parallelogram polyomino associated with a Dyck path. St001041The depth of the label 1 in the decreasing labelled binary unordered tree associated with the perfect matching. St001048The number of leaves in the subtree containing 1 in the decreasing labelled binary unordered tree associated with the perfect matching. St001050The number of terminal closers of a set partition. St001051The depth of the label 1 in the decreasing labelled unordered tree associated with the set partition. St001052The length of the exterior of a permutation. St001061The number of indices that are both descents and recoils 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. St001080The minimal length of a factorization of a permutation using the transposition (12) and the cycle (1,. St001081The number of minimal length factorizations of a permutation into star transpositions. St001082The number of boxed occurrences of 123 in a permutation. St001108The 2-dynamic chromatic number of a graph. St001115The number of even descents of a permutation. St001116The game chromatic number of a graph. St001119The length of a shortest maximal path in a graph. St001120The length of a longest path in a graph. St001182Number of indecomposable injective modules with codominant dimension at least two in the corresponding Nakayama algebra. St001189The number of simple modules with dominant and codominant dimension equal to zero in the Nakayama algebra corresponding to the Dyck path. St001190Number of simple modules with projective dimension at most 4 in the corresponding Nakayama algebra. St001220The width of a permutation. St001226The number of integers i such that the radical of the i-th indecomposable projective module has vanishing first extension group with the Jacobson radical J in the corresponding Nakayama algebra. 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. St001233The number of indecomposable 2-dimensional modules with projective dimension one. St001235The global dimension of the corresponding Comp-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. St001247The number of parts of a partition that are not congruent 2 modulo 3. St001249Sum of the odd parts of a partition. St001250The number of parts of a partition that are not congruent 0 modulo 3. St001255The vector space dimension of the double dual of A/J when A is the corresponding Nakayama algebra with Jacobson radical J. St001286The annihilation number of a graph. St001287The number of primes obtained by multiplying preimage and image of a permutation and subtracting one. St001295Gives the vector space dimension of the homomorphism space between J^2 and J^2. St001296The maximal torsionfree index of an indecomposable non-projective module in the corresponding Nakayama algebra. St001304The number of maximally independent sets of vertices of a graph. St001313The number of Dyck paths above the lattice path given by a binary word. St001322The size of a minimal independent dominating set in a graph. St001337The upper domination number of a graph. St001338The upper irredundance number of a graph. St001339The irredundance number of a graph. St001342The number of vertices in the center of a graph. St001363The Euler characteristic of a graph according to Knill. St001371The length of the longest Yamanouchi prefix of a binary word. St001400The total number of Littlewood-Richardson tableaux of given shape. St001417The length of a longest palindromic subword of a binary word. St001432The order dimension of the partition. St001462The number of factors of a standard tableaux under concatenation. St001480The number of simple summands of the module J^2/J^3. St001483The number of simple module modules that appear in the socle of the regular module but have no nontrivial selfextensions with the regular module. St001488The number of corners of a skew partition. 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. St001579The number of cyclically simple transpositions decreasing the number of cyclic descents needed to sort a permutation. St001595The number of standard Young tableaux of the skew partition. St001616The number of neutral elements in a lattice. St001649The length of a longest trail in a graph. St001650The order of Ringel's homological bijection associated to the linear Nakayama algebra corresponding to the Dyck path. St001652The length of a longest interval of consecutive numbers. St001662The length of the longest factor of consecutive numbers in a permutation. St001665The number of pure excedances of a permutation. St001671Haglund's hag of a permutation. St001674The number of vertices of the largest induced star graph in the graph. St001722The number of minimal chains with small intervals between a binary word and the top element. St001729The number of visible descents of a permutation. St001733The number of weak left to right maxima of a Dyck path. St001734The lettericity of a graph. St001741The largest integer such that all patterns of this size are contained in the permutation. St001761The maximal multiplicity of a letter in a reduced word of a permutation. St001769The reflection length of a signed permutation. St001782The order of rowmotion on the set of order ideals of a poset. St001801Half the number of preimage-image pairs of different parity in a permutation. St001807The lower middle entry of a permutation. St001820The size of the image of the pop stack sorting operator. St001828The Euler characteristic of a graph. St001829The common independence number of a graph. St001863The number of weak excedances of a signed permutation. St001874Lusztig's a-function for the symmetric group. St001884The number of borders of a binary word. St001889The size of the connectivity set of a signed permutation. St001904The length of the initial strictly increasing segment of a parking function. St001914The size of the orbit of an integer partition in Bulgarian solitaire. 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. St001937The size of the center of a parking function. St001948The number of augmented double ascents of a permutation. St001963The tree-depth of a graph. St000004The major index of a permutation. St000018The number of inversions of a permutation. St000023The number of inner peaks of a permutation. St000035The number of left outer peaks of a permutation. St000057The Shynar inversion number of a standard tableau. St000083The number of left oriented leafs of a binary tree except the first one. St000161The sum of the sizes of the right subtrees of a binary tree. St000175Degree of the polynomial counting the number of semistandard Young tableaux when stretching the shape. St000212The number of standard Young tableaux for an integer partition such that no two consecutive entries appear in the same row. St000215The number of adjacencies of a permutation, zero appended. St000220The number of occurrences of the pattern 132 in a permutation. St000223The number of nestings in the permutation. St000228The size of a partition. St000237The number of small exceedances. St000241The number of cyclical small excedances. St000242The number of indices that are not cyclical small weak excedances. St000246The number of non-inversions of a permutation. St000290The major index of a binary word. St000292The number of ascents of a binary word. St000319The spin of an integer partition. St000320The dinv adjustment of an integer partition. St000327The number of cover relations in a poset. St000334The maz index, the major index of a permutation after replacing fixed points by zeros. St000353The number of inner valleys of a permutation. St000356The number of occurrences of the pattern 13-2. St000358The number of occurrences of the pattern 31-2. St000359The number of occurrences of the pattern 23-1. St000365The number of double ascents of a permutation. St000371The number of mid points of decreasing subsequences of length 3 in a permutation. St000373The number of weak exceedences of a permutation that are also mid-points of a decreasing subsequence of length $3$. St000377The dinv defect of an integer partition. St000424The number of occurrences of the pattern 132 or of the pattern 231 in a permutation. St000425The number of occurrences of the pattern 132 or of the pattern 213 in a permutation. St000430The number of occurrences of the pattern 123 or of the pattern 312 in a permutation. St000431The number of occurrences of the pattern 213 or of the pattern 321 in a permutation. St000433The number of occurrences of the pattern 132 or of the pattern 321 in a permutation. St000434The number of occurrences of the pattern 213 or of the pattern 312 in a permutation. St000441The number of successions of a permutation. St000448The number of pairs of vertices of a graph with distance 2. St000463The number of admissible inversions of a permutation. St000480The number of lower covers of a partition in dominance order. St000481The number of upper covers of a partition in dominance order. St000483The number of times a permutation switches from increasing to decreasing or decreasing to increasing. St000491The number of inversions of a set partition. St000494The number of inversions of distance at most 3 of a permutation. St000496The rcs statistic of a set partition. St000497The lcb statistic of a set partition. St000512The number of invariant subsets of size 3 when acting with a permutation of given cycle type. St000538The number of even inversions of a permutation. St000552The number of cut vertices of a graph. St000565The major index of a set partition. St000572The dimension exponent of a set partition. St000581The number of occurrences of the pattern {{1,3},{2}} such that 1 is minimal, 2 is maximal. St000585The number of occurrences of the pattern {{1,3},{2}} such that 2 is maximal, (1,3) are consecutive in a block. St000594The number of occurrences of the pattern {{1,3},{2}} such that 1,2 are minimal, (1,3) are consecutive in a block. St000600The number of occurrences of the pattern {{1,3},{2}} such that 1 is minimal, (1,3) are consecutive in a block. St000610The number of occurrences of the pattern {{1,3},{2}} such that 2 is maximal. St000613The number of occurrences of the pattern {{1,3},{2}} such that 2 is minimal, 3 is maximal, (1,3) are consecutive in a block. 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. St000624The normalized sum of the minimal distances to a greater element. St000646The number of big ascents of a permutation. St000663The number of right floats of a permutation. St000677The standardized bi-alternating inversion number of a permutation. St000682The Grundy value of Welter's game on a binary word. St000688The global dimension minus the dominant dimension of the LNakayama algebra associated to a Dyck path. St000691The number of changes of a binary word. St000710The number of big deficiencies of a permutation. St000711The number of big exceedences of a permutation. St000732The number of double deficiencies of a permutation. St000741The Colin de Verdière graph invariant. St000778The metric dimension of a graph. St000795The mad of a permutation. St000799The number of occurrences of the vincular pattern |213 in a permutation. St000800The number of occurrences of the vincular pattern |231 in a permutation. St000803The number of occurrences of the vincular pattern |132 in a permutation. St000834The number of right outer peaks of a permutation. St000836The number of descents of distance 2 of a permutation. St000931The number of occurrences of the pattern UUU in a Dyck path. St000934The 2-degree of an integer partition. St000940The number of characters of the symmetric group whose value on the partition is zero. St000941The number of characters of the symmetric group whose value on the partition is even. St000970Number of peaks minus the dominant dimension of the corresponding LNakayama algebra. St001033The normalized area of the parallelogram polyomino associated with the Dyck path. St001067The number of simple modules of dominant dimension at least two in the corresponding Nakayama algebra. St001078The minimal number of occurrences of (12) in a factorization of a permutation into transpositions (12) and cycles (1,. St001079The minimal length of a factorization of a permutation using the permutations (12)(34). St001084The number of occurrences of the vincular pattern |1-23 in a permutation. St001086The number of occurrences of the consecutive pattern 132 in a permutation. St001087The number of occurrences of the vincular pattern |12-3 in a permutation. St001091The number of parts in an integer partition whose next smaller part has the same size. St001117The game chromatic index of a graph. St001126Number of simple module that are 1-regular in the corresponding Nakayama algebra. St001163The number of simple modules with dominant dimension at least three in the corresponding Nakayama algebra. St001164Number of indecomposable injective modules whose socle has projective dimension at most g-1 (g the global dimension) minus the number of indecomposable projective-injective modules. St001167The number of simple modules that appear as the top of an indecomposable non-projective modules that is reflexive in the corresponding Nakayama algebra. St001188The number of simple modules $S$ with grade $\inf \{ i \geq 0 | Ext^i(S,A) \neq 0 \}$ at least two in the Nakayama algebra $A$ corresponding to the Dyck path. St001218Smallest index k greater than or equal to one such that the Coxeter matrix C of the corresponding Nakayama algebra has C^k=1. 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. St001231The number of simple modules that are non-projective and non-injective with the property that they have projective dimension equal to one and that also the Auslander-Reiten translates of the module and the inverse Auslander-Reiten translate of the module have the same projective dimension. St001234The number of indecomposable three dimensional modules with projective dimension one. St001244The number of simple modules of projective dimension one that are not 1-regular for the Nakayama algebra associated to a Dyck path. St001253The number of non-projective indecomposable reflexive modules in the corresponding Nakayama algebra. St001263The index of the maximal parabolic seaweed algebra associated with the composition. St001273The projective dimension of the first term in an injective coresolution of the regular module. St001294The maximal torsionfree index of a simple 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. St001340The cardinality of a minimal non-edge isolating set of a graph. St001375The pancake length of a permutation. St001388The number of non-attacking neighbors of a permutation. St001394The genus of a permutation. St001403The number of vertical separators in a permutation. St001411The number of patterns 321 or 3412 in a permutation. St001414Half the length of the longest odd length 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. St001442The number of standard Young tableaux whose major index is divisible by the size of a given integer partition. St001470The cyclic holeyness of a permutation. St001485The modular major index of a binary word. St001511The minimal number of transpositions needed to sort a permutation in either direction. St001520The number of strict 3-descents. St001557The number of inversions of the second entry of a permutation. St001558The number of transpositions that are smaller or equal to a permutation in Bruhat order. St001565The number of arithmetic progressions of length 2 in a permutation. 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. St001640The number of ascent tops in the permutation such that all smaller elements appear before. St001682The number of distinct positions of the pattern letter 1 in occurrences of 123 in a permutation. St001684The reduced word complexity of a permutation. St001687The number of distinct positions of the pattern letter 2 in occurrences of 213 in a permutation. St001692The number of vertices with higher degree than the average degree in a graph. St001693The excess length of a longest path consisting of elements and blocks of a set partition. St001723The differential of a graph. St001724The 2-packing differential of a graph. St001742The difference of the maximal and the minimal degree in a graph. St001743The discrepancy of a graph. St001759The Rajchgot index of a permutation. St001760The number of prefix or suffix reversals needed to sort a permutation. St001777The number of weak descents in an integer composition. St001781The interlacing number of a set partition. St001810The number of fixed points of a permutation smaller than its largest moved point. St001811The Castelnuovo-Mumford regularity of a permutation. St001812The biclique partition number of a graph. St001816Eigenvalues of the top-to-random operator acting on a simple module. St001821The sorting index of a signed permutation. St001822The number of alignments of a signed permutation. St001839The number of excedances of a set partition. St001841The number of inversions of a set partition. St001843The Z-index of a set partition. St001861The number of Bruhat lower covers of a permutation. St001894The depth of a signed permutation. St001918The degree of the cyclic sieving polynomial corresponding to an integer partition. St001935The number of ascents in a parking function. St001949The rigidity index of a graph. St001960The number of descents of a permutation minus one if its first entry is not one. St000351The determinant of the adjacency matrix of a graph. St000402Half the size of the symmetry class of a permutation. St000530The number of permutations with the same descent word as the given permutation. St001035The convexity degree of the parallelogram polyomino associated with the Dyck path. St000714The number of semistandard Young tableau of given shape, with entries at most 2. St000515The number of invariant set partitions when acting with a permutation of given cycle type. St000100The number of linear extensions of a poset. St000478Another weight of a partition according to Alladi. St000529The number of permutations whose descent word is the given binary word. St000543The size of the conjugacy class of a binary word. St000627The exponent of a binary word. St000630The length of the shortest palindromic decomposition of a binary word. St000631The number of distinct palindromic decompositions of a binary word. St000633The size of the automorphism group of a poset. St000640The rank of the largest boolean interval in a poset. St000704The number of semistandard tableaux on a given integer partition with minimal maximal entry. St000832The number of permutations obtained by reversing blocks of three consecutive numbers. St001105The number of greedy linear extensions of a poset. St001106The number of supergreedy linear extensions of a poset. St001128The exponens consonantiae of a partition. St001603The number of colourings of a polygon such that the multiplicities of a colour are given by a partition. St001632The number of indecomposable injective modules $I$ with $dim Ext^1(I,A)=1$ for the incidence algebra A of a poset. St001915The size of the component corresponding to a necklace in Bulgarian solitaire. St000295The length of the border of a binary word. St000804The number of occurrences of the vincular pattern |123 in a permutation. St000848The balance constant multiplied with the number of linear extensions of a poset. St000850The number of 1/2-balanced pairs in a poset. St000938The number of zeros of the symmetric group character corresponding to the partition. St001124The multiplicity of the standard representation in the Kronecker square corresponding to a partition. St001130The number of two successive successions in a permutation. St001413Half the length of the longest even length palindromic prefix of a binary word. St001524The degree of symmetry of a binary word. St001930The weak major index of a binary word. St000718The largest Laplacian eigenvalue of a graph if it is integral. St000249The number of singletons (St000247) plus the number of antisingletons (St000248) of a set partition. St000307The number of rowmotion orbits of a poset. St000668The least common multiple of the parts of the partition. St000925The number of topologically connected components of a set partition. St000933The number of multipartitions of sizes given by an integer partition. St000939The number of characters of the symmetric group whose value on the partition is positive. St000990The first ascent of a permutation. St001198The number of simple modules in the algebra $eAe$ with projective dimension at most 1 in the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. 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 $eA$. St001206The maximal dimension of an indecomposable projective $eAe$-module (that is the height of the corresponding Dyck path) of the corresponding Nakayama algebra with minimal faithful projective-injective module $eA$. St001330The hat guessing number of a graph. St001637The number of (upper) dissectors of a poset. St001645The pebbling number of a connected graph. St001686The order of promotion on a Gelfand-Tsetlin pattern. St001875The number of simple modules with projective dimension at most 1. St001876The number of 2-regular simple modules in the incidence algebra of the lattice. St000020The rank of the permutation. St000033The number of permutations greater than or equal to the given permutation in (strong) Bruhat order. St000040The number of regions of the inversion arrangement of a permutation. St000109The number of elements less than or equal to the given element in Bruhat order. St000243The number of cyclic valleys and cyclic peaks of a permutation. St000288The number of ones in a binary word. St000454The largest eigenvalue of a graph if it is integral. St000460The hook length of the last cell along the main diagonal of an integer partition. St000545The number of parabolic double cosets with minimal element being the given permutation. St000657The smallest part of an integer composition. St000694The number of affine bounded permutations that project to a given permutation. St000744The length of the path to the largest entry in a standard Young tableau. St000753The Grundy value for the game of Kayles on a binary word. St000794The mak of a permutation. 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. St000886The number of permutations with the same antidiagonal sums. St000898The number of maximal entries in the last diagonal of the monotone triangle. St000900The minimal number of repetitions of a part in an integer composition. St000902 The minimal number of repetitions of an integer composition. St000932The number of occurrences of the pattern UDU in a Dyck path. St000989The number of final rises of a permutation. St001101The coefficient times the product of the factorials of the parts of the monomial symmetric function indexed by the partition in the formal group law for increasing trees. St001118The acyclic chromatic index of a graph. St001236The dominant dimension of the corresponding Comp-Nakayama algebra. St001285The number of primes in the column sums of the two line notation of a permutation. St001312Number of parabolic noncrossing partitions indexed by the composition. St001346The number of parking functions that give the same permutation. St001360The number of covering relations in Young's lattice below a partition. St001378The product of the cohook lengths of the integer partition. St001380The number of monomer-dimer tilings of a Ferrers diagram. St001482The product of the prefix sums of a permutation. St001491The number of indecomposable projective-injective modules in the algebra corresponding to a subset. St001604The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on polygons. St001607The number of coloured graphs such that the multiplicities of colours are given by a partition. St001611The number of multiset partitions such that the multiplicities of elements are given by a partition. St001661Half the permanent of the Identity matrix plus the permutation matrix associated to the permutation. St001675The number of parts equal to the part in the reversed composition. St001806The upper middle entry of a permutation. St000008The major index of the composition. St000055The inversion sum of a permutation. St000154The sum of the descent bottoms of a permutation. St000219The number of occurrences of the pattern 231 in a permutation. St000304The load of a permutation. St000305The inverse major index of a permutation. St000341The non-inversion sum of a permutation. St000347The inversion sum of a binary word. St000348The non-inversion sum of a binary word. St000352The Elizalde-Pak rank of a permutation. St000369The dinv deficit of a Dyck path. St000376The bounce deficit of a Dyck path. St000432The number of occurrences of the pattern 231 or of the pattern 312 in a permutation. St000435The number of occurrences of the pattern 213 or of the pattern 231 in a permutation. St000436The number of occurrences of the pattern 231 or of the pattern 321 in a permutation. St000437The number of occurrences of the pattern 312 or of the pattern 321 in a permutation. St000446The disorder of a permutation. St000461The rix statistic of a permutation. St000486The number of cycles of length at least 3 of a permutation. St000557The number of occurrences of the pattern {{1},{2},{3}} in a set partition. St000580The number of occurrences of the pattern {{1},{2},{3}} such that 2 is minimal, 3 is maximal. St000584The number of occurrences of the pattern {{1},{2},{3}} such that 1 is minimal, 3 is maximal. St000587The number of occurrences of the pattern {{1},{2},{3}} such that 1 is minimal. St000588The number of occurrences of the pattern {{1},{2},{3}} such that 1,3 are minimal, 2 is maximal. St000591The number of occurrences of the pattern {{1},{2},{3}} such that 2 is maximal. St000592The number of occurrences of the pattern {{1},{2},{3}} such that 1 is maximal. St000593The number of occurrences of the pattern {{1},{2},{3}} such that 1,2 are minimal. St000596The number of occurrences of the pattern {{1},{2},{3}} such that 3 is minimal, 1 is maximal. St000603The number of occurrences of the pattern {{1},{2},{3}} such that 2,3 are minimal. St000604The number of occurrences of the pattern {{1},{2},{3}} such that 3 is minimal, 2 is maximal. St000608The number of occurrences of the pattern {{1},{2},{3}} such that 1,2 are minimal, 3 is maximal. St000615The number of occurrences of the pattern {{1},{2},{3}} such that 1,3 are maximal. St000779The tier of a permutation. St000802The number of occurrences of the vincular pattern |321 in a permutation. St000928The sum of the coefficients of the character polynomial of an integer partition. 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 $K[x]/(x^n)$. 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 $Af$. St001412Number of minimal entries in the Bruhat order matrix of a permutation. St001465The number of adjacent transpositions in the cycle decomposition of a permutation. St001466The number of transpositions swapping cyclically adjacent numbers in a permutation. St001502The global dimension minus the dominant dimension of magnitude 1 Nakayama algebras. St001552The number of inversions between excedances and fixed points of a permutation. 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. St001731The factorization defect of a permutation. St001737The number of descents of type 2 in a permutation. St001767The largest minimal number of arrows pointing to a cell in the Ferrers diagram in any assignment. St001859The number of factors of the Stanley symmetric function associated with a permutation. St001931The weak major index of an integer composition regarded as a word. St001510The number of self-evacuating linear extensions of a finite poset. St001633The number of simple modules with projective dimension two in the incidence algebra of the poset. St001621The number of atoms of a lattice. St001623The number of doubly irreducible elements of a lattice. St001880The number of 2-Gorenstein indecomposable injective modules in the incidence algebra of the lattice. St001555The order of a signed permutation. St001644The dimension 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. St001638The book thickness of a graph. St001570The minimal number of edges to add to make a graph Hamiltonian. St000044The number of vertices of the unicellular map given by a perfect matching. St000487The length of the shortest cycle of a permutation. St000527The width of the poset. St001019Sum of the projective dimensions of the simple modules in the Nakayama algebra corresponding to the Dyck path. 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. St000632The jump number of the poset. 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. St001060The distinguishing index of a graph. St001168The vector space dimension of the tilting module corresponding to the permutation in the Auslander algebra of $K[x]/(x^n)$. St001232The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2. St000280The size of the preimage of the map 'to labelling permutation' from Parking functions to Permutations. St000285The size of the preimage of the map 'to inverse des composition' from Parking functions to Integer compositions. 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. St001605The number of colourings of a cycle such that the multiplicities of colours are given by a partition. St000260The radius of a connected graph. St000466The Gutman (or modified Schultz) index of a connected graph. St000472The sum of the ascent bottoms of a permutation. St000782The indicator function of whether a given perfect matching is an L & P matching. St000796The stat' of a permutation. St000798The makl of a permutation. St000455The second largest eigenvalue of a graph if it is integral. St001926Sparre Andersen's position of the maximum of a signed permutation. St000739The first entry in the last row of a semistandard tableau. St001401The number of distinct entries in a semistandard tableau. St000101The cocharge of a semistandard tableau. St001556The number of inversions of the third entry of a permutation. St001856The number of edges in the reduced word graph of a permutation. St000251The number of nonsingleton blocks of a set partition. St000493The los statistic of a set partition. St000499The rcb statistic of a set partition. St000504The cardinality of the first block of a set partition. St000508Eigenvalues of the random-to-random operator acting on a simple module. St000558The number of occurrences of the pattern {{1,2}} in a set partition. St000605The number of occurrences of the pattern {{1},{2,3}} such that 3 is maximal, (2,3) are consecutive in a block. St000822The Hadwiger number of the graph. St000823The number of unsplittable factors of the set partition. St000873The aix statistic of a permutation. St000961The shifted major index of a permutation. St000963The 2-shifted major index of a permutation. St001062The maximal size of a block of a set partition. St001075The minimal size of a block of a set partition. St001642The Prague dimension of a graph. St001738The minimal order of a graph which is not an induced subgraph of the given graph. St000116The major index of a semistandard tableau obtained by standardizing. St000135The number of lucky cars of the parking function. St000168The number of internal nodes of an ordered tree. St000173The segment statistic of a semistandard tableau. St000174The flush statistic of a semistandard tableau. St000375The number of non weak exceedences of a permutation that are mid-points of a decreasing subsequence of length $3$. 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. St000736The last entry in the first row of a semistandard tableau. St000880The number of connected components of long braid edges in the graph of braid moves of a permutation. St000958The number of Bruhat factorizations of a permutation. St001002Number of indecomposable modules with projective and injective dimension at most 1 in the Nakayama algebra corresponding to the Dyck path. St001487The number of inner corners of a skew partition. St001591The number of graphs with the given composition of multiplicities of Laplacian eigenvalues. St001596The number of two-by-two squares inside a skew partition. St001630The global dimension of the incidence algebra of the lattice over the rational numbers. St001744The number of occurrences of the arrow pattern 1-2 with an arrow from 1 to 2 in a permutation. St001768The number of reduced words of a signed permutation. St001864The number of excedances of a signed permutation. St001877Number of indecomposable injective modules with projective dimension 2. St001878The projective dimension of the simple modules corresponding to the minimum of L in the incidence algebra of the lattice L. St001896The number of right descents of a signed permutations. St001905The number of preferred parking spots in a parking function less than the index of the car. St001946The number of descents in a parking function. St000002The number of occurrences of the pattern 123 in a permutation. St000095The number of triangles of a graph. St000102The charge of a semistandard tableau. St000357The number of occurrences of the pattern 12-3. St000422The energy of a graph, if it is integral. St000879The number of long braid edges in the graph of braid moves of a permutation. St000881The number of short braid edges in the graph of braid moves of a permutation. St001314The number of tilting modules of arbitrary projective dimension that have no simple modules as a direct summand in the corresponding Nakayama algebra. St001431Half of the Loewy length minus one of a modified stable Auslander algebra of the Nakayama algebra corresponding to the Dyck path. St001435The number of missing boxes in the first row. St001438The number of missing boxes of a skew partition. St001572The minimal number of edges to remove to make a graph bipartite. St001573The minimal number of edges to remove to make a graph triangle-free. St001575The minimal number of edges to add or remove to make a graph edge transitive. St001577The minimal number of edges to add or remove to make a graph a cograph. St001578The minimal number of edges to add or remove to make a graph a line graph. St001745The number of occurrences of the arrow pattern 13 with an arrow from 1 to 2 in a permutation. St001857The number of edges in the reduced word graph of a signed permutation. St001882The number of occurrences of a type-B 231 pattern in a signed permutation. St001964The interval resolution global dimension of a poset. St000735The last entry on the main diagonal of a standard tableau.