St001020Sum of the codominant dimensions of the non-projective indecomposable injective modules of the Nakayama algebra corresponding to the Dyck path. St001034The area of the parallelogram polyomino associated with the 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. St001342The number of vertices in the center of a graph. St001800The number of 3-Catalan paths having this Dyck path as first and last coordinate projections. St000998Number of indecomposable projective modules with injective dimension smaller than or equal to the dominant dimension in the Nakayama algebra corresponding to the Dyck path. St001012Number of simple modules with projective dimension at most 2 in the Nakayama algebra corresponding to the Dyck path. St000010The length of the partition. St000012The area of a Dyck path. St000018The number of inversions of a permutation. St000019The cardinality of the support 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. St000148The number of odd parts of a partition. St000160The multiplicity of the smallest part of a partition. St000161The sum of the sizes of the right subtrees of a binary tree. St000171The degree of the graph. St000237The number of small exceedances. St000246The number of non-inversions of a permutation. St000384The maximal part of the shifted composition of an integer partition. St000394The sum of the heights of the peaks of a Dyck path minus the number of peaks. St000459The hook length of the base cell of a partition. St000475The number of parts equal to 1 in a partition. St000651The maximal size of a rise in a permutation. St000692Babson and Steingrímsson's statistic of a permutation. St000784The maximum of the length and the largest part of the integer partition. St000867The sum of the hook lengths in the first row of an integer partition. St000996The number of exclusive left-to-right maxima of a permutation. St001004The number of indices that are either left-to-right maxima or right-to-left minima. St001027Number of simple modules with projective dimension equal to injective dimension in the Nakayama algebra corresponding to the Dyck path. St001090The number of pop-stack-sorts needed to sort a permutation. St001120The length of a longest path in a graph. St001127The sum of the squares of the parts of a partition. St001161The major index north count of a Dyck path. St001189The number of simple modules with dominant and codominant dimension equal to zero in the Nakayama algebra corresponding to the Dyck path. St001245The cyclic maximal difference between two consecutive entries of a permutation. St001382The number of boxes in the diagram of a partition that do not lie in its Durfee square. St001384The number of boxes in the diagram of a partition that do not lie in the largest triangle it contains. St001641The number of ascent tops in the flattened set partition such that all smaller elements appear before. St001759The Rajchgot index of a permutation. St001955The number of natural descents for set-valued two row standard Young tableaux. St001958The degree of the polynomial interpolating the values of a 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. St000032The number of elements smaller than the given Dyck path in the Tamari Order. St000048The multinomial of the parts of a partition. St000050The depth or height of a binary tree. St000058The order of a permutation. St000063The number of linear extensions of a certain poset defined for an integer partition. St000085The number of linear extensions of the tree. St000108The number of partitions contained in the given partition. St000110The number of permutations less than or equal to a permutation in left weak order. St000184The size of the centralizer of any permutation of given cycle type. St000203The number of external nodes of a binary tree. St000288The number of ones in a binary word. St000290The major index of a binary word. St000336The leg major index of a standard tableau. St000460The hook length of the last cell along the main diagonal of an integer partition. St000505The biggest entry in the block containing the 1. St000531The leading coefficient of the rook polynomial of an integer partition. St000532The total number of rook placements on a Ferrers board. St000636The hull number of a graph. St000655The length of the minimal rise of a Dyck path. St000725The smallest label of a leaf 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. St000740The last entry of a permutation. St000777The number of distinct eigenvalues of the distance Laplacian of a connected graph. St000839The largest opener of a set partition. St000870The product of the hook lengths of the diagonal cells in an integer partition. St000875The semilength of the longest Dyck word in the Catalan factorisation of a binary word. St000975The length of the boundary minus the length of the trunk of an ordered tree. 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. St001048The number of leaves in the subtree containing 1 in the decreasing labelled binary unordered tree associated with the perfect matching. St001088Number of indecomposable projective non-injective modules with dominant dimension equal to the injective dimension in the corresponding Nakayama algebra. St001102The number of words with multiplicities of the letters given by the composition, avoiding the consecutive pattern 132. St001103The number of words with multiplicities of the letters given by the partition, avoiding the consecutive pattern 123. St001126Number of simple module that are 1-regular in the corresponding Nakayama algebra. St001312Number of parabolic noncrossing partitions indexed by the composition. St001348The bounce of the parallelogram polyomino associated with the Dyck path. St001360The number of covering relations in Young's lattice below a partition. St001400The total number of Littlewood-Richardson tableaux of given shape. St001497The position of the largest weak excedence of a permutation. St001523The degree of symmetry of a Dyck path. St001554The number of distinct nonempty subtrees of a binary tree. 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. St001672The restrained domination number of a graph. St001707The length of a longest path in a graph such that the remaining vertices can be partitioned into two sets of the same size without edges between them. St001746The coalition number of a graph. St001778The largest greatest common divisor of an element and its image in a permutation. St001786The number of total orderings of the north steps of a Dyck path such that steps after the k-th east step are not among the first k positions in the order. St001809The index of the step at the first peak of maximal height in a Dyck path. St001910The height of the middle non-run of a Dyck path. St000380Half of the maximal perimeter of a rectangle fitting into the diagram of an integer partition. St000439The position of the first down step of a Dyck path. St001166Number of indecomposable projective non-injective modules with dominant dimension equal to the global dimension plus the number of indecomposable projective injective modules in the corresponding Nakayama algebra. St001211The number of simple modules in the corresponding Nakayama algebra that have vanishing second Ext-group with the regular module. St001279The sum of the parts of an integer partition that are at least two. 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. 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. St001643The Frobenius dimension of the Nakayama algebra corresponding to the Dyck path. St000189The number of elements in the poset. St000296The length of the symmetric border of a binary word. St000393The number of strictly increasing runs in a binary word. St000419The number of Dyck paths that are weakly above the Dyck path, except for the path itself. St000444The length of the maximal rise of a Dyck path. St000529The number of permutations whose descent word is the given binary word. St000543The size of the conjugacy class of a binary word. St000626The minimal period of a binary word. St000627The exponent of a binary word. St000844The size of the largest block in the direct sum decomposition of 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. St000922The minimal number such that all substrings of this length are unique. St000982The length of the longest constant subword. St001267The length of the Lyndon factorization of the binary word. St001371The length of the longest Yamanouchi prefix of a binary word. St001415The length of the longest palindromic prefix of a binary word. St001416The length of a longest palindromic factor of a binary word. St001417The length of a longest palindromic subword of a binary word. St001437The flex of a binary word. St001622The number of join-irreducible elements of a lattice. St001884The number of borders of a binary word. St000294The number of distinct factors of a binary word. St000295The length of the border of a binary word. St000369The dinv deficit of a Dyck path. St000376The bounce deficit of a Dyck path. St000420The number of Dyck paths that are weakly above a Dyck path. St000442The maximal area to the right of an up step of a Dyck path. St000503The maximal difference between two elements in a common block. St000518The number of distinct subsequences in a binary word. St000519The largest length of a factor maximising the subword complexity. St000730The maximal arc length of a set partition. St000956The maximal displacement of a permutation. St001436The index of a given binary word in the lex-order among all its cyclic shifts. St000438The position of the last up step in a Dyck path. St000826The stopping time of the decimal representation of the binary word for the 3x+1 problem. St000054The first entry of the permutation. St000144The pyramid weight of the Dyck path. St000326The position of the first one in a binary word after appending a 1 at the end. St000381The largest part of an integer composition. St000382The first part of an integer composition. St000383The last part of an integer composition. St000385The number of vertices with out-degree 1 in a binary tree. St000391The sum of the positions of the ones in a binary word. St000414The binary logarithm of the number of binary trees with the same underlying unordered tree. St000476The sum of the semi-lengths of tunnels before a valley of a Dyck path. St000493The los statistic of a set partition. St000498The lcs statistic of a set partition. St000501The size of the first part in the decomposition of a permutation. St000564The number of occurrences of the pattern {{1},{2}} in a set partition. St000567The sum of the products of all pairs of parts. St000577The number of occurrences of the pattern {{1},{2}} such that 1 is a maximal element. St000578The number of occurrences of the pattern {{1},{2}} such that 1 is a singleton. St000657The smallest part of an integer composition. St000668The least common multiple of the parts of the partition. St000675The number of centered multitunnels of a Dyck path. St000678The number of up steps after the last double rise of a Dyck path. St000681The Grundy value of Chomp on Ferrers diagrams. St000704The number of semistandard tableaux on a given integer partition with minimal maximal entry. St000708The product of the parts of an integer partition. St000714The number of semistandard Young tableau of given shape, with entries at most 2. St000808The number of up steps of the associated bargraph. St000874The position of the last double rise in a Dyck path. St000877The depth of the binary word interpreted as a path. St000946The sum of the skew hook positions in a Dyck path. St000947The major index east count of a Dyck path. St000983The length of the longest alternating subword. St000984The number of boxes below precisely one peak. St001018Sum of projective dimension of the indecomposable injective modules of the Nakayama algebra corresponding to the Dyck path. St001039The maximal height of a column in the parallelogram polyomino associated with a Dyck path. St001062The maximal size of a block of a set partition. St001128The exponens consonantiae of a partition. 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. St001313The number of Dyck paths above the lattice path given by a binary word. St001418Half of the global dimension of the stable Auslander algebra of the Nakayama algebra corresponding to the Dyck path. St001498The normalised height of a Nakayama algebra with magnitude 1. St001499The number of indecomposable projective-injective modules of a magnitude 1 Nakayama algebra. St001631The number of simple modules $S$ with $dim Ext^1(S,A)=1$ in the incidence algebra $A$ of the poset. St001636The number of indecomposable injective modules with projective dimension at most one in the incidence algebra of the poset. St001721The degree of a binary word. St001933The largest multiplicity of a part in an integer partition. St000133The "bounce" of a permutation. St000141The maximum drop size of a permutation. St000167The number of leaves of an ordered tree. St000209Maximum difference of elements in cycles. St000248The number of anti-singletons of a set partition. St000250The number of blocks (St000105) plus the number of antisingletons (St000248) of a set partition. St000316The number of non-left-to-right-maxima of a permutation. St000392The length of the longest run of ones in a binary word. St000502The number of successions of a set partitions. St000528The height of a poset. St000586The number of occurrences of the pattern {{1},{2,3}} such that 2 is minimal. St000589The number of occurrences of the pattern {{1},{2,3}} such that 1 is maximal, (2,3) are consecutive in a block. St000599The number of occurrences of the pattern {{1},{2,3}} such that (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. St000674The number of hills of a Dyck path. St000682The Grundy value of Welter's game on a binary word. St000691The number of changes of a binary word. St000727The largest label of a leaf in the binary search tree associated with the permutation. St000728The dimension of a set partition. 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. St000931The number of occurrences of the pattern UUU in a Dyck path. St000932The number of occurrences of the pattern UDU in a Dyck path. St000957The number of Bruhat lower covers of a permutation. St001023Number of simple modules with projective dimension at most 3 in the Nakayama algebra corresponding to the Dyck path. St001032The number of horizontal steps in the bicoloured Motzkin path associated with the Dyck path. St001082The number of boxed occurrences of 123 in a permutation. St001107The number of times one can erase the first up and the last down step in a Dyck path and still remain a Dyck path. St001176The size of a partition minus its first part. 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. 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. St001240The number of indecomposable modules e_i J^2 that have injective dimension at most one 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. St001343The dimension of the reduced incidence algebra of a poset. St001365The number of lattice paths of the same length weakly above the path given by a binary word. St001372The length of a longest cyclic run of ones of a binary word. St001419The length of the longest palindromic factor beginning with a one of a binary word. St001485The modular major index of a binary word. St001650The order of Ringel's homological bijection associated to the linear Nakayama algebra corresponding to the Dyck path. St001714The number of subpartitions of an integer partition that do not dominate the conjugate subpartition. St001808The box weight or horizontal decoration of a Dyck path. St001827The number of two-component spanning forests of a graph. St001869The maximum cut size of a graph. St000070The number of antichains in a poset. St000477The weight of a partition according to Alladi. St000806The semiperimeter of the associated bargraph. St000813The number of zero-one matrices with weakly decreasing column sums and row sums given by the partition. St000878The number of ones minus the number of zeros of a binary word. 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. St001118The acyclic chromatic index of a graph. St000993The multiplicity of the largest part of an integer partition. 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. St000060The greater neighbor of the maximum. St000652The maximal difference between successive positions of a permutation. St000653The last descent of a permutation. St001199The dominant dimension of $eAe$ for the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. St001246The maximal difference between two consecutive entries of a permutation. St001880The number of 2-Gorenstein indecomposable injective modules in the incidence algebra of the lattice. St001268The size of the largest ordinal summand in the poset. St001430The number of positive entries in a signed permutation. St001645The pebbling number of a connected graph. St000719The number of alignments in a perfect matching. St000485The length of the longest cycle of a permutation. St001081The number of minimal length factorizations of a permutation into star transpositions. St000837The number of ascents of distance 2 of a permutation. St000809The reduced reflection length of the permutation. St001925The minimal number of zeros in a row of an alternating sign matrix. St000890The number of nonzero entries in an alternating sign matrix. St000794The mak of a permutation. St000271The chromatic index of a graph. St001725The harmonious chromatic number of a graph. St000924The number of topologically connected components of a perfect matching. St000014The number of parking functions supported by a Dyck path. St001170Number of indecomposable injective modules whose socle has projective dimension at most g-1 when g denotes the global dimension in the corresponding Nakayama algebra. St001291The number of indecomposable summands of the tensor product of two copies of the dual of the Nakayama algebra associated to a Dyck path. St000718The largest Laplacian eigenvalue of a graph if it is integral. St001065Number of indecomposable reflexive modules in the corresponding Nakayama algebra. St001237The number of simple modules with injective dimension at most one or dominant dimension at least one. St000004The major index of a permutation. St000005The bounce statistic of a Dyck path. St000029The depth of a permutation. St000030The sum of the descent differences of a permutations. St000051The size of the left subtree of a binary tree. St000052The number of valleys of a Dyck path not on the x-axis. St000120The number of left tunnels of a Dyck path. St000155The number of exceedances (also excedences) of a permutation. St000210Minimum over maximum difference of elements in cycles. St000224The sorting index of a permutation. St000304The load of a permutation. St000329The number of evenly positioned ascents of the Dyck path, with the initial position equal to 1. St000334The maz index, the major index of a permutation after replacing fixed points by zeros. St000339The maf index of a permutation. St000446The disorder of a permutation. St000868The aid statistic in the sense of Shareshian-Wachs. St001185The number of indecomposable injective modules of grade at least 2 in the corresponding Nakayama algebra. St001192The maximal dimension of $Ext_A^2(S,A)$ for a simple module $S$ over the corresponding Nakayama algebra $A$. St001194The injective dimension of $A/AfA$ in the corresponding Nakayama algebra $A$ when $Af$ is the minimal faithful projective-injective left $A$-module St001215Let X be the direct sum of all simple modules of the corresponding Nakayama algebra. St001216The number of indecomposable injective modules in the corresponding Nakayama algebra that have non-vanishing second Ext-group with the regular module. St001225The vector space dimension of the first extension group between J and itself when J is the Jacobson radical of the corresponding Nakayama algebra. St001233The number of indecomposable 2-dimensional modules with projective dimension one. St001265The maximal i such that the i-th simple module has projective dimension equal to the global dimension in the corresponding Nakayama algebra. St001274The number of indecomposable injective modules with projective dimension equal to two. St001278The number of indecomposable modules that are fixed by $\tau \Omega^1$ composed with its inverse in the corresponding Nakayama algebra. St001295Gives the vector space dimension of the homomorphism space between J^2 and J^2. St001311The cyclomatic number of a graph. St001317The minimal number of occurrences of the forest-pattern in a linear ordering of the vertices of the graph. St001328The minimal number of occurrences of the bipartite-pattern in a linear ordering of the vertices of the graph. St001375The pancake length of a permutation. St001391The disjunction number of a graph. St001508The degree of the standard monomial associated to a Dyck path relative to the diagonal boundary. St001558The number of transpositions that are smaller or equal to a permutation in Bruhat order. St001579The number of cyclically simple transpositions decreasing the number of cyclic descents needed to sort a permutation. St001723The differential of a graph. St001724The 2-packing differential of a graph. St001726The number of visible inversions of a permutation. St001761The maximal multiplicity of a letter in a reduced word of a permutation. St000031The number of cycles in the cycle decomposition of a permutation. St000066The column of the unique '1' in the first row of the alternating sign matrix. St000117The number of centered tunnels of a Dyck path. St000229Sum of the difference between the maximal and the minimal elements of the blocks plus the number of blocks of a set partition. St000236The number of cyclical small weak excedances. St000240The number of indices that are not small excedances. St000241The number of cyclical small excedances. St000335The difference of lower and upper interactions. St000337The lec statistic, the sum of the inversion numbers of the hook factors of a permutation. St000374The number of exclusive right-to-left minima of a permutation. St000443The number of long tunnels of a Dyck path. St000553The number of blocks of a graph. St000632The jump number of the poset. St000703The number of deficiencies of a permutation. St000733The row containing the largest entry of a standard tableau. St000863The length of the first row of the shifted shape of a permutation. St000994The number of cycle peaks and the number of cycle valleys of a permutation. St000999Number of indecomposable projective module with injective dimension equal to the global dimension in the Nakayama algebra corresponding to the Dyck path. St001006Number of simple modules with projective dimension equal to the global dimension of the Nakayama algebra corresponding to the Dyck path. St001008Number of indecomposable injective modules with projective dimension 1 in the Nakayama algebra corresponding to the Dyck path. St001013Number of indecomposable injective modules with codominant dimension equal to the global dimension in the Nakayama algebra corresponding to the Dyck path. St001014Number of indecomposable injective modules with codominant dimension equal to the dominant dimension of the Nakayama algebra corresponding to the Dyck path. St001015Number of indecomposable injective modules with codominant dimension equal to one in the Nakayama algebra corresponding to the Dyck path. St001016Number of indecomposable injective modules with codominant dimension at most 1 in the Nakayama algebra corresponding to the Dyck path. St001017Number of indecomposable injective modules with projective dimension equal to the codominant dimension in the Nakayama algebra corresponding to the Dyck path. St001019Sum of the projective dimensions of the simple modules in the Nakayama algebra corresponding to the Dyck path. St001052The length of the exterior of a permutation. St001096The size of the overlap set of a permutation. St001183The maximum of $projdim(S)+injdim(S)$ over all simple modules in the Nakayama algebra corresponding to the Dyck path. St001184Number of indecomposable injective modules with grade at least 1 in the corresponding Nakayama algebra. St001187The number of simple modules with grade at least one in the corresponding Nakayama algebra. St001191Number of simple modules $S$ with $Ext_A^i(S,A)=0$ for all $i=0,1,...,g-1$ in the corresponding Nakayama algebra $A$ with global dimension $g$. St001210Gives the maximal vector space dimension of the first Ext-group between an indecomposable module X and the regular module A, when A is the Nakayama algebra corresponding to the Dyck path. St001224Let X be the direct sum of all simple modules of the corresponding Nakayama algebra. St001235The global dimension of the corresponding Comp-Nakayama algebra. St001236The dominant dimension of the corresponding Comp-Nakayama algebra. St001239The largest vector space dimension of the double dual of a simple module in 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. St001258Gives the maximum of injective plus projective dimension of an indecomposable module over the corresponding Nakayama algebra. 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. St001439The number of even weak deficiencies and of odd weak exceedences. 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. St000068The number of minimal elements in a poset. St000071The number of maximal chains in a poset. St000312The number of leaves in a graph. St000451The length of the longest pattern of the form k 1 2. St000527The width of the poset. St001180Number of indecomposable injective modules with projective dimension at most 1. St001213The number of indecomposable modules in the corresponding Nakayama algebra that have vanishing first Ext-group with the regular module. St001226The number of integers i such that the radical of the i-th indecomposable projective module has vanishing first extension group with the Jacobson radical J in the corresponding Nakayama algebra. St001259The vector space dimension of the double dual of D(A) in the corresponding Nakayama algebra. St000197The number of entries equal to positive one in the alternating sign matrix. St001959The product of the heights of the peaks of a Dyck path. St000216The absolute length 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. St001480The number of simple summands of the module J^2/J^3. St000080The rank of the poset. St000280The size of the preimage of the map 'to labelling permutation' from Parking functions to Permutations. St000488The number of cycles of a permutation of length at most 2. St000489The number of cycles of a permutation of length at most 3. St000530The number of permutations with the same descent word as the given permutation. St000619The number of cyclic descents of a permutation. St000654The first descent of a permutation. St000702The number of weak deficiencies of a permutation. St000831The number of indices that are either descents or recoils. St000833The comajor index of a permutation. St000887The maximal number of nonzero entries on a diagonal of a permutation matrix. St001076The minimal length of a factorization of a permutation into transpositions that are cyclic shifts of (12). St001077The prefix exchange distance of a permutation. St000064The number of one-box pattern of a permutation. St000082The number of elements smaller than a binary tree in Tamari order. St000083The number of left oriented leafs of a binary tree except the first one. St000354The number of recoils of a permutation. St000432The number of occurrences of the pattern 231 or of the pattern 312 in a permutation. St000434The number of occurrences of the pattern 213 or of the pattern 312 in a permutation. St000435The number of occurrences of the pattern 213 or of the pattern 231 in a permutation. St000461The rix statistic of a permutation. St000471The sum of the ascent tops of a permutation. St000487The length of the shortest cycle of a permutation. St000538The number of even inversions of a permutation. St000625The sum of the minimal distances to a greater element. St000656The number of cuts of a poset. St000673The number of non-fixed points of a permutation. St000680The Grundy value for Hackendot on posets. St000717The number of ordinal summands of a poset. St000724The label of the leaf of the path following the smaller label in the increasing binary tree associated to a permutation. St000795The mad of a permutation. St000801The number of occurrences of the vincular pattern |312 in a permutation. St000829The Ulam distance of a permutation to the identity permutation. St000836The number of descents of distance 2 of a permutation. St000906The length of the shortest maximal chain in a poset. St000989The number of final rises 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. St001061The number of indices that are both descents and recoils of a permutation. St001074The number of inversions of the cyclic embedding of a permutation. 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. St000642The size of the smallest orbit of antichains under Panyushev complementation. St000643The size of the largest orbit of antichains under Panyushev complementation. St001664The number of non-isomorphic subposets of a poset. St001782The order of rowmotion on the set of order ideals of a poset. St000045The number of linear extensions of a binary tree. St000327The number of cover relations in a poset. St000219The number of occurrences of the pattern 231 in a permutation. St001557The number of inversions of the second entry of a permutation. St001603The number of colourings of a polygon such that the multiplicities of a colour are given by a partition. St001604The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on polygons. St000898The number of maximal entries in the last diagonal of the monotone triangle. St000672The number of minimal elements in Bruhat order not less than the permutation. St001917The order of toric promotion on the set of labellings of a graph. 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. St000454The largest eigenvalue of a graph if it is integral. St001392The largest nonnegative integer which is not a part and is smaller than the largest part of the partition. St000147The largest part of an integer partition. St000093The cardinality of a maximal independent set of vertices of a graph. St001429The number of negative entries in a signed permutation. St001468The smallest fixpoint of a permutation. St000095The number of triangles of a graph. St000426The number of occurrences of the pattern 132 or of the pattern 312 in a permutation. St000689The maximal n such that the minimal generator-cogenerator module in the LNakayama algebra of a Dyck path is n-rigid. 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. St001553The number of indecomposable summands of the square of the Jacobson radical as a bimodule in the Nakayama algebra corresponding to the Dyck path. St001684The reduced word complexity of a permutation. St001742The difference of the maximal and the minimal degree in a graph. St000067The inversion number of the alternating sign matrix. St000193The row of the unique '1' in the first column of the alternating sign matrix. St000450The number of edges minus the number of vertices plus 2 of a graph. St000780The size of the orbit under rotation of a perfect matching. St000945The number of matchings in the dihedral orbit of a perfect matching. St000988The orbit size of a permutation under Foata's bijection. St001041The depth of the label 1 in the decreasing labelled binary unordered tree associated with the perfect matching. St001045The number of leaves in the subtree not containing one in the decreasing labelled binary unordered tree associated with the perfect matching. St001131The number of trivial trees on the path to label one in the decreasing labelled binary unordered tree associated with the perfect matching. St001132The number of leaves in the subtree whose sister has label 1 in the decreasing labelled binary unordered tree associated with the perfect matching. St001401The number of distinct entries in a semistandard tableau. St001515The vector space dimension of the socle of the first syzygy module of the regular module (as a bimodule). St001526The Loewy length of the Auslander-Reiten translate of the regular module as a bimodule of the Nakayama algebra corresponding to the Dyck path. St001817The number of flag weak exceedances of a signed permutation. St001892The flag excedance statistic of a signed permutation. St000235The number of indices that are not cyclical small weak excedances. St000949Gives the number of generalised tilting modules of the corresponding LNakayama algebra. St001040The depth of the decreasing labelled binary unordered tree associated with the perfect matching. St001134The largest label in the subtree rooted at the sister of 1 in the leaf labelled binary unordered tree associated with the perfect matching. St001003The number of indecomposable modules with projective dimension at most 1 in the Nakayama algebra corresponding to the Dyck path. St001255The vector space dimension of the double dual of A/J when A is the corresponding Nakayama algebra with Jacobson radical J. St001706The number of closed sets in a graph. St000135The number of lucky cars of the parking function. St000186The sum of the first row in a Gelfand-Tsetlin pattern. St000744The length of the path to the largest entry in a standard Young tableau. St001431Half of the Loewy length minus one of a modified stable Auslander algebra of the Nakayama algebra corresponding to the Dyck path. St001637The number of (upper) dissectors of a poset. St001668The number of points of the poset minus the width of the poset. St001948The number of augmented double ascents of a permutation. St000044The number of vertices of the unicellular map given by a perfect matching. St001811The Castelnuovo-Mumford regularity of a permutation. St001960The number of descents of a permutation minus one if its first entry is not one. St001491The number of indecomposable projective-injective modules in the algebra corresponding to a subset. St001927Sparre Andersen's number of positives of a signed permutation. 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 $eA$. St001207The Lowey length of the algebra $A/T$ when $T$ is the 1-tilting module corresponding to the permutation in the Auslander algebra of $K[x]/(x^n)$. St001876The number of 2-regular simple modules in the incidence algebra of the lattice. St001875The number of simple modules with projective dimension at most 1. St001621The number of atoms of a lattice.