St001300The rank of the boundary operator in degree 1 of the chain complex of the order complex of the poset. St001664The number of non-isomorphic subposets of a poset. St000020The rank of the permutation. St000207Number of integral Gelfand-Tsetlin polytopes with prescribed top row and integer composition weight. St000208Number of integral Gelfand-Tsetlin polytopes with prescribed top row and integer partition weight. St000228The size of a partition. St000321The number of integer partitions of n that are dominated by an integer partition. St000419The number of Dyck paths that are weakly above the Dyck path, except for the path itself. St000459The hook length of the base cell of a partition. St000460The hook length of the last cell along the main diagonal of an integer partition. St000479The Ramsey number of a graph. St000636The hull number of a graph. St000870The product of the hook lengths of the diagonal cells in an integer partition. St000917The open packing number of a graph. St000918The 2-limited packing number of a graph. St001034The area of the parallelogram polyomino associated with the Dyck path. St001108The 2-dynamic chromatic number of a graph. St001110The 3-dynamic chromatic number of a graph. St001315The dissociation number of a graph. St001318The number of vertices of the largest induced subforest with the same number of connected components of a graph. St001321The number of vertices of the largest induced subforest of a graph. St001342The number of vertices in the center of a graph. St001348The bounce of the parallelogram polyomino associated with the Dyck path. St001611The number of multiset partitions such that the multiplicities of elements are given by a partition. St001612The number of coloured multisets of cycles such that the multiplicities of colours are given by a partition. 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. St001654The monophonic hull number of a graph. St001655The general position number of a graph. St001656The monophonic position number of a graph. 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. St001725The harmonious chromatic number of a graph. St001746The coalition number of a graph. St001800The number of 3-Catalan paths having this Dyck path as first and last coordinate projections. St000004The major index of a permutation. St000009The charge of a standard tableau. St000018The number of inversions of a permutation. St000089The absolute variation of a composition. St000136The dinv of a parking function. St000156The Denert index of a permutation. St000161The sum of the sizes of the right subtrees of a binary tree. St000194The number of primary dinversion pairs of a labelled dyck path corresponding to a parking function. St000305The inverse major index of a permutation. St000420The number of Dyck paths that are weakly above a Dyck path. St000446The disorder of a permutation. St000987The number of positive eigenvalues of the Laplacian matrix of the graph. St001065Number of indecomposable reflexive modules in the corresponding Nakayama algebra. St001079The minimal length of a factorization of a permutation using the permutations (12)(34). St001117The game chromatic index of a graph. St001119The length of a shortest maximal path in a graph. St001120The length of a longest path in a graph. St001209The pmaj statistic of a parking function. St001287The number of primes obtained by multiplying preimage and image of a permutation and subtracting one. St001382The number of boxes in the diagram of a partition that do not lie in its Durfee square. St001541The Gini index of an integer partition. St001558The number of transpositions that are smaller or equal to a permutation in Bruhat order. St001658The total number of rook placements on a Ferrers board. St001759The Rajchgot index of a permutation. St001772The number of occurrences of the signed pattern 12 in a signed permutation. St001019Sum of the projective dimensions of the simple modules in the Nakayama algebra corresponding to the Dyck path. St001838The number of nonempty primitive factors of a binary word. St000030The sum of the descent differences of a permutations. St000071The number of maximal chains in a poset. St000086The number of subgraphs. St000229Sum of the difference between the maximal and the minimal elements of the blocks plus the number of blocks of a set partition. St000346The number of coarsenings of a partition. St000393The number of strictly increasing runs in a binary word. St000395The sum of the heights of the peaks of a Dyck path. St000468The Hosoya index of a graph. St000548The number of different non-empty partial sums of an integer partition. St000631The number of distinct palindromic decompositions of a binary word. St000725The smallest label of a leaf of the increasing binary tree associated to a permutation. St000867The sum of the hook lengths in the first row of an integer partition. St001018Sum of projective dimension of the indecomposable injective modules of the Nakayama algebra corresponding to the Dyck path. St001365The number of lattice paths of the same length weakly above the path given by a binary word. St001482The product of the prefix sums of a permutation. St001645The pebbling number of a connected graph. St001684The reduced word complexity of 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. St001794Half the number of sets of vertices in a graph which are dominating and non-blocking. St001861The number of Bruhat lower covers of a permutation. St001929The number of meanders with top half given by the noncrossing matching corresponding to the Dyck path. St001951The number of factors in the disjoint direct product decomposition of the automorphism group of a graph. St001959The product of the heights of the peaks of a Dyck path. St000005The bounce statistic of a Dyck path. St000006The dinv of a Dyck path. St000008The major index of the composition. St000012The area of a Dyck path. St000028The number of stack-sorts needed to sort a permutation. St000041The number of nestings of a perfect matching. St000059The inversion number of a standard tableau as defined by Haglund and Stevens. St000067The inversion number of the alternating sign matrix. St000070The number of antichains in a poset. St000081The number of edges of a graph. St000104The number of facets in the order polytope of this poset. St000110The number of permutations less than or equal to a permutation in left weak order. St000111The sum of the descent tops (or Genocchi descents) of a permutation. St000151The number of facets in the chain polytope of the poset. St000152The number of boxed plus the number of special entries. St000154The sum of the descent bottoms of a permutation. St000155The number of exceedances (also excedences) of a permutation. St000169The cocharge of a standard tableau. St000171The degree of the graph. St000173The segment statistic of a semistandard tableau. St000180The number of chains of a poset. St000224The sorting index of a permutation. St000238The number of indices that are not small weak excedances. St000300The number of independent sets of vertices of a graph. St000301The number of facets of the stable set polytope of a graph. St000330The (standard) major index of a standard tableau. St000332The positive inversions of an alternating sign matrix. St000334The maz index, the major index of a permutation after replacing fixed points by zeros. St000339The maf index of a permutation. St000426The number of occurrences of the pattern 132 or of the pattern 312 in a permutation. St000432The number of occurrences of the pattern 231 or of the pattern 312 in a permutation. St000434The number of occurrences of the pattern 213 or of the pattern 312 in a permutation. St000448The number of pairs of vertices of a graph with distance 2. St000471The sum of the ascent tops of a permutation. St000537The cutwidth of a graph. St000625The sum of the minimal distances to a greater element. St000662The staircase size of the code of a permutation. St000692Babson and Steingrímsson's statistic of a permutation. St000719The number of alignments in a perfect matching. St000868The aid statistic in the sense of Shareshian-Wachs. St001094The depth index of a set partition. St001102The number of words with multiplicities of the letters given by the composition, avoiding the consecutive pattern 132. St001160The number of proper blocks (or intervals) of a permutations. St001161The major index north count of a Dyck path. St001229The vector space dimension of the first extension group between the Jacobson radical J and J^2. St001295Gives the vector space dimension of the homomorphism space between J^2 and J^2. St001298The number of repeated entries in the Lehmer code of a permutation. St001304The number of maximally independent sets of vertices of a graph. St001308The number of induced paths on three vertices in a graph. St001312Number of parabolic noncrossing partitions indexed by the composition. St001313The number of Dyck paths above the lattice path given by a binary word. St001345The Hamming dimension of a graph. St001350Half of the Albertson index of a graph. St001362The normalized Knill dimension of a graph. St001375The pancake length of a permutation. St001391The disjunction number of a graph. St001397Number of pairs of incomparable elements in a finite poset. St001428The number of B-inversions of a signed permutation. St001464The number of bases of the positroid corresponding to the permutation, with all fixed points counterclockwise. St001512The minimum rank of a graph. St001574The minimal number of edges to add or remove to make a graph regular. St001576The minimal number of edges to add or remove to make a graph vertex transitive. St001582The grades of the simple modules corresponding to the points in the poset of the symmetric group under the Bruhat order. St001646The number of edges that can be added without increasing the maximal degree of a graph. St001649The length of a longest trail in a graph. St001667The maximal size of a pair of weak twins for a permutation. St001671Haglund's hag of a permutation. St001697The shifted natural comajor index of a standard Young tableau. St001721The degree of a binary word. St001727The number of invisible inversions of a permutation. St001822The number of alignments of a signed permutation. St001827The number of two-component spanning forests of a graph. St001866The nesting alignments of a signed permutation. St001930The weak major index of a binary word. St001956The comajor index for set-valued two-row standard Young tableaux. St000250The number of blocks (St000105) plus the number of antisingletons (St000248) of a set partition. St001182Number of indecomposable injective modules with codominant dimension at least two in the corresponding Nakayama 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. St001228The vector space dimension of the space of module homomorphisms between J and itself when J denotes the Jacobson radical of the corresponding Nakayama algebra. 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. St001643The Frobenius dimension of the Nakayama algebra corresponding to the Dyck path. St001650The order of Ringel's homological bijection associated to the linear Nakayama algebra corresponding to the Dyck path. St001213The number of indecomposable modules in the corresponding Nakayama algebra that have vanishing first Ext-group with the regular module. St000520The number of patterns in a permutation. St000294The number of distinct factors of a binary word. St000518The number of distinct subsequences in a binary word. St000656The number of cuts of a poset. St000690The size of the conjugacy class of a permutation. St001583The projective dimension of the simple module corresponding to the point in the poset of the symmetric group under bruhat order. St000280The size of the preimage of the map 'to labelling permutation' from Parking functions to Permutations. St000289The decimal representation of a binary word. St000438The position of the last up step in a Dyck path. St000472The sum of the ascent bottoms of a permutation. St000493The los statistic of a set partition. St000494The number of inversions of distance at most 3 of a permutation. St000495The number of inversions of distance at most 2 of a permutation. St000498The lcs statistic of a set partition. 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. St000681The Grundy value of Chomp on Ferrers diagrams. St000794The mak of a permutation. St000795The mad of a permutation. St000796The stat' of a permutation. St000797The stat`` of a permutation. St000798The makl of a permutation. St000833The comajor index of a permutation. St001099The 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 leaf labelled binary trees. St001118The acyclic chromatic index of a graph. St001875The number of simple modules with projective dimension at most 1. St001915The size of the component corresponding to a necklace in Bulgarian solitaire. St000354The number of recoils of a permutation. 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. 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. St001080The minimal length of a factorization of a permutation using the transposition (12) and the cycle (1,. St000477The weight of a partition according to Alladi. St000928The sum of the coefficients of the character polynomial of an integer partition. St000639The number of relations in a poset. St000641The number of non-empty boolean intervals in a poset. St000770The major index of an integer partition when read from bottom to top. St000981The length of the longest zigzag subpath. St001259The vector space dimension of the double dual of D(A) in the corresponding Nakayama algebra. St001500The global dimension of magnitude 1 Nakayama algebras. St001501The dominant dimension of magnitude 1 Nakayama algebras. St001834The number of non-isomorphic minors of a graph. St000061The number of nodes on the left branch of a binary tree. St000391The sum of the positions of the ones in a binary word. St000444The length of the maximal rise of a Dyck path. St000485The length of the longest cycle of a permutation. St000488The number of cycles of a permutation of length at most 2. St000489The number of cycles of a permutation of length at most 3. St000490The intertwining number of a set partition. St000492The rob statistic of a set partition. St000499The rcb statistic of a set partition. St000574The number of occurrences of the pattern {{1},{2}} such that 1 is a minimal and 2 a maximal element. St000579The number of occurrences of the pattern {{1},{2}} such that 2 is a maximal element. St000654The first descent of a permutation. St000668The least common multiple of the parts of the partition. St000675The number of centered multitunnels of a Dyck path. St000699The toughness times the least common multiple of 1,. St000702The number of weak deficiencies of a permutation. St000708The product of the parts of an integer partition. St000727The largest label of a leaf in the binary search tree associated with the permutation. St000792The Grundy value for the game of ruler on a binary word. St000812The sum of the entries in the column specified by the partition of the change of basis matrix from complete homogeneous symmetric functions to monomial symmetric functions. St000844The size of the largest block in the direct sum decomposition of a permutation. St000849The number of 1/3-balanced pairs in a poset. St000887The maximal number of nonzero entries on a diagonal of a permutation matrix. St000898The number of maximal entries in the last diagonal of the monotone triangle. St000914The sum of the values of the Möbius function of a poset. St000933The number of multipartitions of sizes given by an integer partition. St000937The number of positive values of the symmetric group character corresponding to the partition. St000947The major index east count of a Dyck path. St000984The number of boxes below precisely one peak. St000990The first ascent of a permutation. St001077The prefix exchange distance of a permutation. St001242The toal dimension of certain Sn modules determined by LLT polynomials associated with a Dyck path. St001243The sum of coefficients in the Schur basis of certain LLT polynomials associated with a Dyck path. St001281The normalized isoperimetric number of a graph. St001343The dimension of the reduced incidence algebra of a poset. St001346The number of parking functions that give the same permutation. St001380The number of monomer-dimer tilings of a Ferrers diagram. St001441The number of non-empty connected induced subgraphs of a graph. St001808The box weight or horizontal decoration of a Dyck path. St001815The number of order preserving surjections from a poset to a total order. St000216The absolute length of a permutation. St000288The number of ones in a binary word. St000297The number of leading ones in a binary word. St000392The length of the longest run of ones in a binary word. St000442The maximal area to the right of an up step of a Dyck path. St000462The major index minus the number of excedences of a permutation. St000476The sum of the semi-lengths of tunnels before a valley of a Dyck path. St000512The number of invariant subsets of size 3 when acting with a permutation of given cycle type. St000624The normalized sum of the minimal distances to a greater element. St000653The last descent of a permutation. St000730The maximal arc length of a set partition. St000753The Grundy value for the game of Kayles on a binary word. St000809The reduced reflection length of the permutation. St000831The number of indices that are either descents or recoils. St000866The number of admissible inversions of a permutation in the sense of Shareshian-Wachs. St000874The position of the last double rise in a Dyck path. St000956The maximal displacement of a permutation. St000957The number of Bruhat lower covers of a permutation. St000961The shifted major index of a permutation. St000989The number of final rises 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). 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. St001207The Lowey length of the algebra $A/T$ when $T$ is the 1-tilting module corresponding to the permutation in the Auslander algebra of $K[x]/(x^n)$. St001372The length of a longest cyclic run of ones of a binary word. St001418Half of the global dimension of the stable Auslander algebra of the Nakayama algebra corresponding to the Dyck path. St001419The length of the longest palindromic factor beginning with a one of a binary word. St001431Half of the Loewy length minus one of a modified stable Auslander algebra of the Nakayama algebra corresponding to the Dyck path. St001480The number of simple summands of the module J^2/J^3. St001592The maximal number of simple paths between any two different vertices of a graph. St001948The number of augmented double ascents of a permutation. St001742The difference of the maximal and the minimal degree in a graph. St001869The maximum cut size of a graph. St001880The number of 2-Gorenstein indecomposable injective modules in the incidence algebra of the lattice. St001195The global dimension of the algebra $A/AfA$ of the corresponding Nakayama algebra $A$ with minimal left faithful projective-injective module $Af$. St001629The coefficient of the integer composition in the quasisymmetric expansion of the relabelling action of the symmetric group on cycles. St001060The distinguishing index of a graph. St001168The vector space dimension of the tilting module corresponding to the permutation in the Auslander algebra of $K[x]/(x^n)$. St001570The minimal number of edges to add to make a graph Hamiltonian. St000285The size of the preimage of the map 'to inverse des composition' from Parking functions to Integer compositions. St000487The length of the shortest cycle of a permutation. St000817The sum of the entries in the column specified by the composition of the change of basis matrix from dual immaculate quasisymmetric functions to monomial quasisymmetric functions. St000818The sum of the entries in the column specified by the composition of the change of basis matrix from quasisymmetric Schur functions to monomial quasisymmetric functions. St001605The number of colourings of a cycle such that the multiplicities of colours are given by a partition. St000219The number of occurrences of the pattern 231 in a permutation. St000677The standardized bi-alternating inversion number of a permutation. St001114The number of odd descents of a permutation. St001569The maximal modular displacement of a permutation. St001604The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on polygons. St001859The number of factors of the Stanley symmetric function associated with a permutation. St000634The number of endomorphisms of a poset. St000813The number of zero-one matrices with weakly decreasing column sums and row sums given by the partition. St000515The number of invariant set partitions when acting with a permutation of given cycle type. St000827The decimal representation of a binary word with a leading 1. St000045The number of linear extensions of a binary tree. St000100The number of linear extensions of a poset. St000326The position of the first one in a binary word after appending a 1 at the end. St000418The number of Dyck paths that are weakly below a Dyck path. St000467The hyper-Wiener index of a connected graph. St000504The cardinality of the first block of a set partition. St000633The size of the automorphism group of a poset. St000678The number of up steps after the last double rise of a Dyck path. St000704The number of semistandard tableaux on a given integer partition with minimal maximal entry. St000706The product of the factorials of the multiplicities of an integer partition. St000707The product of the factorials of the parts. St000714The number of semistandard Young tableau of given shape, with entries at most 2. St000815The number of semistandard Young tableaux of partition weight of given shape. St000823The number of unsplittable factors of the set partition. St000910The number of maximal chains of minimal length in a poset. St000939The number of characters of the symmetric group whose value on the partition is positive. St000993The multiplicity of the largest part of an integer partition. St001038The minimal height of a column in the parallelogram polyomino associated with the Dyck path. St001039The maximal height of a column in the parallelogram polyomino associated with a Dyck path. St001062The maximal size of a block of a set partition. St001075The minimal size of a block of a set partition. St001105The number of greedy linear extensions of a poset. St001106The number of supergreedy linear extensions of a poset. St001128The exponens consonantiae of a partition. St001491The number of indecomposable projective-injective modules in the algebra corresponding to a subset. St001531Number of partial orders contained in the poset determined by the Dyck path. St001568The smallest positive integer that does not appear twice in the partition. St001603The number of colourings of a polygon such that the multiplicities of a colour are given by a partition. St001637The number of (upper) dissectors of a poset. St000251The number of nonsingleton blocks of a set partition. St000253The crossing number of a set partition. St000254The nesting number of a set partition. St000389The number of runs of ones of odd length in a binary word. St000390The number of runs of ones in a binary word. St000421The number of Dyck paths that are weakly below a Dyck path, except for the path itself. St000478Another weight of a partition according to Alladi. St000502The number of successions of a set partitions. St000503The maximal difference between two elements in a common block. St000558The number of occurrences of the pattern {{1,2}} in a set partition. St000566The number of ways to select a row of a Ferrers shape and two cells in this row. St000621The number of standard tableaux of shape equal to the given partition such that the minimal cyclic descent is even. St000658The number of rises of length 2 of a Dyck path. St000659The number of rises of length at least 2 of a Dyck path. St000683The number of points below the Dyck path such that the diagonal to the north-east hits the path between two down steps, and the diagonal to the north-west hits the path between two up steps. St000693The modular (standard) major index of a standard tableau. St000728The dimension of a set partition. St000790The number of pairs of centered tunnels, one strictly containing the other, of a Dyck path. St000848The balance constant multiplied with the number of linear extensions of a poset. St000850The number of 1/2-balanced pairs in a poset. St000877The depth of the binary word interpreted as a path. St000919The number of maximal left branches of a binary tree. St000929The constant term of the character polynomial of an integer partition. St000932The number of occurrences of the pattern UDU in a Dyck path. St000934The 2-degree of an integer partition. St000938The number of zeros of the symmetric group character corresponding to the 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. St000946The sum of the skew hook positions in a Dyck path. St000976The sum of the positions of double up-steps of a Dyck path. St001030Half the number of non-boundary horizontal edges in the fully packed loop corresponding to the alternating sign matrix. St001031The height of the bicoloured Motzkin path associated with the Dyck path. St001095The number of non-isomorphic posets with precisely one further covering relation. St001100The 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 leaf labelled trees. St001124The multiplicity of the standard representation in the Kronecker square corresponding to a partition. St001139The number of occurrences of hills of size 2 in a Dyck path. St001204Call 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. St001371The length of the longest Yamanouchi prefix of a binary word. St001860The number of factors of the Stanley symmetric function associated with a signed permutation. St000509The diagonal index (content) of a partition. St000741The Colin de Verdière graph invariant. St001232The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2. St000080The rank of the poset. St000307The number of rowmotion orbits of a poset. St001330The hat guessing number of a graph. St000454The largest eigenvalue of a graph if it is integral. St000718The largest Laplacian eigenvalue of a graph if it is integral. St001621The number of atoms of a lattice. St001623The number of doubly irreducible elements of a lattice. St001626The number of maximal proper sublattices of a lattice. St000455The second largest eigenvalue of a graph if it is integral. St000550The number of modular elements of a lattice. St000551The number of left modular elements of a lattice. St000264The girth of a graph, which is not a tree. St001651The Frankl number of a lattice. St000777The number of distinct eigenvalues of the distance Laplacian of a connected graph. St000927The alternating sum of the coefficients of the character polynomial of an integer partition. 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 $eA$. St001668The number of points of the poset minus the width of the poset. St000259The diameter of a connected graph. St001199The dominant dimension of $eAe$ for the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. St000260The radius of a connected graph. St000466The Gutman (or modified Schultz) index of a connected graph. 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. St000736The last entry in the first row of a semistandard tableau. St001514The dimension of the top of the Auslander-Reiten translate of the regular modules as a bimodule. St001624The breadth of a lattice. St001630The global dimension of the incidence algebra of the lattice over the rational numbers. St001644The dimension of a graph. St001686The order of promotion on a Gelfand-Tsetlin pattern. St001812The biclique partition number 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. St000102The charge of a semistandard tableau. St001314The number of tilting modules of arbitrary projective dimension that have no simple modules as a direct summand in the corresponding Nakayama algebra. St001526The Loewy length of the Auslander-Reiten translate of the regular module as a bimodule of the Nakayama algebra corresponding to the Dyck path. St001556The number of inversions of the third entry of a permutation. 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. St001642The Prague dimension of a graph. St001738The minimal order of a graph which is not an induced subgraph of the given graph. St001820The size of the image of the pop stack sorting operator. St001856The number of edges in the reduced word graph of a permutation. St001876The number of 2-regular simple modules in the incidence algebra of the lattice. St001877Number of indecomposable injective modules with projective dimension 2. St001926Sparre Andersen's position of the maximum of a signed permutation. St001960The number of descents of a permutation minus one if its first entry is not one. St001964The interval resolution global dimension of a poset. St001002Number of indecomposable modules with projective and injective dimension at most 1 in the Nakayama algebra corresponding to the Dyck path. St001720The minimal length of a chain of small intervals in a lattice.