St000394The sum of the heights of the peaks of a Dyck path minus the number of peaks. St001717The largest size of an interval in a poset. St001065Number of indecomposable reflexive modules 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. St001650The order of Ringel's homological bijection associated to the linear Nakayama algebra corresponding to the Dyck path. St000018The number of inversions of a permutation. St000208Number of integral Gelfand-Tsetlin polytopes with prescribed top row and integer partition weight. St000224The sorting index of a permutation. St000228The size of a partition. St000240The number of indices that are not small excedances. St000321The number of integer partitions of n that are dominated by an integer partition. 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. St000476The sum of the semi-lengths of tunnels before a valley of a Dyck path. St000479The Ramsey number of a graph. St000494The number of inversions of distance at most 3 of a permutation. St000519The largest length of a factor maximising the subword complexity. St000636The hull number of a graph. St000645The sum of the areas of the rectangles formed by two consecutive peaks and the valley in between. St000728The dimension of a set partition. St000743The number of entries in a standard Young tableau such that the next integer is a neighbour. St000794The mak of a permutation. St000809The reduced reflection length of the permutation. 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. St000922The minimal number such that all substrings of this length are unique. St000957The number of Bruhat lower covers of a permutation. St001033The normalized area of the parallelogram polyomino associated with the Dyck path. St001076The minimal length of a factorization of a permutation into transpositions that are cyclic shifts of (12). St001077The prefix exchange distance of a permutation. St001108The 2-dynamic chromatic number of a graph. St001110The 3-dynamic chromatic number of a graph. St001278The number of indecomposable modules that are fixed by $\tau \Omega^1$ composed with its inverse in the corresponding Nakayama algebra. 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. St001579The number of cyclically simple transpositions decreasing the number of cyclic descents needed to sort a permutation. 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. St001726The number of visible inversions of a permutation. St001746The coalition number of a graph. St001869The maximum cut size of a graph. St001894The depth of a signed permutation. St000070The number of antichains 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. St000425The number of occurrences of the pattern 132 or of the pattern 213 in a permutation. St000426The number of occurrences of the pattern 132 or of the pattern 312 in a permutation. St000624The normalized sum of the minimal distances to a greater element. St000625The sum of the minimal distances to a greater element. St000672The number of minimal elements in Bruhat order not less than the permutation. St000987The number of positive eigenvalues of the Laplacian matrix of the graph. 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. 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. St001345The Hamming dimension of a graph. St001382The number of boxes in the diagram of a partition that do not lie in its Durfee square. St001511The minimal number of transpositions needed to sort a permutation in either direction. St001664The number of non-isomorphic subposets of a poset. St000058The order of a permutation. St001003The number of indecomposable modules with projective dimension at most 1 in the Nakayama algebra corresponding to the Dyck path. St000004The major index of a permutation. St000031The number of cycles in the cycle decomposition of a permutation. St000060The greater neighbor of the maximum. St000062The length of the longest increasing subsequence of the permutation. St000067The inversion number of the alternating sign matrix. St000071The number of maximal chains in a poset. St000081The number of edges of a graph. St000087The number of induced subgraphs. St000155The number of exceedances (also excedences) of a permutation. St000156The Denert index of a permutation. St000176The total number of tiles in the Gelfand-Tsetlin pattern. St000199The column of the unique '1' in the last row of the alternating sign matrix. St000213The number of weak exceedances (also weak excedences) of a permutation. St000216The absolute length of a permutation. St000223The number of nestings in the permutation. St000238The number of indices that are not small weak excedances. St000246The number of non-inversions of a permutation. St000293The number of inversions of a binary word. St000305The inverse major index of a permutation. St000308The height of the tree associated to a permutation. St000316The number of non-left-to-right-maxima of a permutation. St000327The number of cover relations in a poset. St000331The number of upper interactions of a Dyck path. St000332The positive inversions of an alternating sign matrix. St000334The maz index, the major index of a permutation after replacing fixed points by zeros. St000337The lec statistic, the sum of the inversion numbers of the hook factors of a permutation. St000339The maf index of a permutation. St000346The number of coarsenings of a partition. St000354The number of recoils of a permutation. St000369The dinv deficit of a Dyck path. St000384The maximal part of the shifted composition of an integer partition. St000488The number of cycles of a permutation of length at most 2. St000489The number of cycles of a permutation of length at most 3. St000495The number of inversions of distance at most 2 of a permutation. St000501The size of the first part in the decomposition of a permutation. St000539The number of odd inversions of a permutation. St000548The number of different non-empty partial sums of an integer partition. St000631The number of distinct palindromic decompositions of a binary word. St000670The reversal length of a permutation. St000702The number of weak deficiencies of a permutation. St000703The number of deficiencies of a permutation. St000727The largest label of a leaf in the binary search tree associated with the permutation. St000730The maximal arc length of a set partition. St000740The last entry of a permutation. St000795The mad of a permutation. St000797The stat`` of a permutation. St000798The makl of a permutation. St000829The Ulam distance of a permutation to the identity permutation. St000833The comajor index of a permutation. St000844The size of the largest block in the direct sum decomposition of a permutation. St000864The number of circled entries of the shifted recording tableau of a permutation. St000867The sum of the hook lengths in the first row of an integer partition. St000868The aid statistic in the sense of Shareshian-Wachs. St000874The position of the last double rise in a Dyck path. St000883The number of longest increasing subsequences of a permutation. St000907The number of maximal antichains of minimal length in a poset. St000911The number of maximal antichains of maximal size in a poset. St000912The number of maximal antichains in a poset. St000926The clique-coclique number of a graph. St000939The number of characters of the symmetric group whose value on the partition is positive. St001030Half the number of non-boundary horizontal edges in the fully packed loop corresponding to the alternating sign matrix. St001080The minimal length of a factorization of a permutation using the transposition (12) and the cycle (1,. St001090The number of pop-stack-sorts needed to sort a permutation. St001118The acyclic chromatic index of a graph. St001286The annihilation number of a graph. St001287The number of primes obtained by multiplying preimage and image of a permutation and subtracting one. St001291The number of indecomposable summands of the tensor product of two copies of the dual of the Nakayama algebra associated to a Dyck path. St001314The number of tilting modules of arbitrary projective dimension that have no simple modules as a direct summand in the corresponding Nakayama algebra. St001343The dimension of the reduced incidence algebra of a poset. St001375The pancake length of a permutation. St001391The disjunction number of a graph. St001397Number of pairs of incomparable elements in a finite poset. St001405The number of bonds in a permutation. St001416The length of a longest palindromic factor of a binary word. St001417The length of a longest palindromic subword of a binary word. St001419The length of the longest palindromic factor beginning with a one of a binary word. St001428The number of B-inversions of a signed permutation. St001441The number of non-empty connected induced subgraphs of a graph. St001461The number of topologically connected components of the chord diagram of a permutation. St001464The number of bases of the positroid corresponding to the permutation, with all fixed points counterclockwise. St001489The maximum of the number of descents and the number of inverse descents. St001497The position of the largest weak excedence of a permutation. St001509The degree of the standard monomial associated to a Dyck path relative to the trivial lower boundary. St001515The vector space dimension of the socle of the first syzygy module of the regular module (as a bimodule). St001533The largest coefficient of the Poincare polynomial of the poset cone. St001541The Gini index of an integer partition. St001558The number of transpositions that are smaller or equal to a permutation in Bruhat order. St001583The projective dimension of the simple module corresponding to the point in the poset of the symmetric group under bruhat order. 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. St001671Haglund's hag of a permutation. St001721The degree of a binary word. St001727The number of invisible inversions of a permutation. St001759The Rajchgot index of a permutation. St001798The difference of the number of edges in a graph and the number of edges in the complement of the Turán graph. St001806The upper middle entry of a permutation. St001821The sorting index of a signed permutation. 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. St000019The cardinality of the support of a permutation. St000028The number of stack-sorts needed to sort a permutation. St000088The row sums of the character table of the symmetric group. St000093The cardinality of a maximal independent set of vertices of a graph. St000108The number of partitions contained in the given partition. St000133The "bounce" of a permutation. St000152The number of boxed plus the number of special entries. St000171The degree of the graph. St000207Number of integral Gelfand-Tsetlin polytopes with prescribed top row and integer composition weight. St000209Maximum difference of elements in cycles. St000218The number of occurrences of the pattern 213 in a permutation. St000220The number of occurrences of the pattern 132 in a permutation. St000222The number of alignments in the permutation. St000235The number of indices that are not cyclical small weak excedances. St000245The number of ascents of a permutation. St000295The length of the border of a binary word. St000299The number of nonisomorphic vertex-induced subtrees. St000319The spin of an integer partition. St000320The dinv adjustment of an integer partition. St000380Half of the maximal perimeter of a rectangle fitting into the diagram of an integer partition. St000393The number of strictly increasing runs in a binary word. St000424The number of occurrences of the pattern 132 or of the pattern 231 in a permutation. St000431The number of occurrences of the pattern 213 or of the pattern 321 in a permutation. St000432The number of occurrences of the pattern 231 or of the pattern 312 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. St000435The number of occurrences of the pattern 213 or of the pattern 231 in a permutation. St000438The position of the last up step in a Dyck path. St000446The disorder of a permutation. St000448The number of pairs of vertices of a graph with distance 2. St000473The number of parts of a partition that are strictly bigger than the number of ones. St000532The total number of rook placements on a Ferrers board. St000537The cutwidth of a graph. St000550The number of modular elements of a lattice. St000551The number of left modular elements of a lattice. St000653The last descent of a permutation. St000656The number of cuts of a poset. St000677The standardized bi-alternating inversion number of a permutation. St000680The Grundy value for Hackendot on posets. St000691The number of changes of a binary word. St000710The number of big deficiencies of a permutation. St000711The number of big exceedences of a permutation. St000725The smallest label of a leaf of the increasing binary tree associated to a permutation. St000786The maximal number of occurrences of a colour in a proper colouring of a graph. St000815The number of semistandard Young tableaux of partition weight of given shape. St000831The number of indices that are either descents or recoils. St000837The number of ascents of distance 2 of a permutation. St000863The length of the first row of the shifted shape of a permutation. St000866The number of admissible inversions of a permutation in the sense of Shareshian-Wachs. St000921The number of internal inversions of a binary word. St000923The minimal number with no two order isomorphic substrings of this length in a permutation. St000935The number of ordered refinements of an integer partition. St000956The maximal displacement of a permutation. St001019Sum of the projective dimensions of the simple modules in the Nakayama algebra corresponding to the Dyck path. 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). St001160The number of proper blocks (or intervals) of a permutations. St001207The Lowey length of the algebra $A/T$ when $T$ is the 1-tilting module corresponding to the permutation in the Auslander algebra of $K[x]/(x^n)$. St001211The number of simple modules in the corresponding Nakayama algebra that have vanishing second Ext-group with the regular module. St001251The number of parts of a partition that are not congruent 1 modulo 3. St001280The number of parts of an integer partition that are at least two. St001298The number of repeated entries in the Lehmer code of a permutation. St001308The number of induced paths on three vertices in a graph. St001323The independence gap of a graph. St001337The upper domination number of a graph. St001338The upper irredundance number of a graph. St001415The length of the longest palindromic prefix of a binary word. St001424The number of distinct squares in a binary word. St001439The number of even weak deficiencies and of odd weak exceedences. 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. St001521Half the total irregularity of a graph. St001554The number of distinct nonempty subtrees of a binary tree. St001565The number of arithmetic progressions of length 2 in a permutation. St001616The number of neutral elements in a lattice. St001651The Frankl number of a lattice. St001658The total number of rook placements on a Ferrers board. St001674The number of vertices of the largest induced star graph in the graph. St001760The number of prefix or suffix reversals needed to sort a permutation. St001801Half the number of preimage-image pairs of different parity in a permutation. St001809The index of the step at the first peak of maximal height in a Dyck path. St001846The number of elements which do not have a complement in the lattice. St001882The number of occurrences of a type-B 231 pattern in a signed permutation. St001911A descent variant minus the number of inversions. St000063The number of linear extensions of a certain poset defined for an integer partition. St000184The size of the centralizer of any permutation of given cycle type. St000250The number of blocks (St000105) plus the number of antisingletons (St000248) of a set partition. St000474Dyson's crank of a partition. St000668The least common multiple of the parts of the partition. St000708The product of the parts of an integer partition. St000770The major index of an integer partition when read from bottom to top. St001020Sum of the codominant dimensions of the non-projective indecomposable injective modules of the Nakayama algebra corresponding to the Dyck path. St001179Number of indecomposable injective modules with projective dimension at most 2 in the corresponding Nakayama algebra. St001213The number of indecomposable modules in the corresponding Nakayama algebra that have vanishing first Ext-group with the regular module. St001400The total number of Littlewood-Richardson tableaux of given shape. St000806The semiperimeter of the associated bargraph. St000294The number of distinct factors of a binary word. St000518The number of distinct subsequences in a binary word. St000520The number of patterns in a permutation. St000681The Grundy value of Chomp on Ferrers diagrams. St000741The Colin de Verdière graph invariant. St001875The number of simple modules with projective dimension at most 1. St000620The number of standard tableaux of shape equal to the given partition such that the minimal cyclic descent is odd. St000080The rank of the poset. St000307The number of rowmotion orbits of a poset. St001330The hat guessing number of a graph. St001637The number of (upper) dissectors of a poset. St001645The pebbling number of a connected graph. St001668The number of points of the poset minus the width of the poset. St001820The size of the image of the pop stack sorting operator. St001876The number of 2-regular simple modules in the incidence algebra of the lattice. St000454The largest eigenvalue of a graph if it is integral. St000485The length of the longest cycle of a permutation. St000528The height of a poset. St000690The size of the conjugacy class of a permutation. St000718The largest Laplacian eigenvalue of a graph if it is integral. St000906The length of the shortest maximal chain in a poset. St000937The number of positive values of the symmetric group character corresponding to the partition. St001281The normalized isoperimetric number of a graph. St001346The number of parking functions that give the same permutation. St001603The number of colourings of a polygon such that the multiplicities of a colour are given by a partition. St001880The number of 2-Gorenstein indecomposable injective modules in the incidence algebra of the lattice. St001915The size of the component corresponding to a necklace in Bulgarian solitaire. St001926Sparre Andersen's position of the maximum of a signed permutation. St000219The number of occurrences of the pattern 231 in a permutation. St000462The major index minus the number of excedences of a permutation. St000512The number of invariant subsets of size 3 when acting with a permutation of given cycle type. St000643The size of the largest orbit of antichains under Panyushev complementation. St000779The tier of a permutation. St000872The number of very big descents of a permutation. St001604The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on polygons. St000910The number of maximal chains of minimal length in a poset. St001105The number of greedy linear extensions of a poset. St001106The number of supergreedy linear extensions of a poset. St001510The number of self-evacuating linear extensions of a finite poset. St000848The balance constant multiplied with the number of linear extensions of a poset. St000849The number of 1/3-balanced pairs in a poset. St001633The number of simple modules with projective dimension two in the incidence algebra of the poset. St001636The number of indecomposable injective modules with projective dimension at most one in the incidence algebra of the poset. St001782The order of rowmotion on the set of order ideals of a poset. St001232The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2. St001644The dimension of a graph. 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. 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. St001638The book thickness of a graph. St001555The order of a signed permutation. St000045The number of linear extensions of a binary tree. St000777The number of distinct eigenvalues of the distance Laplacian of a connected graph. St000259The diameter of a connected graph. St001060The distinguishing index of a graph. St001605The number of colourings of a cycle such that the multiplicities of colours are given by a partition. St001629The coefficient of the integer composition in the quasisymmetric expansion of the relabelling action of the symmetric group on cycles. St000144The pyramid weight of the Dyck path. St000632The jump number of the poset. 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. St001023Number of simple modules with projective dimension at most 3 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. 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. St001183The maximum of $projdim(S)+injdim(S)$ over all simple modules in the Nakayama algebra corresponding to the Dyck path. St001190Number of simple modules with projective dimension at most 4 in the corresponding Nakayama algebra. 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 $eA$. St001237The number of simple modules with injective dimension at most one or dominant dimension at least one. St001240The number of indecomposable modules e_i J^2 that have injective dimension at most one in the corresponding Nakayama algebra St001258Gives the maximum of injective plus projective dimension of an indecomposable module over the corresponding Nakayama algebra. St001267The length of the Lyndon factorization of the binary word. St001437The flex of a binary word. St001914The size of the orbit of an integer partition in Bulgarian solitaire. St000527The width of the poset. St000845The maximal number of elements covered by an element in a poset. St001168The vector space dimension of the tilting module corresponding to the permutation in the Auslander algebra of $K[x]/(x^n)$. St001199The dominant dimension of $eAe$ for the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. St000260The radius of a connected graph. 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. St000466The Gutman (or modified Schultz) index of a connected graph. St000487The length of the shortest cycle of a permutation. St000654The first descent 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. St000887The maximal number of nonzero entries on a diagonal of a permutation matrix. St000990The first ascent of a permutation. St000472The sum of the ascent bottoms 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. St000796The stat' of a permutation. St000989The number of final rises of a permutation. St001061The number of indices that are both descents and recoils of a permutation. St001114The number of odd descents of a permutation. St001195The global dimension of the algebra $A/AfA$ of the corresponding Nakayama algebra $A$ with minimal left faithful projective-injective module $Af$. St001569The maximal modular displacement of a permutation. St001582The grades of the simple modules corresponding to the points in the poset of the symmetric group under the Bruhat order. St001859The number of factors of the Stanley symmetric function associated with a permutation. St001948The number of augmented double ascents of a permutation. St000264The girth of a graph, which is not a tree. St000306The bounce count of a Dyck path. St000882The number of connected components of short braid edges in the graph of braid moves of a permutation. St000739The first entry in the last row of a semistandard tableau. St001401The number of distinct entries in a semistandard tableau. St001491The number of indecomposable projective-injective modules in the algebra corresponding to a subset. St001686The order of promotion on a Gelfand-Tsetlin pattern. 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. St001960The number of descents of a permutation minus one if its first entry is not one. St000116The major index of a semistandard tableau obtained by standardizing. St000168The number of internal nodes of an ordered tree. St000173The segment statistic of a semistandard tableau. St000174The flush statistic of a semistandard tableau. St000338The number of pixed points of a permutation. St000358The number of occurrences of the pattern 31-2. St000371The number of mid points of decreasing subsequences of length 3 in a permutation. St000375The number of non weak exceedences of a permutation that are mid-points of a decreasing subsequence of length $3$. St000569The sum of the heights of the vertices of a binary tree. 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. St000699The toughness times the least common multiple of 1,. St000736The last entry in the first row of a semistandard tableau. St000813The number of zero-one matrices with weakly decreasing column sums and row sums given by the partition. St000880The number of connected components of long braid edges in the graph of braid moves of a permutation. St000942The number of critical left to right maxima of the parking functions. St000958The number of Bruhat factorizations 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. 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 $eA$. St001225The vector space dimension of the first extension group between J and itself when J is the Jacobson radical of the corresponding Nakayama algebra. St001235The global dimension of the corresponding Comp-Nakayama algebra. St001480The number of simple summands of the module J^2/J^3. St001487The number of inner corners of a skew partition. St001514The dimension of the top of the Auslander-Reiten translate of the regular modules as a bimodule. St001570The minimal number of edges to add to make a graph Hamiltonian. St001591The number of graphs with the given composition of multiplicities of Laplacian eigenvalues. St001596The number of two-by-two squares inside a skew partition. St001640The number of ascent tops in the permutation such that all smaller elements appear before. St001684The reduced word complexity of a permutation. St001742The difference of the maximal and the minimal degree in a graph. 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. St001769The reflection length of a signed permutation. St001773The number of minimal elements in Bruhat order not less than the signed permutation. St001863The number of weak excedances of a signed permutation. St001864The number of excedances of a signed permutation. St001877Number of indecomposable injective modules with projective dimension 2. St001896The number of right descents of a signed permutations. St001904The length of the initial strictly increasing segment of a parking function. St001905The number of preferred parking spots in a parking function less than the index of the car. St001928The number of non-overlapping descents in a permutation. St001946The number of descents in a parking function. St000002The number of occurrences of the pattern 123 in a permutation. St000015The number of peaks of a Dyck path. St000021The number of descents of a permutation. St000075The orbit size of a standard tableau under promotion. St000095The number of triangles of a graph. St000102The charge of a semistandard tableau. St000105The number of blocks in the set partition. St000141The maximum drop size of a permutation. St000162The number of nontrivial cycles in the cycle decomposition of a permutation. St000166The depth minus 1 of an ordered tree. St000210Minimum over maximum difference of elements in cycles. St000211The rank of the set partition. St000251The number of nonsingleton blocks of a set partition. St000314The number of left-to-right-maxima of a permutation. St000333The dez statistic, the number of descents of a permutation after replacing fixed points by zeros. St000357The number of occurrences of the pattern 12-3. St000372The number of mid points of increasing subsequences of length 3 in a permutation. St000443The number of long tunnels of a Dyck path. St000461The rix statistic of a permutation. St000493The los statistic of a set partition. St000499The rcb statistic of a set partition. St000504The cardinality of the first block of a set partition. St000522The number of 1-protected nodes of a rooted tree. St000553The number of blocks of a graph. St000558The number of occurrences of the pattern {{1,2}} in a set partition. St000603The number of occurrences of the pattern {{1},{2},{3}} such that 2,3 are minimal. St000605The number of occurrences of the pattern {{1},{2,3}} such that 3 is maximal, (2,3) are consecutive in a block. St000619The number of cyclic descents of a permutation. St000662The staircase size of the code of a permutation. St000695The number of blocks in the first part of the atomic decomposition of a set partition. St000804The number of occurrences of the vincular pattern |123 in a permutation. St000822The Hadwiger number of the graph. St000823The number of unsplittable factors of the set partition. St000873The aix statistic of a permutation. 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. St000925The number of topologically connected components of a set partition. St000961The shifted major index of a permutation. St000963The 2-shifted major index of a permutation. St000991The number of right-to-left minima of a permutation. 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. St001062The maximal size of a block of a set partition. St001075The minimal size of a block of a set partition. St001082The number of boxed occurrences of 123 in a permutation. St001084The number of occurrences of the vincular pattern |1-23 in a permutation. 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 $K[x]/(x^n)$. St001187The number of simple modules with grade at least one in the corresponding Nakayama algebra. 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. St001220The width of a permutation. St001224Let X be the direct sum of all simple modules of the corresponding Nakayama algebra. St001269The sum of the minimum of the number of exceedances and deficiencies in each cycle of a permutation. 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. St001517The length of a longest pair of twins in a permutation. St001520The number of strict 3-descents. St001526The Loewy length of the Auslander-Reiten translate of the regular module as a bimodule of the Nakayama algebra corresponding to the Dyck path. 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. St001642The Prague dimension of a graph. St001649The length of a longest trail in a graph. St001665The number of pure excedances of a permutation. St001667The maximal size of a pair of weak twins for a permutation. St001682The number of distinct positions of the pattern letter 1 in occurrences of 123 in a permutation. St001722The number of minimal chains with small intervals between a binary word and the top element. St001729The number of visible descents of a permutation. St001738The minimal order of a graph which is not an induced subgraph of the given graph. St001745The number of occurrences of the arrow pattern 13 with an arrow from 1 to 2 in a permutation. St001778The largest greatest common divisor of an element and its image in a permutation. St001811The Castelnuovo-Mumford regularity of a permutation. St001857The number of edges in the reduced word graph of a signed permutation. St001874Lusztig's a-function for the symmetric group. St001935The number of ascents in a parking function. St001964The interval resolution global dimension of a poset. St000094The depth of an ordered tree. St000135The number of lucky cars of the parking function. St000325The width of the tree associated to a permutation. St000455The second largest eigenvalue of a graph if it is integral. St000470The number of runs in a permutation. St000521The number of distinct subtrees of an ordered tree. St000744The length of the path to the largest entry in a standard Young tableau. St000973The length of the boundary of an ordered tree. St000975The length of the boundary minus the length of the trunk of an ordered tree. St000988The orbit size of a permutation under Foata's bijection. St001002Number of indecomposable modules with projective and injective dimension at most 1 in the Nakayama algebra corresponding to the Dyck path. St001004The number of indices that are either left-to-right maxima or right-to-left minima. St001005The number of indices for a permutation that are either left-to-right maxima or right-to-left minima but not both. 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. St001290The first natural number n such that the tensor product of n copies of D(A) is zero for the corresponding Nakayama algebra A. 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. St001927Sparre Andersen's number of positives of a signed permutation. St000044The number of vertices of the unicellular map given by a perfect matching. St000422The energy of a graph, if it is integral. St000735The last entry on the main diagonal of a standard tableau.