St000484The sum of St000483 over all subsequences of length at least three. St000070The number of antichains in a poset. St000104The number of facets in the order polytope of this poset. St000108The number of partitions contained in the given partition. St000151The number of facets in the chain polytope of the poset. St000532The total number of rook placements on a Ferrers board. St001213The number of indecomposable modules in the corresponding Nakayama algebra that have vanishing first Ext-group with the regular module. St001658The total number of rook placements on a Ferrers board. St001664The number of non-isomorphic subposets of a poset. St000071The number of maximal chains in a poset. St000087The number of induced subgraphs. St000189The number of elements in the poset. St000228The size of a partition. St000395The sum of the heights of the peaks of a Dyck path. St000631The number of distinct palindromic decompositions of a binary word. St000656The number of cuts of a poset. St000770The major index of an integer partition when read from bottom to top. St000808The number of up steps of the associated bargraph. St000867The sum of the hook lengths in the first row of an integer partition. St000926The clique-coclique number of a graph. St001003The number of indecomposable modules with projective dimension at most 1 in the Nakayama algebra corresponding to the Dyck path. St001018Sum of projective dimension of the indecomposable injective modules of the Nakayama algebra corresponding to the Dyck path. St001019Sum of the projective dimensions of the simple modules in the Nakayama algebra corresponding to the Dyck path. St001218Smallest index k greater than or equal to one such that the Coxeter matrix C of the corresponding Nakayama algebra has C^k=1. 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. St001348The bounce of the parallelogram polyomino associated with the Dyck path. St001441The number of non-empty connected induced subgraphs of a graph. 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. St001717The largest size of an interval in a poset. St001894The depth of a signed permutation. St000004The major index of a permutation. St000018The number of inversions of a permutation. St000058The order of a permutation. St000152The number of boxed plus the number of special entries. St000156The Denert index of a permutation. St000182The number of permutations whose cycle type is the given integer partition. St000224The sorting index of a permutation. St000238The number of indices that are not small weak excedances. 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. St000485The length of the longest cycle of a permutation. St000494The number of inversions of distance at most 3 of a permutation. St000495The number of inversions of distance at most 2 of a permutation. St000509The diagonal index (content) of a partition. St000690The size of the conjugacy class of a permutation. St000794The mak of a permutation. St000795The mad of a permutation. St000868The aid statistic in the sense of Shareshian-Wachs. St001079The minimal length of a factorization of a permutation using the permutations (12)(34). St001300The rank of the boundary operator in degree 1 of the chain complex of the order complex of the poset. St001346The number of parking functions that give the same permutation. St001464The number of bases of the positroid corresponding to the permutation, with all fixed points counterclockwise. St001497The position of the largest weak excedence of a permutation. St001528The number of permutations such that the product with the permutation has the same number of fixed points. St001558The number of transpositions that are smaller or equal to a permutation in Bruhat order. St001599The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on rooted trees. St001627The number of coloured connected graphs such that the multiplicities of colours are given by a partition. St001759The Rajchgot index of a permutation. St001806The upper middle entry of a permutation. St001820The size of the image of the pop stack sorting operator. St001915The size of the component corresponding to a necklace in Bulgarian solitaire. St001926Sparre Andersen's position of the maximum of a signed permutation. St001957The number of Hasse diagrams with a given underlying undirected graph. St000028The number of stack-sorts needed to sort a permutation. St000137The Grundy value of an integer partition. St000155The number of exceedances (also excedences) of a permutation. St000216The absolute length of a permutation. St000246The number of non-inversions of a permutation. St000549The number of odd partial sums of an integer partition. St000651The maximal size of a rise in a permutation. St000670The reversal length of a permutation. St000809The reduced reflection length of the permutation. St000996The number of exclusive left-to-right maxima of a permutation. St001030Half the number of non-boundary horizontal edges in the fully packed loop corresponding to the alternating sign 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. St001090The number of pop-stack-sorts needed to sort a permutation. St001375The pancake length of a permutation. St001402The number of separators in a permutation. St001579The number of cyclically simple transpositions decreasing the number of cyclic descents needed to sort a permutation. St001583The projective dimension of the simple module corresponding to the point in the poset of the symmetric group under bruhat order. St001651The Frankl number of a lattice. St001760The number of prefix or suffix reversals needed to sort a permutation. St001956The comajor index for set-valued two-row standard Young tableaux. St000093The cardinality of a maximal independent set of vertices of a graph. St000110The number of permutations less than or equal to a permutation in left weak order. St000180The number of chains of a poset. St000300The number of independent sets of vertices of a graph. St000301The number of facets of the stable set polytope of a graph. St000393The number of strictly increasing runs in a binary word. St000420The number of Dyck paths that are weakly above a Dyck path. St000438The position of the last up step in a Dyck path. St000550The number of modular elements of a lattice. St000551The number of left modular elements of a lattice. St000619The number of cyclic descents of a permutation. St000786The maximal number of occurrences of a colour in a proper colouring of a graph. St000912The number of maximal antichains in a poset. St000915The Ore degree of a graph. St000981The length of the longest zigzag subpath. St001065Number of indecomposable reflexive modules in the corresponding Nakayama algebra. St001093The detour number of a graph. St001119The length of a shortest maximal path in a graph. St001259The vector space dimension of the double dual of D(A) in the corresponding Nakayama algebra. St001286The annihilation number of a graph. St001337The upper domination number of a graph. St001338The upper irredundance number of a graph. St001350Half of the Albertson index of a graph. St001417The length of a longest palindromic subword of a binary word. St001554The number of distinct nonempty subtrees of a binary tree. St001616The number of neutral elements in a lattice. St001636The number of indecomposable injective modules with projective dimension at most one in the incidence algebra of the poset. St001672The restrained domination number of a graph. St001721The degree of a binary word. St001838The number of nonempty primitive factors of a binary word. St001855The number of signed permutations less than or equal to a signed permutation in left weak order. St001875The number of simple modules with projective dimension at most 1. St000012The area of a Dyck path. St000020The rank of the permutation. St000027The major index of a Dyck path. St000029The depth of a permutation. St000030The sum of the descent differences of a permutations. St000081The number of edges of a graph. St000086The number of subgraphs. St000172The Grundy number of a graph. St000197The number of entries equal to positive one in the alternating sign matrix. St000203The number of external nodes of a binary tree. St000207Number of integral Gelfand-Tsetlin polytopes with prescribed top row and integer composition weight. St000235The number of indices that are not cyclical small weak excedances. St000240The number of indices that are not small excedances. St000242The number of indices that are not cyclical small weak excedances. St000250The number of blocks (St000105) plus the number of antisingletons (St000248) of a set partition. St000290The major index of a binary word. St000331The number of upper interactions of a Dyck path. St000394The sum of the heights of the peaks of a Dyck path minus the number of peaks. St000400The path length of an ordered tree. St000419The number of Dyck paths that are weakly above the Dyck path, except for the path itself. St000432The number of occurrences of the pattern 231 or of the pattern 312 in a permutation. St000456The monochromatic index of a connected graph. St000468The Hosoya index of a graph. St000507The number of ascents of a standard tableau. St000519The largest length of a factor maximising the subword complexity. St000537The cutwidth of a graph. St000637The length of the longest cycle in a graph. St000639The number of relations in a poset. St000641The number of non-empty boolean intervals in a poset. St000645The sum of the areas of the rectangles formed by two consecutive peaks and the valley in between. St000702The number of weak deficiencies of a permutation. St000724The label of the leaf of the path following the smaller label in the increasing binary tree associated to a permutation. St000727The largest label of a leaf in the binary search tree associated with the permutation. St000743The number of entries in a standard Young tableau such that the next integer is a neighbour. St000796The stat' of a permutation. St000798The makl of a permutation. St000825The sum of the major and the inverse major index of a permutation. St000833The comajor index of a permutation. St000841The largest opener of a perfect matching. St000918The 2-limited packing number of a graph. St000922The minimal number such that all substrings of this length are unique. St000923The minimal number with no two order isomorphic substrings of this length in a permutation. St000957The number of Bruhat lower covers of a permutation. St000979Half of MacMahon's equal index of a Dyck path. St000984The number of boxes below precisely one peak. St001033The normalized area of the parallelogram polyomino associated with the Dyck path. St001108The 2-dynamic chromatic number of a graph. St001112The 3-weak dynamic number of a graph. St001180Number of indecomposable injective modules with projective dimension at most 1. St001211The number of simple modules in the corresponding Nakayama algebra that have vanishing second Ext-group with the regular module. St001271The competition 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. St001287The number of primes obtained by multiplying preimage and image of a permutation and subtracting one. St001295Gives the vector space dimension of the homomorphism space between J^2 and J^2. St001304The number of maximally independent sets of vertices 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. St001365The number of lattice paths of the same length weakly above the path given by a binary word. St001379The number of inversions plus the major index of a permutation. St001406The number of nonzero entries in a Gelfand Tsetlin pattern. St001428The number of B-inversions of a signed permutation. St001437The flex of a binary word. St001439The number of even weak deficiencies and of odd weak exceedences. St001482The product of the prefix sums of a permutation. 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. St001500The global dimension of magnitude 1 Nakayama algebras. St001508The degree of the standard monomial associated to a Dyck path relative to the diagonal boundary. St001509The degree of the standard monomial associated to a Dyck path relative to the trivial lower boundary. St001512The minimum rank of a graph. St001581The achromatic number of a graph. 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. St001645The pebbling number of a connected graph. St001650The order of Ringel's homological bijection associated to the linear Nakayama algebra corresponding to the Dyck path. St001684The reduced word complexity of a permutation. St001726The number of visible inversions of a permutation. St001746The coalition number of a graph. St001798The difference of the number of edges in a graph and the number of edges in the complement of the Turán graph. St001809The index of the step at the first peak of maximal height in a Dyck path. St001834The number of non-isomorphic minors of a graph. St001861The number of Bruhat lower covers of a permutation. St001959The product of the heights of the peaks of a Dyck path. St001963The tree-depth of a graph. St000007The number of saliances of the permutation. St000008The major index of the composition. St000009The charge of a standard tableau. St000010The length of the partition. St000031The number of cycles in the cycle decomposition of a permutation. St000054The first entry of the permutation. St000056The decomposition (or block) number of a permutation. St000059The inversion number of a standard tableau as defined by Haglund and Stevens. St000062The length of the longest increasing subsequence of the permutation. St000067The inversion number of the alternating sign matrix. St000088The row sums of the character table of the symmetric group. St000133The "bounce" of a permutation. St000147The largest part of an integer partition. St000153The number of adjacent cycles of a permutation. St000154The sum of the descent bottoms of a permutation. St000169The cocharge of a standard tableau. St000175Degree of the polynomial counting the number of semistandard Young tableaux when stretching the shape. St000199The column of the unique '1' in the last row of the alternating sign matrix. St000208Number of integral Gelfand-Tsetlin polytopes with prescribed top row and integer partition weight. St000213The number of weak exceedances (also weak excedences) of a permutation. St000231Sum of the maximal elements of the blocks of a set partition. St000239The number of small weak excedances. St000271The chromatic index of a graph. St000280The size of the preimage of the map 'to labelling permutation' from Parking functions to Permutations. St000289The decimal representation of a binary word. St000295The length of the border of a binary word. St000299The number of nonisomorphic vertex-induced subtrees. St000304The load of a permutation. St000305The inverse major index of a permutation. St000308The height of the tree associated to a permutation. St000314The number of left-to-right-maxima of a permutation. St000321The number of integer partitions of n that are dominated by an integer partition. St000325The width of the tree associated to a permutation. St000330The (standard) major index of a standard tableau. St000332The positive inversions of an alternating sign matrix. St000345The number of refinements of a partition. St000346The number of coarsenings of a partition. St000362The size of a minimal vertex cover of a graph. St000378The diagonal inversion number of an integer partition. St000391The sum of the positions of the ones in a binary word. St000398The sum of the depths of the vertices (or total internal path length) of a binary tree. St000448The number of pairs of vertices of a graph with distance 2. St000451The length of the longest pattern of the form k 1 2. St000452The number of distinct eigenvalues of a graph. St000453The number of distinct Laplacian eigenvalues of a graph. St000470The number of runs in 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. St000501The size of the first part in the decomposition of a permutation. St000504The cardinality of the first block of a set partition. St000513The number of invariant subsets of size 2 when acting with a permutation of given cycle type. St000539The number of odd inversions of a permutation. St000542The number of left-to-right-minima of a permutation. St000567The sum of the products of all pairs of parts. St000612The number of occurrences of the pattern {{1},{2,3}} such that 1 is minimal, (2,3) are consecutive in a block. St000624The normalized sum of the minimal distances to a greater element. St000638The number of up-down runs of a permutation. St000654The first descent of a permutation. St000668The least common multiple of the parts of the partition. St000672The number of minimal elements in Bruhat order not less than the permutation. St000675The number of centered multitunnels of a Dyck path. St000692Babson and Steingrímsson's statistic of a permutation. St000699The toughness times the least common multiple of 1,. St000708The product of the parts of an integer partition. St000734The last entry in the first row of a standard tableau. St000737The last entry on the main diagonal of a semistandard tableau. St000740The last entry of a permutation. St000759The smallest missing part in an integer partition. St000792The Grundy value for the game of ruler on a binary word. St000797The stat`` of a permutation. St000810The sum of the entries in the column specified by the partition of the change of basis matrix from powersum symmetric functions to monomial symmetric functions. 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. St000823The number of unsplittable factors of the set partition. St000832The number of permutations obtained by reversing blocks of three consecutive numbers. St000844The size of the largest block in the direct sum decomposition of a permutation. St000849The number of 1/3-balanced pairs in a poset. St000864The number of circled entries of the shifted recording tableau of a permutation. St000874The position of the last double rise in a Dyck path. St000887The maximal number of nonzero entries on a diagonal of a permutation matrix. St000904The maximal number of repetitions of an integer composition. St000933The number of multipartitions of sizes given by an integer partition. St000935The number of ordered refinements of an integer partition. St000937The number of positive values of the symmetric group character corresponding to the partition. St000939The number of characters of the symmetric group whose value on the partition is positive. St000971The smallest closer of a set partition. St000990The first ascent 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. 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. St001032The number of horizontal steps in the bicoloured Motzkin path associated with the Dyck path. St001038The minimal height of a column in the parallelogram polyomino associated with the Dyck path. St001062The maximal size of a block of a set partition. 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. St001111The weak 2-dynamic chromatic number of a graph. St001117The game chromatic index of a graph. St001118The acyclic chromatic index of a graph. St001176The size of a partition minus its first part. St001214The aft of an integer partition. St001239The largest vector space dimension of the double dual of a simple module in the corresponding Nakayama algebra. 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. St001250The number of parts of a partition that are not congruent 0 modulo 3. St001291The number of indecomposable summands of the tensor product of two copies of the dual of the Nakayama algebra associated to a Dyck path. St001308The number of induced paths on three vertices in a graph. 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. St001324The minimal number of occurrences of the chordal-pattern in a linear ordering of the vertices of the graph. St001386The number of prime labellings of a graph. St001389The number of partitions of the same length below the given integer partition. St001390The number of bumps occurring when Schensted-inserting the letter 1 of a permutation. St001397Number of pairs of incomparable elements in a finite poset. St001416The length of a longest palindromic factor of a binary word. St001424The number of distinct squares in a binary word. St001461The number of topologically connected components of the chord diagram of a permutation. St001468The smallest fixpoint of a permutation. St001480The number of simple summands of the module J^2/J^3. St001485The modular major index of a binary word. St001515The vector space dimension of the socle of the first syzygy module of the regular module (as a bimodule). St001517The length of a longest pair of twins in a permutation. St001521Half the total irregularity of a graph. St001532The leading coefficient of the Poincare polynomial of the poset cone. St001533The largest coefficient of the Poincare polynomial of the poset cone. St001541The Gini index of an integer partition. St001555The order of a signed permutation. St001582The grades of the simple modules corresponding to the points in the poset of the symmetric group under the Bruhat order. St001609The number of coloured trees such that the multiplicities of colours are given by a partition. St001633The number of simple modules with projective dimension two in the incidence algebra of the poset. St001649The length of a longest trail in a graph. St001652The length of a longest interval of consecutive numbers. St001662The length of the longest factor of consecutive numbers in a permutation. St001671Haglund's hag of a permutation. St001674The number of vertices of the largest induced star graph in the graph. St001697The shifted natural comajor index of a standard Young tableau. St001723The differential of a graph. St001724The 2-packing differential of a graph. St001778The largest greatest common divisor of an element and its image in a permutation. St001783The number of odd automorphisms of a graph. St001808The box weight or horizontal decoration of a Dyck path. St001821The sorting index of a signed permutation. St001822The number of alignments of a signed permutation. St001823The Stasinski-Voll length of a signed permutation. St001827The number of two-component spanning forests of a graph. St001846The number of elements which do not have a complement in the lattice. St001929The number of meanders with top half given by the noncrossing matching corresponding to the Dyck path. St001930The weak major index of a binary word. St000002The number of occurrences of the pattern 123 in a permutation. St000005The bounce statistic of a Dyck path. St000006The dinv of a Dyck path. St000019The cardinality of the support of a permutation. St000021The number of descents of a permutation. St000120The number of left tunnels of a Dyck path. St000136The dinv of a parking function. St000141The maximum drop size of a permutation. St000142The number of even parts of a partition. St000194The number of primary dinversion pairs of a labelled dyck path corresponding to a parking function. St000209Maximum difference of elements in cycles. St000211The rank of the set partition. St000223The number of nestings in the permutation. St000234The number of global ascents of a permutation. St000237The number of small exceedances. St000245The number of ascents of a permutation. St000288The number of ones in a binary word. St000316The number of non-left-to-right-maxima of a permutation. St000319The spin of an integer partition. St000320The dinv adjustment of an integer partition. St000327The number of cover relations in a poset. St000329The number of evenly positioned ascents of the Dyck path, with the initial position equal to 1. St000333The dez statistic, the number of descents of a permutation after replacing fixed points by zeros. St000337The lec statistic, the sum of the inversion numbers of the hook factors of a permutation. St000340The number of non-final maximal constant sub-paths of length greater than one. St000354The number of recoils of a permutation. St000357The number of occurrences of the pattern 12-3. St000371The number of mid points of decreasing subsequences of length 3 in a permutation. St000372The number of mid points of increasing subsequences of length 3 in a permutation. St000373The number of weak exceedences of a permutation that are also mid-points of a decreasing subsequence of length $3$. St000374The number of exclusive right-to-left minima of a permutation. St000389The number of runs of ones of odd length in a binary word. St000392The length of the longest run of ones in a binary word. St000427The number of occurrences of the pattern 123 or of the pattern 231 in a permutation. St000429The number of occurrences of the pattern 123 or of the pattern 321 in a permutation. St000430The number of occurrences of the pattern 123 or of the pattern 312 in a permutation. St000441The number of successions of a permutation. St000462The major index minus the number of excedences of a permutation. St000463The number of admissible inversions of a permutation. St000472The sum of the ascent bottoms of a permutation. St000476The sum of the semi-lengths of tunnels before a valley of a Dyck path. St000541The number of indices greater than or equal to 2 of a permutation such that all smaller indices appear to its right. St000546The number of global descents of a permutation. St000603The number of occurrences of the pattern {{1},{2},{3}} such that 2,3 are minimal. St000618The number of self-evacuating tableaux of given shape. St000653The last descent of a permutation. St000662The staircase size of the code of a permutation. St000677The standardized bi-alternating inversion number of a permutation. St000703The number of deficiencies of a permutation. St000742The number of big ascents of a permutation after prepending zero. St000753The Grundy value for the game of Kayles on a binary word. St000779The tier of a permutation. St000793The length of the longest partition in the vacillating tableau corresponding to a set partition. St000829The Ulam distance of a permutation to the identity permutation. St000831The number of indices that are either descents or recoils. St000837The number of ascents of distance 2 of a permutation. St000846The maximal number of elements covering an element of a poset. St000866The number of admissible inversions of a permutation in the sense of Shareshian-Wachs. St000872The number of very big descents of a permutation. St000947The major index east count of a Dyck path. St000956The maximal displacement of a permutation. St000961The shifted major index of a permutation. St000989The number of final rises of a permutation. St001057The Grundy value of the game of creating an independent set in a graph. St001069The coefficient of the monomial xy of the Tutte polynomial of the graph. St001080The minimal length of a factorization of a permutation using the transposition (12) and the cycle (1,. St001082The number of boxed occurrences of 123 in a permutation. St001084The number of occurrences of the vincular pattern |1-23 in a permutation. St001087The number of occurrences of the vincular pattern |12-3 in a permutation. St001092The number of distinct even parts of a partition. 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. St001104The number of descents of the invariant in a tensor power of the adjoint representation of the rank two general linear group. 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 St001207The Lowey length of the algebra $A/T$ when $T$ is the 1-tilting module corresponding to the permutation in the Auslander algebra of $K[x]/(x^n)$. 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. 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. St001232The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2. St001273The projective dimension of the first term in an injective coresolution of the regular module. St001274The number of indecomposable injective modules with projective dimension equal to two. St001298The number of repeated entries in the Lehmer code of a permutation. St001314The number of tilting modules of arbitrary projective dimension that have no simple modules as a direct summand in the corresponding Nakayama algebra. St001323The independence gap of a graph. St001327The minimal number of occurrences of the split-pattern in a linear ordering of the vertices of the graph. St001329The minimal number of occurrences of the outerplanar pattern in a linear ordering of the vertices of the graph. St001372The length of a longest cyclic run of ones of a binary word. St001391The disjunction number of a graph. 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. St001423The number of distinct cubes in 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. St001470The cyclic holeyness of a permutation. St001484The number of singletons of an integer partition. St001489The maximum of the number of descents and the number of inverse descents. St001510The number of self-evacuating linear extensions of a finite poset. St001553The number of indecomposable summands of the square of the Jacobson radical as a bimodule in the Nakayama algebra corresponding to the Dyck path. St001584The area statistic between a Dyck path and its bounce path. St001628The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on simple connected graphs. St001640The number of ascent tops in the permutation such that all smaller elements appear before. St001682The number of distinct positions of the pattern letter 1 in occurrences of 123 in a permutation. St001689The number of celebrities in a graph. St001692The number of vertices with higher degree than the average degree in a graph. St001743The discrepancy of a graph. St001761The maximal multiplicity of a letter in a reduced word of a permutation. St001769The reflection length of a signed permutation. St001772The number of occurrences of the signed pattern 12 in a signed permutation. St001785The number of ways to obtain a partition as the multiset of antidiagonal lengths of the Ferrers diagram of a partition. St001860The number of factors of the Stanley symmetric function associated with a signed permutation. St001864The number of excedances of a signed permutation. St001907The number of Bastidas - Hohlweg - Saliola excedances of a signed permutation. St001912The length of the preperiod in Bulgarian solitaire corresponding to an integer partition. St001918The degree of the cyclic sieving polynomial corresponding to an integer partition. St001948The number of augmented double ascents of a permutation. St000477The weight of a partition according to Alladi. St000928The sum of the coefficients of the character polynomial of an integer partition. St001625The Möbius invariant of a lattice. St001138The number of indecomposable modules with projective dimension or injective dimension at most one in the corresponding Nakayama algebra. St000680The Grundy value for Hackendot on posets. St000045The number of linear extensions of a binary tree. St000219The number of occurrences of the pattern 231 in a permutation. St001604The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on polygons. St001629The coefficient of the integer composition in the quasisymmetric expansion of the relabelling action of the symmetric group on cycles. St001168The vector space dimension of the tilting module corresponding to the permutation in the Auslander algebra of $K[x]/(x^n)$. St000080The rank of the poset. St000307The number of rowmotion orbits of a poset. St001880The number of 2-Gorenstein indecomposable injective modules in the incidence algebra of the lattice. St000454The largest eigenvalue of a graph if it is integral. 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. St001603The number of colourings of a polygon such that the multiplicities of a colour are given by a partition. St001605The number of colourings of a cycle such that the multiplicities of colours are given by a partition. 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. St001570The minimal number of edges to add to make a graph Hamiltonian. St001859The number of factors of the Stanley symmetric function associated with a permutation. St000553The number of blocks of a graph. St000718The largest Laplacian eigenvalue of a graph if it is integral. St000450The number of edges minus the number of vertices plus 2 of a graph. St000777The number of distinct eigenvalues of the distance Laplacian of a connected graph. St000822The Hadwiger number of the graph. 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 $eA$. St001642The Prague dimension of a graph. St001734The lettericity of a graph. St001858The number of covering elements of a signed permutation in absolute order. St000259The diameter of a connected graph. St000642The size of the smallest orbit of antichains under Panyushev complementation. St000643The size of the largest orbit of antichains under Panyushev complementation. St000741The Colin de Verdière graph invariant. St000827The decimal representation of a binary word with a leading 1. St001060The distinguishing index of a graph. 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 $K[x]/(x^n)$. St001199The dominant dimension of $eAe$ for the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. St001491The number of indecomposable projective-injective modules in the algebra corresponding to a subset. St001644The dimension of a graph. St001812The biclique partition number of a graph. St000082The number of elements smaller than a binary tree in Tamari order. St000095The number of triangles of a graph. St000260The radius of a connected graph. 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. St000444The length of the maximal rise of a Dyck path. St000466The Gutman (or modified Schultz) index of a connected graph. St000678The number of up steps after the last double rise of a Dyck path. St000706The product of the factorials of the multiplicities of an integer partition. St000707The product of the factorials of the parts. St000717The number of ordinal summands of a poset. St000729The minimal arc length of a set partition. St000815The number of semistandard Young tableaux of partition weight of given shape. St000888The maximal sum of entries on a diagonal of an alternating sign matrix. St000892The maximal number of nonzero entries on a diagonal of an alternating sign matrix. St000906The length of the shortest maximal chain in a poset. St000925The number of topologically connected components of a set partition. St000993The multiplicity of the largest part of an integer partition. St001039The maximal height of a column in the parallelogram polyomino associated with a Dyck path. St001097The coefficient of the monomial symmetric function indexed by the partition in the formal group law for linear orders. St001501The dominant dimension of magnitude 1 Nakayama algebras. 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. 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. St001742The difference of the maximal and the minimal degree in a graph. St000083The number of left oriented leafs of a binary tree except the first one. St000282The size of the preimage of the map 'to poset' from Ordered trees to Posets. St000297The number of leading ones 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. St000442The maximal area to the right of an up step of a Dyck path. St000478Another weight of a partition according to Alladi. St000490The intertwining number of a set partition. St000492The rob statistic of a set partition. St000493The los statistic of a set partition. St000498The lcs statistic of a set partition. St000499The rcb statistic of a set partition. St000510The number of invariant oriented cycles when acting with a permutation of given cycle type. St000564The 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. St000573The number of occurrences of the pattern {{1},{2}} such that 1 is a singleton and 2 a maximal element. St000574The number of occurrences of the pattern {{1},{2}} such that 1 is a minimal and 2 a maximal element. St000575The number of occurrences of the pattern {{1},{2}} such that 1 is a maximal element and 2 a singleton. St000576The number of occurrences of the pattern {{1},{2}} such that 1 is a maximal and 2 a minimal element. 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. St000579The number of occurrences of the pattern {{1},{2}} such that 2 is a maximal element. St000620The number of standard tableaux of shape equal to the given partition such that the minimal cyclic descent is odd. St000621The number of standard tableaux of shape equal to the given partition such that the minimal cyclic descent is even. St000640The rank of the largest boolean interval in a poset. St000658The number of rises of length 2 of a Dyck path. St000659The number of rises of length at least 2 of a Dyck path. St000681The Grundy value of Chomp on Ferrers diagrams. 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. St000698The number of 2-rim hooks removed from an integer partition to obtain its associated 2-core. St000790The number of pairs of centered tunnels, one strictly containing the other, of a Dyck path. St000877The depth of the binary word interpreted as a path. 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. St000946The sum of the skew hook positions in a Dyck path. St000976The sum of the positions of double up-steps of a Dyck path. St001031The height of the bicoloured Motzkin path associated with the Dyck path. 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. 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. St001281The normalized isoperimetric number of a graph. St001371The length of the longest Yamanouchi prefix of a binary word. St001498The normalised height of a Nakayama algebra with magnitude 1. St001592The maximal number of simple paths between any two different vertices of a graph. St001668The number of points of the poset minus the width of the poset. St000455The second largest eigenvalue of a graph if it is integral. St001637The number of (upper) dissectors of a poset. St000264The girth of a graph, which is not a tree. St000927The alternating sum of the coefficients of the character polynomial of an integer partition. St001621The number of atoms of a lattice. St001623The number of doubly irreducible elements of a lattice. St000422The energy of a graph, if it is integral. St001330The hat guessing number of a graph. St001877Number of indecomposable injective modules with projective dimension 2. St001917The order of toric promotion on the set of labellings of a graph. St000882The number of connected components of short braid edges in the graph of braid moves of a permutation. St000467The hyper-Wiener index of a connected graph. St000302The determinant of the distance matrix of a connected graph.