St001616The number of neutral elements in a lattice. St001706The number of closed sets in a graph. St001754The number of tolerances of a finite lattice. St001762The number of convex subsets of vertices in a graph. St001909The number of interval-closed sets of a poset. St001619The number of non-isomorphic sublattices of a lattice. St001666The number of non-isomorphic subposets of a lattice which are lattices. St000027The major index of a Dyck path. St000111The sum of the descent tops (or Genocchi descents) of a permutation. St000198A decimal representation of a binary tree as a code word. St000311The number of vertices of odd degree in a graph. St000312The number of leaves in a graph. St000350The sum of the vertex degrees of a graph. St000380Half of the maximal perimeter of a rectangle fitting into the diagram of an integer partition. St000422The energy of a graph, if it is integral. St000465The first Zagreb index of a graph. St000467The hyper-Wiener index of a connected graph. St000484The sum of St000483 over all subsequences of length at least three. St000571The F-index (or forgotten topological index) of a graph. St000616The inversion index of a permutation. St000718The largest Laplacian eigenvalue of a graph if it is integral. St000793The length of the longest partition in the vacillating tableau corresponding to a set partition. St000825The sum of the major and the inverse major index of a permutation. St000828The spearman's rho of a permutation and the identity permutation. St000915The Ore degree of a graph. St000951The dimension of $Ext^{1}(D(A),A)$ of the corresponding LNakayama algebra. St000979Half of MacMahon's equal index of a Dyck path. St000995The largest even part of an integer partition. St001177Twice the mean value of the major index among all standard Young tableaux of a partition. St001248Sum of the even parts of a partition. St001275The projective dimension of the second term in a minimal injective coresolution of the regular module. St001279The sum of the parts of an integer partition that are at least two. St001287The number of primes obtained by multiplying preimage and image of a permutation and subtracting one. St001379The number of inversions plus the major index of a permutation. St001391The disjunction number of a graph. St001458The rank of the adjacency matrix of a graph. St001459The number of zero columns in the nullspace of a graph. St001626The number of maximal proper sublattices of a lattice. St001902The number of potential covers of a poset. St001956The comajor index for set-valued two-row standard Young tableaux. St000037The sign of a permutation. St000055The inversion sum of a permutation. St000114The sum of the entries of the Gelfand-Tsetlin pattern. St000146The Andrews-Garvan crank of a partition. St000230Sum of the minimal elements of the blocks of a set partition. St000231Sum of the maximal elements of the blocks of a set partition. St000347The inversion sum of a binary word. St000400The path length of an ordered tree. St000524The number of posets with the same order polynomial. St000525The number of posets with the same zeta polynomial. St000526The number of posets with combinatorially isomorphic order polytopes. St000652The maximal difference between successive positions of a permutation. St000705The number of semistandard tableaux on a given integer partition of n with maximal entry n. St000715The number of semistandard Young tableaux of given shape and entries at most 3. 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. St000867The sum of the hook lengths in the first row of an integer partition. St000964Gives the dimension of Ext^g(D(A),A) of the corresponding LNakayama algebra, when g denotes the global dimension of that algebra. St000965The sum of the dimension of Ext^i(D(A),A) for i=1,. St001000Number of indecomposable modules with projective dimension equal to the global dimension in the Nakayama algebra corresponding to the Dyck path. St001019Sum of the projective dimensions of the simple modules in the Nakayama algebra corresponding to the Dyck path. St001072The evaluation of the Tutte polynomial of the graph at x and y equal to 3. St001102The number of words with multiplicities of the letters given by the composition, avoiding the consecutive pattern 132. 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 $K[x]/(x^n)$. St001182Number of indecomposable injective modules with codominant dimension at least two in the corresponding Nakayama algebra. 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. 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. 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. St001255The vector space dimension of the double dual of A/J when A is the corresponding Nakayama algebra with Jacobson radical J. St001262The dimension of the maximal parabolic seaweed algebra corresponding to the partition. St001300The rank of the boundary operator in degree 1 of the chain complex of the order complex of the poset. St001303The number of dominating sets of vertices of a graph. St001312Number of parabolic noncrossing partitions indexed by the composition. St001412Number of minimal entries in the Bruhat order matrix of a permutation. St001433The flag major index of a signed permutation. St001441The number of non-empty connected induced subgraphs of a graph. St001468The smallest fixpoint of a permutation. St001472The permanent of the Coxeter matrix of the poset. St001473The absolute value of the sum of all entries of the Coxeter matrix of the corresponding LNakayama algebra. St001486The number of corners of the ribbon associated with an integer composition. St001564The value of the forgotten symmetric functions when all variables set to 1. St001602The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on endofunctions. St001610The number of coloured endofunctions such that the multiplicities of colours are given by a partition. St001635The trace of the square of the Coxeter matrix of the incidence algebra of a poset. St001643The Frobenius dimension of the Nakayama algebra corresponding to the Dyck path. St001694The number of maximal dissociation sets in a graph. St001721The degree of a binary word. St001817The number of flag weak exceedances of a signed permutation. St001821The sorting index of a signed permutation. St001833The number of linear intervals in a lattice. St001838The number of nonempty primitive factors of a binary word. St001872The number of indecomposable injective modules with even projective dimension in the corresponding Nakayama algebra. St001930The weak major index of a binary word. St000040The number of regions of the inversion arrangement of a permutation. St000109The number of elements less than or equal to the given element in Bruhat order. St000189The number of elements in the poset. St000294The number of distinct factors of a binary word. St000300The number of independent sets of vertices of a graph. St000301The number of facets of the stable set polytope of a graph. St000401The size of the symmetry class of a permutation. St000415The size of the automorphism group of the rooted tree underlying the ordered tree. St000511The number of invariant subsets when acting with a permutation of given cycle type. St000518The number of distinct subsequences in a binary word. St000656The number of cuts of a poset. St000830The total displacement of a permutation. St000953The largest degree of an irreducible factor of the Coxeter polynomial of the Dyck path over the rational numbers. St000973The length of the boundary of an ordered tree. St001213The number of indecomposable modules in the corresponding Nakayama algebra that have vanishing first Ext-group with the regular module. St001259The vector space dimension of the double dual of D(A) in the corresponding Nakayama algebra. St001361The number of lattice paths of the same length that stay weakly above a Dyck path. St001437The flex of a binary word. St001620The number of sublattices of a lattice. St001669The number of single rises in a Dyck path. St001679The number of subsets of a lattice whose meet is the bottom element. St001717The largest size of an interval in a poset. St001834The number of non-isomorphic minors of a graph. St001885The number of binary words with the same proper border set. St000520The number of patterns in a permutation. St001002Number of indecomposable modules with projective and injective dimension at most 1 in the Nakayama algebra corresponding to the Dyck path. St001138The number of indecomposable modules with projective dimension or injective dimension at most one in the corresponding Nakayama algebra. St000712The number of semistandard Young tableau of given shape, with entries at most 4. St000009The charge of a standard tableau. St000011The number of touch points (or returns) of a Dyck path. St000012The area of a Dyck path. St000043The number of crossings plus two-nestings of a perfect matching. St000148The number of odd parts of a partition. St000161The sum of the sizes of the right subtrees of a binary tree. St000211The rank of the set partition. St000222The number of alignments in the permutation. St000225Difference between largest and smallest parts in a partition. St000242The number of indices that are not cyclical small weak excedances. St000245The number of ascents of a permutation. St000246The number of non-inversions of a permutation. St000251The number of nonsingleton blocks of a set partition. St000268The number of strongly connected orientations of a graph. St000290The major index of a binary word. St000293The number of inversions of a binary word. St000295The length of the border of a binary word. St000304The load of a permutation. St000305The inverse major index of a permutation. St000329The number of evenly positioned ascents of the Dyck path, with the initial position equal to 1. St000336The leg major index of a standard tableau. St000340The number of non-final maximal constant sub-paths of length greater than one. St000391The sum of the positions of the ones in a binary word. St000394The sum of the heights of the peaks of a Dyck path minus the number of peaks. St000419The number of Dyck paths that are weakly above the Dyck path, except for the path itself. St000424The number of occurrences of the pattern 132 or of the pattern 231 in a permutation. St000425The number of occurrences of the pattern 132 or of the pattern 213 in a permutation. St000426The number of occurrences of the pattern 132 or of the pattern 312 in a permutation. St000431The number of occurrences of the pattern 213 or of the pattern 321 in a permutation. St000433The number of occurrences of the pattern 132 or of the pattern 321 in a permutation. St000434The number of occurrences of the pattern 213 or of the pattern 312 in a permutation. St000435The number of occurrences of the pattern 213 or of the pattern 231 in a permutation. St000445The number of rises of length 1 of a Dyck path. St000447The number of pairs of vertices of a graph with distance 3. St000448The number of pairs of vertices of a graph with distance 2. St000457The number of occurrences of one of the patterns 132, 213 or 321 in a permutation. St000461The rix statistic of a permutation. St000462The major index minus the number of excedences of a permutation. St000471The sum of the ascent tops of a permutation. St000483The number of times a permutation switches from increasing to decreasing or decreasing to increasing. St000493The los statistic of a set partition. St000519The largest length of a factor maximising the subword complexity. St000538The number of even inversions of a permutation. St000549The number of odd partial sums of an integer partition. St000558The number of occurrences of the pattern {{1,2}} in a set partition. St000567The sum of the products of all pairs of parts. St000620The number of standard tableaux of shape equal to the given partition such that the minimal cyclic descent is odd. St000644The number of graphs with given frequency partition. St000645The sum of the areas of the rectangles formed by two consecutive peaks and the valley in between. St000651The maximal size of a rise in a permutation. St000672The number of minimal elements in Bruhat order not less than the permutation. St000673The number of non-fixed points of a permutation. St000676The number of odd rises of a Dyck path. St000677The standardized bi-alternating inversion number of a permutation. 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. St000688The global dimension minus the dominant dimension of the LNakayama algebra associated to a Dyck path. St000691The number of changes of a binary word. St000692Babson and Steingrímsson's statistic of a permutation. St000726The normalized sum of the leaf labels of the increasing binary tree associated to a permutation. St000792The Grundy value for the game of ruler on a binary word. St000796The stat' of a permutation. St000797The stat`` of a permutation. St000798The makl of a permutation. St000824The sum of the number of descents and the number of recoils of a permutation. St000834The number of right outer peaks of a permutation. St000836The number of descents of distance 2 of a permutation. St000866The number of admissible inversions of a permutation in the sense of Shareshian-Wachs. St000873The aix statistic of a permutation. St000877The depth of the binary word interpreted as a path. St000896The number of zeros on the main diagonal of an alternating sign matrix. St000921The number of internal inversions of a binary word. St000936The number of even values 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. St000961The shifted major index of a permutation. St000963The 2-shifted major index of a permutation. St000970Number of peaks minus the dominant dimension of the corresponding LNakayama algebra. St000984The number of boxes below precisely one peak. St000986The multiplicity of the eigenvalue zero of the adjacency matrix of the graph. St001005The number of indices for a permutation that are either left-to-right maxima or right-to-left minima but not both. St001030Half the number of non-boundary horizontal edges in the fully packed loop corresponding to the alternating sign matrix. St001034The area of the parallelogram polyomino associated with the Dyck path. St001073The number of nowhere zero 3-flows of a graph. St001078The minimal number of occurrences of (12) in a factorization of a permutation into transpositions (12) and cycles (1,. St001094The depth index 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. St001104The number of descents of the invariant in a tensor power of the adjoint representation of the rank two general linear group. St001160The number of proper blocks (or intervals) of a permutations. St001161The major index north count of a Dyck path. St001185The number of indecomposable injective modules of grade at least 2 in the corresponding Nakayama algebra. St001192The maximal dimension of $Ext_A^2(S,A)$ for a simple module $S$ over the corresponding Nakayama algebra $A$. St001194The injective dimension of $A/AfA$ in the corresponding Nakayama algebra $A$ when $Af$ is the minimal faithful projective-injective left $A$-module St001215Let X be the direct sum of all simple modules of the corresponding Nakayama algebra. St001216The number of indecomposable injective modules in the corresponding Nakayama algebra that have non-vanishing second Ext-group with the regular module. St001225The vector space dimension of the first extension group between J and itself when J is the Jacobson radical of the corresponding Nakayama algebra. St001232The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2. St001245The cyclic maximal difference between two consecutive entries of a permutation. St001247The number of parts of a partition that are not congruent 2 modulo 3. St001274The number of indecomposable injective modules with projective dimension equal to two. St001278The number of indecomposable modules that are fixed by $\tau \Omega^1$ composed with its inverse in the corresponding Nakayama algebra. St001295Gives the vector space dimension of the homomorphism space between J^2 and J^2. St001306The number of induced paths on four vertices in a graph. St001319The minimal number of occurrences of the star-pattern in a linear ordering of the vertices of the graph. St001320The minimal number of occurrences of the path-pattern in a linear ordering of the vertices of the graph. St001332The number of steps on the non-negative side of the walk associated with the permutation. St001347The number of pairs of vertices of a graph having the same neighbourhood. St001351The Albertson index of a graph. St001371The length of the longest Yamanouchi prefix of a binary word. St001374The Padmakar-Ivan index of a graph. St001402The number of separators in a permutation. St001418Half of the global dimension of the stable Auslander algebra of the Nakayama algebra corresponding to the Dyck path. St001424The number of distinct squares in a binary word. St001429The number of negative entries in a signed permutation. St001431Half of the Loewy length minus one of a modified stable Auslander algebra of the Nakayama algebra corresponding to the Dyck path. St001436The index of a given binary word in the lex-order among all its cyclic shifts. St001480The number of simple summands of the module J^2/J^3. St001484The number of singletons of an integer partition. St001485The modular major index of a binary word. St001502The global dimension minus the dominant dimension of magnitude 1 Nakayama algebras. St001508The degree of the standard monomial associated to a Dyck path relative to the diagonal boundary. St001521Half the total irregularity of a graph. St001522The total irregularity of a graph. St001524The degree of symmetry of a binary word. St001535The number of cyclic alignments of a permutation. St001536The number of cyclic misalignments of a permutation. St001541The Gini index of an integer partition. St001553The number of indecomposable summands of the square of the Jacobson radical as a bimodule in the Nakayama algebra corresponding to the Dyck path. St001557The number of inversions of the second entry of a permutation. St001561The value of the elementary symmetric function evaluated at 1. St001582The grades of the simple modules corresponding to the points in the poset of the symmetric group under the Bruhat order. St001583The projective dimension of the simple module corresponding to the point in the poset of the symmetric group under bruhat order. St001600The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on simple graphs. St001647The number of edges that can be added without increasing the clique number. St001648The number of edges that can be added without increasing the chromatic number. St001651The Frankl number of a lattice. St001671Haglund's hag of a permutation. St001690The length of a longest path in a graph such that after removing the paths edges, every vertex of the path has distance two from some other vertex of the path. St001692The number of vertices with higher degree than the average degree in a graph. St001693The excess length of a longest path consisting of elements and blocks of a set partition. St001695The natural comajor index of a standard Young tableau. St001696The natural major index of a standard Young tableau. St001698The comajor index of a standard tableau minus the weighted size of its shape. St001699The major index of a standard tableau minus the weighted size of its shape. St001703The villainy 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. St001708The number of pairs of vertices of different degree in a graph. St001718The number of non-empty open intervals in a poset. St001759The Rajchgot index of a permutation. St001766The number of cells which are not occupied by the same tile in all reduced pipe dreams corresponding to a permutation. St001783The number of odd automorphisms 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. St001799The number of proper separations of a graph. St001819The flag Denert index of a signed permutation. St001823The Stasinski-Voll length of a signed permutation. St001861The number of Bruhat lower covers of a permutation. St001865The number of alignments of a signed permutation. St001892The flag excedance statistic of a signed permutation. St001893The flag descent of a signed permutation. St001894The depth of a signed permutation. St001910The height of the middle non-run of a Dyck path. St001916The number of transient elements in the orbit of Bulgarian solitaire corresponding to a necklace. St001958The degree of the polynomial interpolating the values of a permutation. St000003The number of standard Young tableaux of the partition. St000004The major index of a permutation. St000014The number of parking functions supported by a Dyck path. St000016The number of attacking pairs of a standard tableau. St000017The number of inversions of a standard tableau. St000018The number of inversions of a permutation. St000019The cardinality of the support of a permutation. St000030The sum of the descent differences of a permutations. St000032The number of elements smaller than the given Dyck path in the Tamari Order. St000047The number of standard immaculate tableaux of a given shape. St000048The multinomial of the parts of a partition. St000049The number of set partitions whose sorted block sizes correspond to the partition. St000060The greater neighbor of the maximum. St000076The rank of the alternating sign matrix in the alternating sign matrix poset. St000081The number of edges of a graph. St000082The number of elements smaller than a binary tree in Tamari order. St000096The number of spanning trees of a graph. St000103The sum of the entries of a semistandard tableau. St000133The "bounce" of a permutation. St000154The sum of the descent bottoms of a permutation. St000156The Denert index of a permutation. St000163The size of the orbit of the set partition under rotation. St000176The total number of tiles in the Gelfand-Tsetlin pattern. St000182The number of permutations whose cycle type is the given integer partition. St000186The sum of the first row in a Gelfand-Tsetlin pattern. St000187The determinant of an alternating sign matrix. St000207Number of integral Gelfand-Tsetlin polytopes with prescribed top row and integer composition weight. St000224The sorting index of a permutation. St000238The number of indices that are not small weak excedances. St000240The number of indices that are not small excedances. St000263The Szeged index of a graph. St000265The Wiener index of a graph. St000267The number of maximal spanning forests contained in a graph. 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. St000296The length of the symmetric border of a binary word. St000341The non-inversion sum of a permutation. St000348The non-inversion sum of a binary word. St000349The number of different adjacency matrices of a graph. St000378The diagonal inversion number of an integer partition. St000393The number of strictly increasing runs in a binary word. St000398The sum of the depths of the vertices (or total internal path length) of a binary tree. St000416The number of inequivalent increasing trees of an ordered tree. St000420The number of Dyck paths that are weakly above a Dyck path. St000421The number of Dyck paths that are weakly below a Dyck path, except for the path itself. St000446The disorder of a permutation. St000452The number of distinct eigenvalues of a graph. St000456The monochromatic index of a connected graph. St000458The number of permutations obtained by switching adjacencies or successions. St000472The sum of the ascent bottoms 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. St000517The Kreweras number of an integer partition. St000529The number of permutations whose descent word is the given binary word. St000540The sum of the entries of a parking function minus its length. St000543The size of the conjugacy class of a binary word. St000548The number of different non-empty partial sums of an integer partition. St000566The number of ways to select a row of a Ferrers shape and two cells in this row. St000619The number of cyclic descents of a permutation. St000626The minimal period of a binary word. St000631The number of distinct palindromic decompositions of a binary word. St000638The number of up-down runs of a permutation. St000653The last descent of a permutation. St000681The Grundy value of Chomp on Ferrers diagrams. St000690The size of the conjugacy class of a permutation. St000704The number of semistandard tableaux on a given integer partition with minimal maximal entry. St000722The number of different neighbourhoods in a graph. St000734The last entry in the first row of a standard tableau. St000759The smallest missing part in an integer partition. St000763The sum of the positions of the strong records of an integer composition. St000794The mak of a permutation. St000815The number of semistandard Young tableaux of partition weight of given shape. St000833The comajor index of a permutation. St000841The largest opener of a perfect matching. St000847The number of standard Young tableaux whose descent set is the binary word. St000849The number of 1/3-balanced pairs in a poset. St000868The aid statistic in the sense of Shareshian-Wachs. St000883The number of longest increasing subsequences of a permutation. St000922The minimal number such that all substrings of this length are unique. St000948The chromatic discriminant of a graph. St000976The sum of the positions of double up-steps of a Dyck path. St000983The length of the longest alternating subword. St000987The number of positive eigenvalues of the Laplacian matrix of the graph. St000988The orbit size of a permutation under Foata's bijection. St001004The number of indices that are either left-to-right maxima or right-to-left minima. St001079The minimal length of a factorization of a permutation using the permutations (12)(34). St001080The minimal length of a factorization of a permutation using the transposition (12) and the cycle (1,. 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. St001103The number of words with multiplicities of the letters given by the partition, avoiding the consecutive pattern 123. St001111The weak 2-dynamic chromatic number of a graph. St001112The 3-weak dynamic number of a graph. St001117The game chromatic index of a graph. St001118The acyclic chromatic index of a graph. St001119The length of a shortest maximal path in a graph. St001120The length of a longest path in a graph. St001128The exponens consonantiae of a partition. 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. St001239The largest vector space dimension of the double dual of a simple module in the corresponding Nakayama algebra. St001246The maximal difference between two consecutive entries of a permutation. St001282The number of graphs with the same chromatic polynomial. St001289The vector space dimension of the n-fold tensor product of D(A), where n is maximal such that this n-fold tensor product is nonzero. St001341The number of edges in the center of a graph. St001349The number of different graphs obtained from the given graph by removing an edge. St001350Half of the Albertson index of a graph. St001352The number of internal nodes in the modular decomposition of a graph. St001362The normalized Knill dimension of a graph. St001365The number of lattice paths of the same length weakly above the path given by a binary word. St001373The logarithm of the number of winning configurations of the lights out game on a graph. St001376The Colless index of a binary tree. St001382The number of boxes in the diagram of a partition that do not lie in its Durfee square. St001386The number of prime labellings of a graph. St001388The number of non-attacking neighbors of a permutation. St001404The number of distinct entries in a Gelfand Tsetlin pattern. St001415The length of the longest palindromic prefix of a binary word. St001416The length of a longest palindromic factor of a binary word. St001417The length of a longest palindromic subword of a binary word. St001419The length of the longest palindromic factor beginning with a one of a binary word. St001428The number of B-inversions of a signed permutation. St001463The number of distinct columns in the nullspace of a graph. St001475The evaluation of the Tutte polynomial of the graph at (x,y) equal to (1,0). St001482The product of the prefix sums of a permutation. St001500The global dimension of magnitude 1 Nakayama algebras. St001501The dominant dimension of magnitude 1 Nakayama algebras. St001511The minimal number of transpositions needed to sort a permutation in either direction. St001515The vector space dimension of the socle of the first syzygy module of the regular module (as a bimodule). St001528The number of permutations such that the product with the permutation has the same number of fixed points. St001532The leading coefficient of the Poincare polynomial of the poset cone. St001546The number of monomials in the Tutte polynomial of a graph. St001558The number of transpositions that are smaller or equal to a permutation in Bruhat order. 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. 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. 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. St001711The number of permutations such that conjugation with a permutation of given cycle type yields the squared permutation. St001740The number of graphs with the same symmetric edge polytope as the given graph. St001763The Hurwitz number of an integer partition. St001776The degree of the minimal polynomial of the largest Laplacian eigenvalue of a graph. St001780The order of promotion on the set of standard tableaux of given shape. St001794Half the number of sets of vertices in a graph which are dominating and non-blocking. St001796The absolute value of the quotient of the Tutte polynomial of the graph at (1,1) and (-1,-1). St001800The number of 3-Catalan paths having this Dyck path as first and last coordinate projections. St001806The upper middle entry of a permutation. St001815The number of order preserving surjections from a poset to a total order. St001827The number of two-component spanning forests of a graph. St001848The atomic length of a signed permutation. St001850The number of Hecke atoms of a permutation. St001851The number of Hecke atoms of a signed permutation. St001874Lusztig's a-function for the symmetric group. St001899The total number of irreducible representations contained in the higher Lie character for an integer partition. St001900The number of distinct irreducible representations contained in the higher Lie character for an integer partition. St001908The number of semistandard tableaux of distinct weight whose maximal entry is the length of the partition. St001915The size of the component corresponding to a necklace in Bulgarian solitaire. St001917The order of toric promotion on the set of labellings of a graph. St001924The number of cells in an integer partition whose arm and leg length coincide. St001929The number of meanders with top half given by the noncrossing matching corresponding to the Dyck path. St001936The number of transitive factorisations of a permutation of given cycle type into star transpositions. St001957The number of Hasse diagrams with a given underlying undirected graph. St000033The number of permutations greater than or equal to the given permutation in (strong) Bruhat order. St000038The product of the heights of the descending steps of a Dyck path. St000064The number of one-box pattern of a permutation. St000070The number of antichains in a poset. St000086The number of subgraphs. St000087The number of induced subgraphs. St000104The number of facets in the order polytope of this poset. St000151The number of facets in the chain polytope of the poset. St000208Number of integral Gelfand-Tsetlin polytopes with prescribed top row and integer partition weight. St000228The size of a partition. St000244The cardinality of the automorphism group of a graph. St000269The number of acyclic orientations of a graph. St000270The number of forests contained in a graph. St000279The size of the preimage of the map 'cycle-as-one-line notation' from Permutations to Permutations. St000321The number of integer partitions of n that are dominated by an integer partition. St000327The number of cover relations in a poset. St000343The number of spanning subgraphs of a graph. St000364The exponent of the automorphism group of a graph. St000388The number of orbits of vertices of a graph under automorphisms. St000395The sum of the heights of the peaks of a Dyck path. St000412The number of binary trees with the same underlying unordered tree. St000418The number of Dyck paths that are weakly below a Dyck path. St000438The position of the last up step in a Dyck path. 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. St000468The Hosoya index of a graph. St000474Dyson's crank of a partition. St000479The Ramsey number of a graph. St000501The size of the first part in the decomposition of a permutation. St000507The number of ascents of a standard tableau. St000514The number of invariant simple graphs when acting with a permutation of given cycle type. St000545The number of parabolic double cosets with minimal element being the given permutation. St000553The number of blocks of a graph. St000625The sum of the minimal distances to a greater element. St000636The hull number of a graph. St000639The number of relations in a poset. St000641The number of non-empty boolean intervals in a poset. St000669The number of permutations obtained by switching ascents or descents of size 2. St000680The Grundy value for Hackendot on posets. St000724The label of the leaf of the path following the smaller label in the increasing binary tree associated to a permutation. St000770The major index of an integer partition when read from bottom to top. 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. St000844The size of the largest block in the direct sum decomposition of a permutation. St000870The product of the hook lengths of the diagonal cells in an integer partition. St000876The number of factors in the Catalan decomposition of a binary word. St000885The number of critical steps in the Catalan decomposition of a binary word. St000917The open packing number of a graph. St000918The 2-limited packing number of a graph. St000926The clique-coclique number of a graph. St000950Number of tilting modules of the corresponding LNakayama algebra, where a tilting module is a generalised tilting module of projective dimension 1. St000972The composition number of a graph. St000981The length of the longest zigzag subpath. St001018Sum of projective dimension of the indecomposable injective modules of the Nakayama algebra corresponding to the Dyck path. St001020Sum of the codominant dimensions of the non-projective indecomposable injective modules of the Nakayama algebra corresponding to the Dyck path. St001108The 2-dynamic chromatic number of a graph. St001110The 3-dynamic chromatic number of a graph. St001268The size of the largest ordinal summand in the poset. St001285The number of primes in the column sums of the two line notation of a permutation. St001288The number of primes obtained by multiplying preimage and image of a permutation and adding one. St001302The number of minimally dominating sets of vertices 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. St001345The Hamming dimension of a graph. St001348The bounce of the parallelogram polyomino associated with the Dyck path. St001366The maximal multiplicity of a degree of a vertex of a graph. St001368The number of vertices of maximal degree in a graph. St001375The pancake length of a permutation. St001378The product of the cohook lengths of the integer partition. St001464The number of bases of the positroid corresponding to the permutation, with all fixed points counterclockwise. St001474The evaluation of the Tutte polynomial of the graph at (x,y) equal to (2,-1). St001479The number of bridges of a graph. St001492The number of simple modules that do not appear in the socle of the regular module or have no nontrivial selfextensions with the regular module in the corresponding Nakayama algebra. 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. St001531Number of partial orders contained in the poset determined by the Dyck path. St001555The order of a signed permutation. St001607The number of coloured graphs such that the multiplicities of colours are given by a partition. St001611The number of multiset partitions such that the multiplicities of elements are given by a partition. 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. St001645The pebbling number of a connected graph. St001654The monophonic hull number of a graph. St001655The general position number of a graph. St001656The monophonic position number of a graph. St001661Half the permanent of the Identity matrix plus the permutation matrix associated to the permutation. St001672The restrained domination number of a graph. St001684The reduced word complexity of a permutation. St001704The size of the largest multi-subset-intersection of the deck of a graph with the deck of another graph. St001710The number of permutations such that conjugation with a permutation of given cycle type yields the inverse permutation. St001725The harmonious chromatic number of a graph. St001746The coalition number of a graph. St001758The number of orbits of promotion on a graph. St001774The degree of the minimal polynomial of the smallest eigenvalue of a graph. St001775The degree of the minimal polynomial of the largest eigenvalue of a graph. St001807The lower middle entry of a permutation. St001808The box weight or horizontal decoration of a Dyck path. St001814The number of partitions interlacing the given partition. St001844The maximal degree of a generator of the invariant ring of the automorphism group of a graph. St001855The number of signed permutations less than or equal to a signed permutation in left weak order. St001869The maximum cut size of a graph. 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. St000108The number of partitions contained in the given partition. St000110The number of permutations less than or equal to a permutation in left weak order. St000453The number of distinct Laplacian eigenvalues of a graph. St000532The total number of rook placements on a Ferrers board. St000777The number of distinct eigenvalues of the distance Laplacian of a connected graph. St000827The decimal representation of a binary word with a leading 1. St000978The sum of the positions of double down-steps of a Dyck path. St001023Number of simple modules with projective dimension at most 3 in the Nakayama algebra corresponding to the Dyck path. St001065Number of indecomposable reflexive modules in the corresponding Nakayama algebra. St001190Number of simple modules with projective dimension at most 4 in the corresponding Nakayama algebra. St001636The number of indecomposable injective modules with projective dimension at most one in the incidence algebra of the poset. St001650The order of Ringel's homological bijection associated to the linear Nakayama algebra corresponding to the Dyck path. St001658The total number of rook placements on a Ferrers board. St001664The number of non-isomorphic subposets of a poset. St001854The size of the left Kazhdan-Lusztig cell, St001875The number of simple modules with projective dimension at most 1. St000977MacMahon's equal index of a Dyck path. St001003The number of indecomposable modules with projective dimension at most 1 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. St001562The value of the complete homogeneous symmetric function evaluated at 1. St000949Gives the number of generalised tilting modules of the corresponding LNakayama algebra. St000826The stopping time of the decimal representation of the binary word for the 3x+1 problem.