St000460The hook length of the last cell along the main diagonal of an integer partition. St000870The product of the hook lengths of the diagonal cells in an integer partition. St001020Sum of the codominant dimensions of the non-projective indecomposable injective modules of the Nakayama algebra corresponding to the Dyck path. St001342The number of vertices in the center of a graph. St001622The number of join-irreducible elements of a lattice. St001707The length of a longest path in a graph such that the remaining vertices can be partitioned into two sets of the same size without edges between them. St001746The coalition number of a graph. 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. St000171The degree of the graph. St000645The sum of the areas of the rectangles formed by two consecutive peaks and the valley in between. St000921The number of internal inversions of a binary word. St001004The number of indices that are either left-to-right maxima or right-to-left minima. St001027Number of simple modules with projective dimension equal to injective dimension in the Nakayama algebra corresponding to the Dyck path. St001119The length of a shortest maximal path in a graph. 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. St001332The number of steps on the non-negative side of the walk associated with the permutation. St001641The number of ascent tops in the flattened set partition such that all smaller elements appear before. St000026The position of the first return of a Dyck path. St000293The number of inversions of a binary word. St000394The sum of the heights of the peaks of a Dyck path minus the number of peaks. St000479The Ramsey number of a graph. St000548The number of different non-empty partial sums of an integer partition. St000722The number of different neighbourhoods in a graph. St000725The smallest label of a leaf of the increasing binary tree associated to a permutation. St000734The last entry in the first row of a standard tableau. St000740The last entry of a permutation. St000839The largest opener of a set partition. St001034The area of the parallelogram polyomino associated with the Dyck path. St001348The bounce of the parallelogram polyomino associated with the Dyck path. St001497The position of the largest weak excedence of a permutation. St001523The degree of symmetry of a Dyck path. St001554The number of distinct nonempty subtrees of a binary tree. 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. St001778The largest greatest common divisor of an element and its image in a permutation. St001800The number of 3-Catalan paths having this Dyck path as first and last coordinate projections. 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. St001279The sum of the parts of an integer partition that are at least two. St000806The semiperimeter of the associated bargraph. St001643The Frobenius dimension of the Nakayama algebra corresponding to the Dyck path. St000543The size of the conjugacy class of a binary word. 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. St001437The flex of a binary word. St000519The largest length of a factor maximising the subword complexity. St001869The maximum cut size of a graph. St000054The first entry of the permutation. St000189The number of elements in the poset. St000240The number of indices that are not small excedances. St000296The length of the symmetric border of a binary word. St000385The number of vertices with out-degree 1 in a binary tree. St000393The number of strictly increasing runs in a binary word. St000414The binary logarithm of the number of binary trees with the same underlying unordered tree. St000419The number of Dyck paths that are weakly above the Dyck path, except for the path itself. St000444The length of the maximal rise of a Dyck path. St000476The sum of the semi-lengths of tunnels before a valley of a Dyck path. St000501The size of the first part in the decomposition of a permutation. St000529The number of permutations whose descent word is the given binary word. St000626The minimal period of a binary word. St000627The exponent of a binary word. St000844The size of the largest block in the direct sum decomposition of a permutation. St000922The minimal number such that all substrings of this length are unique. St000982The length of the longest constant subword. St001267The length of the Lyndon factorization of the binary word. St001313The number of Dyck paths above the lattice path given by a binary word. St001371The length of the longest Yamanouchi prefix of a binary word. St001415The length of the longest palindromic prefix of a binary word. St001416The length of a longest palindromic factor of a binary word. St001417The length of a longest palindromic subword of a binary word. St001430The number of positive entries in a signed permutation. St001884The number of borders of a binary word. St000019The cardinality of the support of a permutation. St000141The maximum drop size of a permutation. St000209Maximum difference of elements in cycles. St000294The number of distinct factors of a binary word. St000295The length of the border of a binary word. St000316The number of non-left-to-right-maxima of a permutation. St000369The dinv deficit of a Dyck path. St000376The bounce deficit of a Dyck path. St000420The number of Dyck paths that are weakly above a Dyck path. St000442The maximal area to the right of an up step of a Dyck path. St000503The maximal difference between two elements in a common block. St000518The number of distinct subsequences in a binary word. St000682The Grundy value of Welter's game on a binary word. St000727The largest label of a leaf in the binary search tree associated with the permutation. St000931The number of occurrences of the pattern UUU in a Dyck path. St000956The maximal displacement of a permutation. St001190Number of simple modules with projective dimension at most 4 in the corresponding Nakayama algebra. St001436The index of a given binary word in the lex-order among all its cyclic shifts. St001958The degree of the polynomial interpolating the values of a permutation. St000438The position of the last up step in a Dyck path. St000826The stopping time of the decimal representation of the binary word for the 3x+1 problem. St000060The greater neighbor of the maximum. St000653The last descent of a permutation. St000957The number of Bruhat lower covers of a permutation. St001118The acyclic chromatic index of a graph. St001246The maximal difference between two consecutive entries of a permutation. St001645The pebbling number of a connected graph. St000800The number of occurrences of the vincular pattern |231 in a permutation. St000454The largest eigenvalue of a graph if it is integral. St000271The chromatic index of a graph. St000452The number of distinct eigenvalues of a graph. St001330The hat guessing number of a graph. St000724The label of the leaf of the path following the smaller label in the increasing binary tree associated to a permutation. St000505The biggest entry in the block containing the 1. St001644The dimension of a graph. St000837The number of ascents of distance 2 of a permutation. St000485The length of the longest cycle of a permutation. St001081The number of minimal length factorizations of a permutation into star transpositions. St001498The normalised height of a Nakayama algebra with magnitude 1. St001392The largest nonnegative integer which is not a part and is smaller than the largest part of the partition. St000050The depth or height of a binary tree. St000288The number of ones in a binary word. St000336The leg major index of a standard tableau. St000875The semilength of the longest Dyck word in the Catalan factorisation of a binary word. St000651The maximal size of a rise in a permutation. St000777The number of distinct eigenvalues of the distance Laplacian of a connected graph. St001615The number of join prime elements of a lattice. St001617The dimension of the space of valuations of a lattice. St001300The rank of the boundary operator in degree 1 of the chain complex of the order complex of the poset. St000528The height of a poset. St000912The number of maximal antichains in a poset. 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. St001875The number of simple modules with projective dimension at most 1. St001880The number of 2-Gorenstein indecomposable injective modules in the incidence algebra of the lattice. St000028The number of stack-sorts needed to sort a permutation. St000625The sum of the minimal distances to a greater element. St001074The number of inversions of the cyclic embedding of a permutation. St001925The minimal number of zeros in a row of an alternating sign matrix. St000890The number of nonzero entries in an alternating sign matrix. St001717The largest size of an interval in a poset. St000809The reduced reflection length of the permutation. St001827The number of two-component spanning forests of a graph. St000167The number of leaves of an ordered tree. St000052The number of valleys of a Dyck path not on the x-axis. 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. St001311The cyclomatic number of a graph. St001317The minimal number of occurrences of the forest-pattern in a linear ordering of the vertices of the graph. St001328The minimal number of occurrences of the bipartite-pattern in a linear ordering of the vertices of the graph. St001341The number of edges in the center of a graph. St001391The disjunction number of a graph. St001723The differential of a graph. St001724The 2-packing differential of a graph. St000144The pyramid weight of the Dyck path. St000453The number of distinct Laplacian eigenvalues of a graph. St000553The number of blocks of a graph. St000632The jump number of the poset. St000863The length of the first row of the shifted shape of a permutation. St001018Sum of projective dimension of the indecomposable injective modules of the Nakayama algebra corresponding to the Dyck path. St001235The global dimension of the corresponding Comp-Nakayama algebra. St001236The dominant dimension of the corresponding Comp-Nakayama algebra. St001291The number of indecomposable summands of the tensor product of two copies of the dual of the Nakayama algebra associated to a Dyck path. St000068The number of minimal elements in a poset. St000071The number of maximal chains in a poset. St000312The number of leaves in a graph. St000527The width of the poset. St000718The largest Laplacian eigenvalue of a graph if it is integral. 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. St001179Number of indecomposable injective modules with projective dimension at most 2 in the corresponding Nakayama algebra. St001240The number of indecomposable modules e_i J^2 that have injective dimension at most one in the corresponding Nakayama algebra St001650The order of Ringel's homological bijection associated to the linear Nakayama algebra corresponding to the Dyck path. St000967The value p(1) for the Coxeterpolynomial p of the corresponding LNakayama algebra. St001218Smallest index k greater than or equal to one such that the Coxeter matrix C of the corresponding Nakayama algebra has C^k=1. St000133The "bounce" of a permutation. St000261The edge connectivity of a graph. St000262The vertex connectivity of a graph. St000306The bounce count of a Dyck path. St000310The minimal degree of a vertex of a graph. St000331The number of upper interactions of a Dyck path. St000362The size of a minimal vertex cover of a graph. St000448The number of pairs of vertices of a graph with distance 2. St000741The Colin de Verdière graph invariant. St000954Number of times the corresponding LNakayama algebra has $Ext^i(D(A),A)=0$ for $i>0$. 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 $eA$. St001223Number of indecomposable projective non-injective modules P such that the modules X and Y in a an Auslander-Reiten sequence ending at P are torsionless. St001225The vector space dimension of the first extension group between J and itself when J is the Jacobson radical of the corresponding Nakayama algebra. St001278The number of indecomposable modules that are fixed by $\tau \Omega^1$ composed with its inverse in the corresponding Nakayama algebra. St001294The maximal torsionfree index of a simple non-projective module in the corresponding Nakayama algebra. St001296The maximal torsionfree index of an indecomposable non-projective module in the corresponding Nakayama algebra. St001509The degree of the standard monomial associated to a Dyck path relative to the trivial lower boundary. St001646The number of edges that can be added without increasing the maximal degree of a graph. St000014The number of parking functions supported by a Dyck path. St000015The number of peaks of a Dyck path. St000031The number of cycles in the cycle decomposition of a permutation. St000087The number of induced subgraphs. St000229Sum of the difference between the maximal and the minimal elements of the blocks plus the number of blocks of a set partition. St000286The number of connected components of the complement of a graph. St000337The lec statistic, the sum of the inversion numbers of the hook factors of a permutation. St000363The number of minimal vertex covers of a graph. St000374The number of exclusive right-to-left minima of a permutation. St000617The number of global maxima of a Dyck path. St000703The number of deficiencies of a permutation. St000733The row containing the largest entry of a standard tableau. St000822The Hadwiger number of the graph. St000930The k-Gorenstein degree of the corresponding Nakayama algebra with linear quiver. 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. St001024Maximum of dominant dimensions of the simple modules in the Nakayama algebra corresponding to the Dyck path. St001052The length of the exterior of a permutation. St001096The size of the overlap set of a permutation. 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. St001183The maximum of $projdim(S)+injdim(S)$ over all simple modules in the Nakayama algebra corresponding to the Dyck path. St001201The grade of the simple module $S_0$ in the special CNakayama algebra corresponding to the Dyck path. 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. 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. St001258Gives the maximum of injective plus projective dimension of an indecomposable module over the corresponding Nakayama algebra. St001530The depth of a Dyck path. St001725The harmonious chromatic number of a graph. St000010The length of the partition. St000058The order of a permutation. St000301The number of facets of the stable set polytope of a graph. St000451The length of the longest pattern of the form k 1 2. St000968We make a CNakayama algebra out of the LNakayama algebra (corresponding to the Dyck path) $[c_0,c_1,...,c_{n−1}]$ by adding $c_0$ to $c_{n−1}$. St001237The number of simple modules with injective dimension at most one or dominant dimension at least one. St001290The first natural number n such that the tensor product of n copies of D(A) is zero for the corresponding Nakayama algebra A. 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. St000652The maximal difference between successive positions of a permutation. St000197The number of entries equal to positive one in the alternating sign matrix. St000619The number of cyclic descents of a permutation. St001480The number of simple summands of the module J^2/J^3. St001959The product of the heights of the peaks of a Dyck path. St000064The number of one-box pattern of a permutation. St000216The absolute length of 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. St000799The number of occurrences of the vincular pattern |213 in a permutation. St000836The number of descents of distance 2 of a permutation. St001570The minimal number of edges to add to make a graph Hamiltonian. St001917The order of toric promotion on the set of labellings of a graph. St000924The number of topologically connected components of a perfect matching. St000744The length of the path to the largest entry in a standard Young tableau. St000680The Grundy value for Hackendot on posets. St000717The number of ordinal summands of a poset. St000906The length of the shortest maximal chain in a poset. St000643The size of the largest orbit of antichains under Panyushev complementation. St000080The rank of the poset. St001623The number of doubly irreducible elements of a lattice. St001704The size of the largest multi-subset-intersection of the deck of a graph with the deck of another graph. St001268The size of the largest ordinal summand in the poset. St001782The order of rowmotion on the set of order ideals of a poset. St000672The number of minimal elements in Bruhat order not less than the permutation. St000018The number of inversions 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. St001343The dimension of the reduced incidence algebra of a poset. St000642The size of the smallest orbit of antichains under Panyushev complementation. St000095The number of triangles of a graph. St000450The number of edges minus the number of vertices plus 2 of a graph. St000673The number of non-fixed points of a permutation. St001468The smallest fixpoint of a permutation. St001706The number of closed sets in a graph. St000689The maximal n such that the minimal generator-cogenerator module in the LNakayama algebra of a Dyck path is n-rigid. St001742The difference of the maximal and the minimal degree in a graph. St001812The biclique partition number of a graph. St000029The depth of a permutation. St000051The size of the left subtree of a binary tree. St000067The inversion number of the alternating sign matrix. St000199The column of the unique '1' in the last row of the alternating sign matrix. St000200The row of the unique '1' in the last column of the alternating sign matrix. St000201The number of leaf nodes in a binary tree. St000210Minimum over maximum difference of elements in cycles. St000547The number of even non-empty partial sums of an integer partition. St000831The number of indices that are either descents or recoils. St001076The minimal length of a factorization of a permutation into transpositions that are cyclic shifts of (12). St001077The prefix exchange distance of a permutation. St001117The game chromatic index of a graph. St001304The number of maximally independent sets of vertices of a graph. St001429The number of negative entries in a signed permutation. St001526The Loewy length of the Auslander-Reiten translate of the regular module as a bimodule of the Nakayama algebra corresponding to the Dyck path. St001558The number of transpositions that are smaller or equal to a permutation in Bruhat order. St001579The number of cyclically simple transpositions decreasing the number of cyclic descents needed to sort a permutation. St001963The tree-depth of a graph. St000235The number of indices that are not cyclical small weak excedances. St000384The maximal part of the shifted composition of an integer partition. St000487The length of the shortest cycle of a permutation. St000549The number of odd partial sums of an integer partition. St000784The maximum of the length and the largest part of the integer partition. St000949Gives the number of generalised tilting modules of the corresponding LNakayama algebra. St001005The number of indices for a permutation that are either left-to-right maxima or right-to-left minima but not both. St000380Half of the maximal perimeter of a rectangle fitting into the diagram of an integer partition. St000456The monochromatic index of a connected graph. St001003The number of indecomposable modules with projective dimension at most 1 in the Nakayama algebra corresponding to the Dyck path. St001255The vector space dimension of the double dual of A/J when A is the corresponding Nakayama algebra with Jacobson radical J. St000327The number of cover relations in a poset. St001637The number of (upper) dissectors of a poset. St001557The number of inversions of the second entry of a permutation. St000299The number of nonisomorphic vertex-induced subtrees. St001093The detour number of a graph. St001512The minimum rank of a graph. St001960The number of descents of a permutation minus one if its first entry is not one. St001668The number of points of the poset minus the width of the poset. 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. St001927Sparre Andersen's number of positives of a signed permutation. St000636The hull number of a graph. St000918The 2-limited packing number of a graph. St001029The size of the core of a graph. St001207The Lowey length of the algebra $A/T$ when $T$ is the 1-tilting module corresponding to the permutation in the Auslander algebra of $K[x]/(x^n)$. St001286The annihilation number of a graph. St001315The dissociation number of a graph. St001316The domatic number of a graph. St001494The Alon-Tarsi number of a graph. St001642The Prague dimension of a graph. St001656The monophonic position number of a graph. St001734The lettericity of a graph. St001951The number of factors in the disjoint direct product decomposition of the automorphism group of a graph. St000260The radius of a connected graph. St000535The rank-width of a graph. St000778The metric dimension of a graph. St001358The largest degree of a regular subgraph of a graph. St001574The minimal number of edges to add or remove to make a graph regular. St001576The minimal number of edges to add or remove to make a graph vertex transitive. St001792The arboricity of a graph. St001882The number of occurrences of a type-B 231 pattern in a signed permutation. St001876The number of 2-regular simple modules in the incidence algebra of the lattice. St000656The number of cuts of a poset. St000104The number of facets in the order polytope of this poset. St000151The number of facets in the chain polytope of the poset. St001664The number of non-isomorphic subposets of a poset. St001060The distinguishing index of a graph.