St000551The number of left modular elements of a lattice. St000723The maximal cardinality of a set of vertices with the same neighbourhood in a graph. St000745The index of the last row whose first entry is the row number in a standard Young tableau. St000759The smallest missing part in an integer partition. St001088Number of indecomposable projective non-injective modules with dominant dimension equal to the injective dimension in the corresponding Nakayama algebra. St001202Call a CNakayama algebra (a Nakayama algebra with a cyclic quiver) with Kupisch series $L=[c_0,c_1,...,c_{n−1}]$ such that $n=c_0 < c_i$ for all $i > 0$ a special CNakayama algebra. St001462The number of factors of a standard tableaux under concatenation. St001616The number of neutral elements in a lattice. St001720The minimal length of a chain of small intervals in a lattice. St000148The number of odd parts of a partition. St000149The number of cells of the partition whose leg is zero and arm is odd. St000150The floored half-sum of the multiplicities of a partition. St000475The number of parts equal to 1 in a partition. St000549The number of odd partial sums of an integer partition. St000835The minimal difference in size when partitioning the integer partition into two subpartitions. St000885The number of critical steps in the Catalan decomposition of a binary word. St000992The alternating sum of the parts of an integer partition. St001026The maximum of the projective dimensions of the indecomposable non-projective injective modules minus the minimum in the Nakayama algebra corresponding to the Dyck path. St001055The Grundy value for the game of removing cells of a row in an integer partition. St001189The number of simple modules with dominant and codominant dimension equal to zero in the Nakayama algebra corresponding to the Dyck path. St001226The number of integers i such that the radical of the i-th indecomposable projective module has vanishing first extension group with the Jacobson radical J in the corresponding Nakayama algebra. St001290The first natural number n such that the tensor product of n copies of D(A) is zero for the corresponding Nakayama algebra A. St001484The number of singletons of an integer partition. St001615The number of join prime elements of a lattice. St001617The dimension of the space of valuations of a lattice. St001619The number of non-isomorphic sublattices of a lattice. St001622The number of join-irreducible elements of a lattice. St001666The number of non-isomorphic subposets of a lattice which are lattices. St000007The number of saliances of the permutation. St000025The number of initial rises of a Dyck path. St000026The position of the first return of a Dyck path. St000028The number of stack-sorts needed to sort a permutation. St000031The number of cycles in the cycle decomposition of a permutation. St000056The decomposition (or block) number of a permutation. St000084The number of subtrees. St000153The number of adjacent cycles of a permutation. St000189The number of elements in the poset. St000314The number of left-to-right-maxima of a permutation. St000363The number of minimal vertex covers of a graph. St000381The largest part of an integer composition. 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. St000413The number of ordered trees with the same underlying unordered tree. St000483The number of times a permutation switches from increasing to decreasing or decreasing to increasing. St000528The height of a poset. St000617The number of global maxima of a Dyck path. St000678The number of up steps after the last double rise of a Dyck path. St000740The last entry of a permutation. St000757The length of the longest weakly inreasing subsequence of parts of an integer composition. St000765The number of weak records in an integer composition. St000767The number of runs in an integer composition. St000808The number of up steps of the associated bargraph. St000820The number of compositions obtained by rotating the composition. St000843The decomposition number of a perfect matching. St000883The number of longest increasing subsequences of a permutation. St000886The number of permutations with the same antidiagonal sums. St000887The maximal number of nonzero entries on a diagonal of a permutation matrix. St000904The maximal number of repetitions of an integer composition. St000912The number of maximal antichains in a poset. St000930The k-Gorenstein degree of the corresponding Nakayama algebra with linear quiver. St000991The number of right-to-left minima of a permutation. St000996The number of exclusive left-to-right maxima of a permutation. St000999Number of indecomposable projective module with injective dimension equal to the global dimension in the Nakayama algebra corresponding to the Dyck path. St001009Number of indecomposable injective modules with projective dimension g when g is the global dimension of the Nakayama algebra corresponding to the Dyck path. St001014Number of indecomposable injective modules with codominant dimension equal to the dominant dimension of the Nakayama algebra corresponding to the Dyck path. St001024Maximum of dominant dimensions of the simple modules in the Nakayama algebra corresponding to the Dyck path. St001050The number of terminal closers of a set partition. St001135The projective dimension of the first simple module in the Nakayama algebra corresponding to the Dyck path. St001184Number of indecomposable injective modules with grade at least 1 in the corresponding Nakayama algebra. St001201The grade of the simple module $S_0$ in the special CNakayama algebra corresponding to the Dyck path. St001210Gives the maximal vector space dimension of the first Ext-group between an indecomposable module X and the regular module A, when A is the Nakayama algebra corresponding to the Dyck path. St001235The global dimension of the corresponding Comp-Nakayama algebra. St001267The length of the Lyndon factorization of the binary word. St001343The dimension of the reduced incidence algebra of a poset. St001372The length of a longest cyclic run of ones of a binary word. St001437The flex of a binary word. St001461The number of topologically connected components of the chord diagram of a permutation. St001481The minimal height of a peak of a Dyck path. St001636The number of indecomposable injective modules with projective dimension at most one in the incidence algebra of the poset. St001652The length of a longest interval of consecutive numbers. St001662The length of the longest factor of consecutive numbers in a permutation. St001717The largest size of an interval in a poset. St001733The number of weak left to right maxima of a Dyck path. St001806The upper middle entry of a permutation. St001955The number of natural descents for set-valued two row standard Young tableaux. St000051The size of the left subtree of a binary tree. St000070The number of antichains in a poset. St000080The rank of the poset. St000104The number of facets in the order polytope of this poset. St000143The largest repeated part of a partition. St000151The number of facets in the chain polytope of the poset. St000214The number of adjacencies of a permutation. St000234The number of global ascents of a permutation. St000237The number of small exceedances. St000288The number of ones in a binary word. St000338The number of pixed points of a permutation. St000439The position of the first down step of a Dyck path. St000441The number of successions of a permutation. St000445The number of rises of length 1 of a Dyck path. St000538The number of even inversions of a permutation. St000546The number of global descents of a permutation. St000624The normalized sum of the minimal distances to a greater element. St000688The global dimension minus the dominant dimension of the LNakayama algebra associated to a Dyck path. St000731The number of double exceedences of a permutation. St000732The number of double deficiencies of a permutation. St000753The Grundy value for the game of Kayles on a binary word. St000836The number of descents of distance 2 of a permutation. St000876The number of factors in the Catalan decomposition of a binary word. St000877The depth of the binary word interpreted as a path. St000884The number of isolated descents of a permutation. St000986The multiplicity of the eigenvalue zero of the adjacency matrix of the graph. St000989The number of final rises of a permutation. St001017Number of indecomposable injective modules with projective dimension equal to the codominant dimension in the Nakayama algebra corresponding to the Dyck path. St001067The number of simple modules of dominant dimension at least two in the corresponding Nakayama algebra. St001153The number of blocks with even minimum in a set partition. St001216The number of indecomposable injective modules in the corresponding Nakayama algebra that have non-vanishing second Ext-group with the regular module. St001222Number of simple modules in the corresponding LNakayama algebra that have a unique 2-extension with the regular module. 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. St001233The number of indecomposable 2-dimensional modules with projective dimension one. St001265The maximal i such that the i-th simple module has projective dimension equal to the global dimension in the corresponding Nakayama algebra. St001274The number of indecomposable injective modules with projective dimension equal to two. St001276The number of 2-regular indecomposable modules in the corresponding Nakayama algebra. St001300The rank of the boundary operator in degree 1 of the chain complex of the order complex of the poset. St001403The number of vertical separators in a permutation. St001414Half the length of the longest odd length palindromic prefix of a binary word. St001419The length of the longest palindromic factor beginning with a one of a binary word. St001479The number of bridges of a graph. St001613The binary logarithm of the size of the center of a lattice. St001621The number of atoms of a lattice. St001640The number of ascent tops in the permutation such that all smaller elements appear before. St001664The number of non-isomorphic subposets of a poset. St001675The number of parts equal to the part in the reversed composition. St001683The number of distinct positions of the pattern letter 3 in occurrences of 132 in a permutation. St001687The number of distinct positions of the pattern letter 2 in occurrences of 213 in a permutation. St001730The number of times the path corresponding to a binary word crosses the base line. St001777The number of weak descents in an integer composition. St001782The order of rowmotion on the set of order ideals of a poset. St001803The maximal overlap of the cylindrical tableau associated with a tableau. St001816Eigenvalues of the top-to-random operator acting on a simple module. St001826The maximal number of leaves on a vertex of a graph. St001240The number of indecomposable modules e_i J^2 that have injective dimension at most one in the corresponding Nakayama algebra St000061The number of nodes on the left branch of a binary tree. St000675The number of centered multitunnels of a Dyck path. St000990The first ascent of a permutation. St001355Number of non-empty prefixes of a binary word that contain equally many 0's and 1's. St001431Half of the Loewy length minus one of a modified stable Auslander algebra of the Nakayama algebra corresponding to the Dyck path. St001553The number of indecomposable summands of the square of the Jacobson radical as a bimodule in the Nakayama algebra corresponding to the Dyck path. St000297The number of leading ones in a binary word. St000502The number of successions of a set partitions. St000658The number of rises of length 2 of a Dyck path. St000683The number of points below the Dyck path such that the diagonal to the north-east hits the path between two down steps, and the diagonal to the north-west hits the path between two up steps. St000689The maximal n such that the minimal generator-cogenerator module in the LNakayama algebra of a Dyck path is n-rigid. St000932The number of occurrences of the pattern UDU in a Dyck path. St001061The number of indices that are both descents and recoils of a permutation. St001114The number of odd descents of a permutation. St001139The number of occurrences of hills of size 2 in a Dyck path. St001948The number of augmented double ascents of a permutation. St000454The largest eigenvalue of a graph if it is integral. St001933The largest multiplicity of a part in an integer partition. St000777The number of distinct eigenvalues of the distance Laplacian of a connected graph. St000259The diameter of a connected graph. St001232The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2. 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. St001199The dominant dimension of $eAe$ for the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. St001247The number of parts of a partition that are not congruent 2 modulo 3. St001249Sum of the odd parts of a partition. St001250The number of parts of a partition that are not congruent 0 modulo 3. St001360The number of covering relations in Young's lattice below a partition. St001380The number of monomer-dimer tilings of a Ferrers diagram. St001645The pebbling number of a connected graph. St001785The number of ways to obtain a partition as the multiset of antidiagonal lengths of the Ferrers diagram of a partition. St001914The size of the orbit of an integer partition in Bulgarian solitaire. St000260The radius of a connected graph. St000466The Gutman (or modified Schultz) index of a connected graph. St000741The Colin de Verdière graph invariant. St001118The acyclic chromatic index of a graph. St000656The number of cuts of a poset. St000668The least common multiple of the parts of the partition. St000680The Grundy value for Hackendot on posets. St000714The number of semistandard Young tableau of given shape, with entries at most 2. St000717The number of ordinal summands of a poset. St000906The length of the shortest maximal chain in a poset. St001128The exponens consonantiae of a partition. St001568The smallest positive integer that does not appear twice in the partition. St000144The pyramid weight of the Dyck path. St000184The size of the centralizer of any permutation of given cycle type. St000228The size of a partition. St000293The number of inversions of a binary word. St000384The maximal part of the shifted composition of an integer partition. St000395The sum of the heights of the peaks of a Dyck path. St000459The hook length of the base cell of a partition. St000519The largest length of a factor maximising the subword complexity. St000531The leading coefficient of the rook polynomial of an integer partition. St000543The size of the conjugacy class of a binary word. St000626The minimal period of a binary word. St000631The number of distinct palindromic decompositions of a binary word. St000674The number of hills of a Dyck path. St000685The dominant dimension of the LNakayama algebra associated to a Dyck path. St000784The maximum of the length and the largest part of the integer partition. 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. St000922The minimal number such that all substrings of this length are unique. St000952Gives the number of irreducible factors of the Coxeter polynomial of the Dyck path over the rational numbers. 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 $c_{n−1}$. St000969We 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 $c_{n-1}$. 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. St001028Number of simple modules with injective dimension equal to the dominant dimension 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. St001180Number of indecomposable injective modules with projective dimension at most 1. St001183The maximum of $projdim(S)+injdim(S)$ over all simple modules in the Nakayama algebra corresponding to the Dyck path. St001211The number of simple modules in the corresponding Nakayama algebra that have vanishing second Ext-group with the regular module. St001257The dominant dimension of the double dual of A/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. St001291The number of indecomposable summands of the tensor product of two copies of the dual of the Nakayama algebra associated to a Dyck path. St001416The length of a longest palindromic factor of a binary word. St001417The length of a longest palindromic subword of a binary word. St001488The number of corners of a skew partition. 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. St001505The number of elements generated by the Dyck path as a map in the full transformation monoid. St001514The dimension of the top of the Auslander-Reiten translate of the regular modules as a bimodule. St001515The vector space dimension of the socle of the first syzygy module of the regular module (as a bimodule). St001523The degree of symmetry of a Dyck path. St001526The Loewy length of the Auslander-Reiten translate of the regular module as a bimodule of the Nakayama algebra corresponding to the Dyck path. St001611The number of multiset partitions such that the multiplicities of elements are given by a partition. St001612The number of coloured multisets of cycles such that the multiplicities of colours are given by a partition. St001659The number of ways to place as many non-attacking rooks as possible on a Ferrers board. St000013The height of a Dyck path. St000015The number of peaks of a Dyck path. St000019The cardinality of the support of a permutation. St000029The depth 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. St000050The depth or height of a binary tree. St000054The first entry of the permutation. St000058The order of a permutation. St000062The length of the longest increasing subsequence of the permutation. St000075The orbit size of a standard tableau under promotion. St000094The depth of an ordered tree. St000110The number of permutations less than or equal to a permutation in left weak order. St000111The sum of the descent tops (or Genocchi descents) of a permutation. St000117The number of centered tunnels of a Dyck path. St000134The size of the orbit of an alternating sign matrix under gyration. St000186The sum of the first row in a Gelfand-Tsetlin pattern. St000197The number of entries equal to positive one in 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. St000203The number of external nodes of a binary tree. St000209Maximum difference of elements in cycles. St000213The number of weak exceedances (also weak excedences) of a permutation. St000216The absolute length of a permutation. St000221The number of strong fixed points of a permutation. St000224The sorting index of a permutation. St000229Sum of the difference between the maximal and the minimal elements of the blocks plus the number of blocks of a set partition. St000236The number of cyclical small weak excedances. St000239The number of small weak excedances. St000241The number of cyclical small excedances. St000247The number of singleton blocks of a set partition. St000280The size of the preimage of the map 'to labelling permutation' from Parking functions to Permutations. St000290The major index of a binary word. St000296The length of the symmetric border of a binary word. St000308The height of the tree associated to a permutation. St000326The position of the first one in a binary word after appending a 1 at the end. St000334The maz index, the major index of a permutation after replacing fixed points by zeros. St000336The leg major index of a standard tableau. St000382The first part of an integer composition. St000383The last part of an integer composition. St000385The number of vertices with out-degree 1 in a binary tree. St000391The sum of the positions of the ones in a binary word. 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. St000402Half the size of the symmetry class of a permutation. 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. St000420The number of Dyck paths that are weakly above a Dyck path. St000432The number of occurrences of the pattern 231 or of the pattern 312 in a permutation. St000434The number of occurrences of the pattern 213 or of the pattern 312 in a permutation. St000443The number of long tunnels of a Dyck path. St000444The length of the maximal rise of a Dyck path. St000458The number of permutations obtained by switching adjacencies or successions. St000461The rix statistic of a permutation. St000485The length of the longest cycle of a permutation. St000487The length of the shortest 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. St000501The size of the first part in the decomposition of a permutation. St000521The number of distinct subtrees of an ordered tree. St000530The number of permutations with the same descent word as the given permutation. St000564The number of occurrences of the pattern {{1},{2}} in a set partition. St000627The exponent of a binary word. St000630The length of the shortest palindromic decomposition of a binary word. St000638The number of up-down runs of a permutation. St000645The sum of the areas of the rectangles formed by two consecutive peaks and the valley in between. St000654The first descent of a permutation. St000655The length of the minimal rise of a Dyck path. St000657The smallest part of an integer composition. St000673The number of non-fixed points of a permutation. St000681The Grundy value of Chomp on Ferrers diagrams. St000684The global dimension of the LNakayama algebra associated to a Dyck path. St000686The finitistic dominant dimension of a Dyck path. St000690The size of the conjugacy class of a permutation. St000696The number of cycles in the breakpoint graph of a permutation. St000719The number of alignments in a perfect matching. St000724The label of the leaf of the path following the smaller label in the increasing binary tree associated to a permutation. St000725The smallest label of a leaf of the increasing binary tree associated to a permutation. St000727The largest label of a leaf in the binary search tree associated with the permutation. St000729The minimal arc length of a set partition. St000734The last entry in the first row of a standard tableau. St000743The number of entries in a standard Young tableau such that the next integer is a neighbour. St000744The length of the path to the largest entry in a standard Young tableau. St000780The size of the orbit under rotation of a perfect matching. St000792The Grundy value for the game of ruler on a binary word. St000795The mad of a permutation. St000797The stat`` of a permutation. St000809The reduced reflection length of the permutation. St000824The sum of the number of descents and the number of recoils of a permutation. St000831The number of indices that are either descents or recoils. St000839The largest opener of a set partition. St000842The breadth of a permutation. St000844The size of the largest block in the direct sum decomposition of a permutation. St000863The length of the first row of the shifted shape of a permutation. St000866The number of admissible inversions of a permutation in the sense of Shareshian-Wachs. St000873The aix statistic of a permutation. St000875The semilength of the longest Dyck word in the Catalan factorisation of a binary word. St000878The number of ones minus the number of zeros of a binary word. 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. St000894The trace of an alternating sign matrix. St000895The number of ones on the main diagonal of an alternating sign matrix. St000899The maximal number of repetitions of an integer composition. St000900The minimal number of repetitions of a part in an integer composition. St000902 The minimal number of repetitions of an integer composition. St000921The number of internal inversions of a binary word. St000924The number of topologically connected components of a perfect matching. St000937The number of positive values of the symmetric group character corresponding to the partition. St000945The number of matchings in the dihedral orbit of a perfect matching. St000955Number of times one has $Ext^i(D(A),A)>0$ for $i>0$ for the corresponding LNakayama algebra. St000956The maximal displacement of a permutation. St000957The number of Bruhat lower covers of a permutation. St000973The length of the boundary of an ordered tree. St000975The length of the boundary minus the length of the trunk of an ordered tree. St000981The length of the longest zigzag subpath. St000982The length of the longest constant subword. St000983The length of the longest alternating subword. St000988The orbit size of a permutation under Foata's bijection. St001005The number of indices for a permutation that are either left-to-right maxima or right-to-left minima but not both. St001006Number of simple modules with projective dimension equal to the global dimension of the Nakayama algebra corresponding to the Dyck path. St001007Number of simple modules with projective dimension 1 in the Nakayama algebra corresponding to the Dyck path. St001008Number of indecomposable injective modules with projective dimension 1 in the Nakayama algebra corresponding to the Dyck path. St001013Number of indecomposable injective modules with codominant dimension equal to the global dimension in 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. St001019Sum of the projective dimensions of the simple modules in the Nakayama algebra corresponding to the Dyck path. St001034The area of the parallelogram polyomino associated with the Dyck path. St001039The maximal height of a column in the parallelogram polyomino associated with a Dyck path. St001049The smallest label in the subtree not containing 1 in the decreasing labelled binary unordered tree associated with the perfect matching. St001068Number of torsionless simple modules in the corresponding Nakayama algebra. St001076The minimal length of a factorization of a permutation into transpositions that are cyclic shifts of (12). St001077The prefix exchange distance of a permutation. St001107The number of times one can erase the first up and the last down step in a Dyck path and still remain a Dyck path. St001126Number of simple module that are 1-regular in the corresponding Nakayama algebra. St001131The number of trivial trees on the path to label one in the decreasing labelled binary unordered tree associated with the perfect matching. St001161The major index north count of a Dyck path. St001165Number of simple modules with even projective dimension in the corresponding Nakayama algebra. St001187The number of simple modules with grade at least one in the corresponding Nakayama algebra. St001191Number of simple modules $S$ with $Ext_A^i(S,A)=0$ for all $i=0,1,...,g-1$ in the corresponding Nakayama algebra $A$ with global dimension $g$. St001203We associate to 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 Dyck path as follows: St001207The Lowey length of the algebra $A/T$ when $T$ is the 1-tilting module corresponding to the permutation in the Auslander algebra of $K[x]/(x^n)$. St001224Let X be the direct sum of all simple modules of 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. St001236The dominant dimension of the corresponding Comp-Nakayama algebra. St001239The largest vector space dimension of the double dual of a simple module in the corresponding Nakayama algebra. St001241The number of non-zero radicals of the indecomposable projective modules that have injective dimension and projective dimension at most one. St001245The cyclic maximal difference between two consecutive entries of a permutation. St001246The maximal difference between two consecutive entries of a permutation. 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. St001288The number of primes obtained by multiplying preimage and image of a permutation and adding one. St001297The number of indecomposable non-injective projective modules minus the number of indecomposable non-injective projective modules that have reflexive Auslander-Reiten sequences in the corresponding Nakayama algebra. St001299The product of all non-zero projective dimensions of simple modules of the corresponding Nakayama algebra. St001313The number of Dyck paths above the lattice path given by a binary word. St001346The number of parking functions that give the same permutation. St001348The bounce of the parallelogram polyomino associated with the Dyck path. St001365The number of lattice paths of the same length weakly above the path given by a binary word. St001415The length of the longest palindromic prefix of a binary word. St001420Half the length of a longest factor which is its own reverse-complement of a binary word. St001421Half the length of a longest factor which is its own reverse-complement and begins with a one of a binary word. St001424The number of distinct squares in a binary word. St001436The index of a given binary word in the lex-order among all its cyclic shifts. St001439The number of even weak deficiencies and of odd weak exceedences. St001464The number of bases of the positroid corresponding to the permutation, with all fixed points counterclockwise. St001471The magnitude of a Dyck path. St001480The number of simple summands of the module J^2/J^3. St001485The modular major index of a binary word. St001486The number of corners of the ribbon associated with an integer composition. St001491The number of indecomposable projective-injective modules in the algebra corresponding to a subset. St001497The position of the largest weak excedence of a permutation. St001500The global dimension of magnitude 1 Nakayama algebras. St001501The dominant dimension of magnitude 1 Nakayama algebras. 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. St001516The number of cyclic bonds of a permutation. St001528The number of permutations such that the product with the permutation has the same number of fixed points. St001530The depth of a Dyck path. St001554The number of distinct nonempty subtrees of a binary tree. St001558The number of transpositions that are smaller or equal to a permutation in Bruhat order. St001566The length of the longest arithmetic progression in a permutation. 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. St001608The number of coloured rooted trees such that the multiplicities of colours are given by a partition. St001641The number of ascent tops in the flattened set partition such that all smaller elements appear before. St001741The largest integer such that all patterns of this size are contained in the permutation. St001759The Rajchgot index of a permutation. St001778The largest greatest common divisor of an element and its image in a permutation. St001807The lower middle entry of a permutation. St001809The index of the step at the first peak of maximal height in a Dyck path. St001813The product of the sizes of the principal order filters in a poset. St001884The number of borders of a binary word. St001910The height of the middle non-run of a Dyck path. St001925The minimal number of zeros in a row of an alternating sign matrix. 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. St001956The comajor index for set-valued two-row standard Young tableaux. St001958The degree of the polynomial interpolating the values of a permutation. St001959The product of the heights of the peaks of a Dyck path. St000515The number of invariant set partitions when acting with a permutation of given cycle type. St000707The product of the factorials of the parts. St000708The product of the parts of an integer partition. St000815The number of semistandard Young tableaux of partition weight of given shape. St000933The number of multipartitions of sizes given by an integer partition. St001545The second Elser number of a connected graph. St000014The number of parking functions supported by a Dyck path. St000285The size of the preimage of the map 'to inverse des composition' from Parking functions to Integer compositions. St000418The number of Dyck paths that are weakly below a Dyck path. St000464The Schultz index of a connected graph. St000477The weight of a partition according to Alladi. St000529The number of permutations whose descent word is the given binary word. St000770The major index of an integer partition when read from bottom to top. St000939The number of characters of the symmetric group whose value on the partition is positive. St000993The multiplicity of the largest part of an integer partition. St000998Number of indecomposable projective modules with injective dimension smaller than or equal to the dominant dimension in the Nakayama algebra corresponding to the Dyck path. St001012Number of simple modules with projective dimension at most 2 in the Nakayama algebra corresponding to the Dyck path. St001023Number of simple modules with projective dimension at most 3 in the Nakayama algebra corresponding to the Dyck path. St001065Number of indecomposable reflexive modules in the corresponding Nakayama algebra. St001166Number of indecomposable projective non-injective modules with dominant dimension equal to the global dimension plus the number of indecomposable projective injective modules in the corresponding Nakayama algebra. St001170Number of indecomposable injective modules whose socle has projective dimension at most g-1 when g denotes the global dimension in the corresponding Nakayama algebra. St001179Number of indecomposable injective modules with projective dimension at most 2 in the corresponding Nakayama algebra. St001190Number of simple modules with projective dimension at most 4 in the corresponding Nakayama algebra. St001200The number of simple modules in $eAe$ with projective dimension at most 2 in the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. St001213The number of indecomposable modules in the corresponding Nakayama algebra that have vanishing first Ext-group with the regular module. St001237The number of simple modules with injective dimension at most one or dominant dimension at least one. St001259The vector space dimension of the double dual of D(A) in the corresponding Nakayama algebra. St001498The normalised height of a Nakayama algebra with magnitude 1. St001531Number of partial orders contained in the poset determined by the Dyck path. 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. St001060The distinguishing index of a graph. St000510The number of invariant oriented cycles when acting with a permutation of given cycle type. St000567The sum of the products of all pairs of parts. St000771The largest multiplicity of a distance Laplacian eigenvalue in a connected graph. St000772The multiplicity of the largest distance Laplacian eigenvalue in a connected graph. 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. 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. St001330The hat guessing number of a graph. St000456The monochromatic index of a connected graph. St000514The number of invariant simple graphs when acting with a permutation of given cycle type. St000704The number of semistandard tableaux on a given integer partition with minimal maximal entry. St000706The product of the factorials of the multiplicities of an integer partition. 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. St001097The coefficient of the monomial symmetric function indexed by the partition in the formal group law for linear orders. St001098The 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 vertex labelled trees. St001198The number of simple modules in the algebra $eAe$ with projective dimension at most 1 in the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. St001206The maximal dimension of an indecomposable projective $eAe$-module (that is the height of the corresponding Dyck path) of the corresponding Nakayama algebra with minimal faithful projective-injective module $eA$. St001570The minimal number of edges to add to make a graph Hamiltonian. St001123The multiplicity of the dual of the standard representation in the Kronecker square corresponding to a partition. St000284The Plancherel distribution on integer partitions. St000698The number of 2-rim hooks removed from an integer partition to obtain its associated 2-core. St000735The last entry on the main diagonal of a standard tableau. St000813The number of zero-one matrices with weakly decreasing column sums and row sums given by the partition. St000901The cube of the number of standard Young tableaux with shape given by the partition. St001499The number of indecomposable projective-injective modules of a magnitude 1 Nakayama algebra. St000045The number of linear extensions of a binary tree. St000060The greater neighbor of the maximum. St000064The number of one-box pattern of a permutation. St000082The number of elements smaller than a binary tree in Tamari order. St000100The number of linear extensions of a poset. St000243The number of cyclic valleys and cyclic peaks of a permutation. St000249The number of singletons (St000247) plus the number of antisingletons (St000248) of a set partition. St000250The number of blocks (St000105) plus the number of antisingletons (St000248) of a set partition. St000327The number of cover relations in a poset. St000411The tree factorial of a binary tree. St000412The number of binary trees with the same underlying unordered tree. St000438The position of the last up step in a Dyck path. St000488The number of cycles of a permutation of length at most 2. St000489The number of cycles of a permutation of length at most 3. St000504The cardinality of the first block of a set partition. 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. St000568The hook number of a binary tree. St000570The Edelman-Greene number of a permutation. St000619The number of cyclic descents of a permutation. St000620The number of standard tableaux of shape equal to the given partition such that the minimal cyclic descent is odd. St000625The sum of the minimal distances to a greater element. St000633The size of the automorphism group of a poset. St000640The rank of the largest boolean interval in a poset. St000642The size of the smallest orbit of antichains under Panyushev complementation. St000695The number of blocks in the first part of the atomic decomposition of a set partition. St000702The number of weak deficiencies of a permutation. St000762The sum of the positions of the weak records of an integer composition. St000782The indicator function of whether a given perfect matching is an L & P matching. St000823The number of unsplittable factors of the set partition. St000832The number of permutations obtained by reversing blocks of three consecutive numbers. St000847The number of standard Young tableaux whose descent set is the binary word. St000880The number of connected components of long braid edges in the graph of braid moves of a permutation. St000890The number of nonzero entries in an alternating sign matrix. St000893The number of distinct diagonal sums of an alternating sign matrix. St000898The number of maximal entries in the last diagonal of the monotone triangle. St000910The number of maximal chains of minimal length in a poset. St000914The sum of the values of the Möbius function of a poset. St000923The minimal number with no two order isomorphic substrings of this length in a permutation. St000925The number of topologically connected components of a set partition. St001052The length of the exterior of a permutation. St001062The maximal size of a block of a set partition. St001074The number of inversions of the cyclic embedding of a permutation. St001075The minimal size of a block of a set partition. St001081The number of minimal length factorizations of a permutation into star transpositions. St001105The number of greedy linear extensions of a poset. St001106The number of supergreedy linear extensions of a poset. St001162The minimum jump of a permutation. St001195The global dimension of the algebra $A/AfA$ of the corresponding Nakayama algebra $A$ with minimal left faithful projective-injective module $Af$. St001220The width of a permutation. St001344The neighbouring number of a permutation. St001404The number of distinct entries in a Gelfand Tsetlin pattern. St001603The number of colourings of a polygon such that the multiplicities of a colour are given by a partition. St001632The number of indecomposable injective modules $I$ with $dim Ext^1(I,A)=1$ for the incidence algebra A of a poset. St001637The number of (upper) dissectors of a poset. St001668The number of points of the poset minus the width of the poset. St001686The order of promotion on a Gelfand-Tsetlin pattern. St001722The number of minimal chains with small intervals between a binary word and the top element. St001808The box weight or horizontal decoration of a Dyck path. St001838The number of nonempty primitive factors of a binary word. St001885The number of binary words with the same proper border set. St001890The maximum magnitude of the Möbius function of a poset. St001915The size of the component corresponding to a necklace in Bulgarian solitaire.