St000058The order of a permutation. St000395The sum of the heights of the peaks of a Dyck path. St000505The biggest entry in the block containing the 1. St001020Sum of the codominant dimensions of the non-projective indecomposable injective modules of the Nakayama algebra corresponding to the Dyck path. 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. St001430The number of positive entries in a signed permutation. 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. 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. St000053The number of valleys of the Dyck path. St000171The degree of the graph. St000479The Ramsey number of a graph. St000645The sum of the areas of the rectangles formed by two consecutive peaks and the valley in between. St001067The number of simple modules of dominant dimension at least two in the corresponding Nakayama algebra. St001120The length of a longest path in a graph. St001197The global dimension of $eAe$ for the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. St001232The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2. St001332The number of steps on the non-negative side of the walk associated with the permutation. St001382The number of boxes in the diagram of a partition that do not lie in its Durfee square. St001506Half the projective dimension of the unique simple module with even projective dimension in a magnitude 1 Nakayama algebra. St001641The number of ascent tops in the flattened set partition such that all smaller elements appear before. St001955The number of natural descents for set-valued two row standard Young tableaux. St000010The length of the partition. St000011The number of touch points (or returns) of a Dyck path. St000293The number of inversions of a binary word. St000445The number of rises of length 1 of a Dyck path. St000460The hook length of the last cell along the main diagonal of an integer partition. St000676The number of odd rises of a Dyck path. St000684The global dimension of the LNakayama algebra associated to a Dyck path. St000685The dominant dimension of the LNakayama algebra associated to a Dyck path. St000686The finitistic dominant dimension of a Dyck path. 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. St000738The first entry in the last row of a standard tableau. St000839The largest opener of a set partition. St000870The product of the hook lengths of the diagonal cells in an integer partition. St001068Number of torsionless simple modules in the corresponding Nakayama algebra. St001135The projective dimension of the first simple module in the Nakayama algebra corresponding to the Dyck path. 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: St001342The number of vertices in the center of a graph. St001348The bounce of the parallelogram polyomino associated with the Dyck path. St001523The degree of symmetry of a Dyck path. St001527The cyclic permutation representation number of an integer partition. St001688The sum of the squares of the heights of the peaks of a Dyck path. 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. St001733The number of weak left to right maxima of a Dyck path. St001746The coalition number of a graph. 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 $c_{n-1}$. St001028Number of simple modules with injective dimension equal to the dominant dimension in the Nakayama algebra corresponding to the Dyck path. St001166Number of indecomposable projective non-injective modules with dominant dimension equal to the global dimension plus the number of indecomposable projective injective modules in the corresponding Nakayama algebra. St001279The sum of the parts of an integer partition that are at least two. St001505The number of elements generated by the Dyck path as a map in the full transformation monoid. St001190Number of simple modules with projective dimension at most 4 in the corresponding Nakayama algebra. St000144The pyramid weight of the Dyck path. St000189The number of elements in the poset. 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. St001018Sum of projective dimension of the indecomposable injective modules of the Nakayama algebra corresponding to the Dyck path. St001291The number of indecomposable summands of the tensor product of two copies of the dual of the Nakayama algebra associated to 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. St001179Number of indecomposable injective modules with projective dimension at most 2 in the corresponding Nakayama algebra. St001227The vector space dimension of the first extension group between the socle of the regular module and the Jacobson radical of the corresponding Nakayama algebra. 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. St001958The degree of the polynomial interpolating the values of a permutation. 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. St000015The number of peaks 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. St000054The first entry of the permutation. St000093The cardinality of a maximal independent set of vertices of a graph. St000141The maximum drop size of a permutation. St000147The largest part of an integer partition. St000229Sum of the difference between the maximal and the minimal elements of the blocks plus the number of blocks of a set partition. St000240The number of indices that are not small excedances. St000337The lec statistic, the sum of the inversion numbers of the hook factors of a permutation. St000374The number of exclusive right-to-left minima of a permutation. St000384The maximal part of the shifted composition of an integer partition. St000453The number of distinct Laplacian eigenvalues of a graph. St000501The size of the first part in the decomposition of a permutation. St000503The maximal difference between two elements in a common block. St000617The number of global maxima of a Dyck path. St000703The number of deficiencies of a permutation. St000722The number of different neighbourhoods in a graph. St000733The row containing the largest entry of a standard tableau. St000740The last entry of a permutation. St000777The number of distinct eigenvalues of the distance Laplacian of a connected graph. St000784The maximum of the length and the largest part of the integer partition. 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. St001497The position of the largest weak excedence of a permutation. St001530The depth of a Dyck path. St001622The number of join-irreducible elements of a lattice. St001636The number of indecomposable injective modules with projective dimension at most one in the incidence algebra of the poset. St001778The largest greatest common divisor of an element and its image in a permutation. St000019The cardinality of the support of a permutation. St000051The size of the left subtree of a binary tree. St000167The number of leaves of an ordered tree. St000209Maximum difference of elements in cycles. St000306The bounce count of a Dyck path. St000316The number of non-left-to-right-maxima of a permutation. St000331The number of upper interactions of a Dyck path. St000380Half of the maximal perimeter of a rectangle fitting into the diagram of an integer partition. St000451The length of the longest pattern of the form k 1 2. St000533The minimum of the number of parts and the size of the first part of an integer partition. St000954Number of times the corresponding LNakayama algebra has $Ext^i(D(A),A)=0$ for $i>0$. 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 $c_{n−1}$. 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. St001237The number of simple modules with injective dimension at most one or dominant dimension at least one. St001245The cyclic maximal difference between two consecutive entries of a permutation. St001278The number of indecomposable modules that are fixed by $\tau \Omega^1$ composed with its inverse 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. 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. St001300The rank of the boundary operator in degree 1 of the chain complex of the order complex of the poset. St001392The largest nonnegative integer which is not a part and is smaller than the largest part of the partition. St001509The degree of the standard monomial associated to a Dyck path relative to the trivial lower boundary. St001827The number of two-component spanning forests of a graph. St001869The maximum cut size of a graph. St000007The number of saliances of the permutation. St000012The area of a Dyck path. St000013The height of a Dyck path. St000014The number of parking functions supported by a Dyck path. St000018The number of inversions of a permutation. St000022The number of fixed points of a permutation. St000025The number of initial rises of a Dyck path. St000032The number of elements smaller than the given Dyck path in the Tamari Order. St000050The depth or height of a binary tree. St000056The decomposition (or block) number of a permutation. St000059The inversion number of a standard tableau as defined by Haglund and Stevens. St000062The length of the longest increasing subsequence of the permutation. St000066The column of the unique '1' in the first row of the alternating sign matrix. St000084The number of subtrees. St000105The number of blocks in the set partition. St000110The number of permutations less than or equal to a permutation in left weak order. St000117The number of centered tunnels of a Dyck path. St000153The number of adjacent cycles of a permutation. St000157The number of descents of a standard tableau. St000164The number of short pairs. St000203The number of external nodes of a binary tree. St000213The number of weak exceedances (also weak excedences) of a permutation. St000215The number of adjacencies of a permutation, zero appended. St000221The number of strong fixed points of a permutation. St000236The number of cyclical small weak excedances. St000239The number of small weak excedances. St000241The number of cyclical small excedances. St000271The chromatic index of a graph. St000291The number of descents of a binary word. St000308The height of the tree associated to a permutation. St000314The number of left-to-right-maxima of a permutation. St000318The number of addable cells of the Ferrers diagram of an integer partition. St000325The width of the tree associated to a permutation. St000328The maximum number of child nodes in a tree. St000335The difference of lower and upper interactions. St000338The number of pixed points of a permutation. St000389The number of runs of ones of odd length in a binary word. St000390The number of runs of ones in a binary word. St000393The number of strictly increasing runs in a binary word. St000400The path length of an ordered tree. St000443The number of long tunnels of a Dyck path. St000452The number of distinct eigenvalues of a graph. St000470The number of runs in a permutation. St000476The sum of the semi-lengths of tunnels before a valley of a Dyck path. St000507The number of ascents of a standard tableau. St000528The height of a poset. St000542The number of left-to-right-minima of a permutation. St000543The size of the conjugacy class of a binary word. St000553The number of blocks of a graph. St000626The minimal period of a binary word. St000627The exponent of a binary word. St000632The jump number of the poset. St000636The hull number of a graph. St000638The number of up-down runs of a permutation. St000655The length of the minimal rise of a Dyck path. St000678The number of up steps after the last double rise of a Dyck path. St000696The number of cycles in the breakpoint graph of a permutation. St000698The number of 2-rim hooks removed from an integer partition to obtain its associated 2-core. St000721The sum of the partition sizes in the oscillating tableau corresponding to a perfect matching. St000728The dimension of a set partition. St000743The number of entries in a standard Young tableau such that the next integer is a neighbour. St000746The number of pairs with odd minimum in a perfect matching. St000757The length of the longest weakly inreasing subsequence of parts of an integer composition. St000759The smallest missing part in an integer partition. St000765The number of weak records in an integer composition. St000843The decomposition number of a perfect matching. St000863The length of the first row of the shifted shape of a permutation. St000876The number of factors in the Catalan decomposition of a binary word. St000883The number of longest increasing subsequences of a permutation. St000885The number of critical steps in the Catalan decomposition of a binary word. 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. St000904The maximal number of repetitions of an integer composition. St000907The number of maximal antichains of minimal length in a poset. St000911The number of maximal antichains of maximal size in a poset. St000912The number of maximal antichains in a poset. St000917The open packing number of a graph. St000918The 2-limited packing number of a graph. St000924The number of topologically connected components of a perfect matching. St000932The number of occurrences of the pattern UDU in a Dyck path. St000984The number of boxes below precisely one peak. St000991The number of right-to-left minima 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. 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. St001009Number of indecomposable injective modules with projective dimension g when g is the global dimension of 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. St001014Number of indecomposable injective modules with codominant dimension equal to the dominant dimension of the Nakayama algebra corresponding to the Dyck path. St001015Number of indecomposable injective modules with codominant dimension equal to one in the Nakayama algebra corresponding to the Dyck path. St001016Number of indecomposable injective modules with codominant dimension at most 1 in the Nakayama algebra corresponding to the Dyck path. St001017Number of indecomposable injective modules with projective dimension equal to the codominant 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. St001050The number of terminal closers of a set partition. St001051The depth of the label 1 in the decreasing labelled unordered tree associated with the set partition. St001058The breadth of the ordered tree. St001088Number of indecomposable projective non-injective modules with dominant dimension equal to the injective dimension in the corresponding Nakayama algebra. St001090The number of pop-stack-sorts needed to sort a permutation. St001126Number of simple module that are 1-regular in the corresponding Nakayama algebra. St001176The size of a partition minus its first part. St001184Number of indecomposable injective modules with grade at least 1 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 $g$. St001199The dominant dimension of $eAe$ for the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. 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. St001224Let X be the direct sum of all simple modules of the corresponding Nakayama algebra. St001235The global dimension of the corresponding Comp-Nakayama algebra. St001236The dominant dimension of the corresponding Comp-Nakayama algebra. St001241The number of non-zero radicals of the indecomposable projective modules that have injective dimension and projective dimension at most one. St001249Sum of the odd parts of a partition. St001252Half the sum of the even parts of a partition. St001267The length of the Lyndon factorization of the binary word. St001268The size of the largest ordinal summand in the poset. 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. St001315The dissociation number of a graph. St001343The dimension of the reduced incidence algebra of a poset. St001371The length of the longest Yamanouchi prefix of a binary word. St001390The number of bumps occurring when Schensted-inserting the letter 1 of a permutation. St001418Half of the global dimension of the stable Auslander algebra of the Nakayama algebra corresponding to the Dyck path. St001437The flex of a binary word. St001439The number of even weak deficiencies and of odd weak exceedences. St001461The number of topologically connected components of the chord diagram of a permutation. St001463The number of distinct columns in the nullspace of a graph. St001464The number of bases of the positroid corresponding to the permutation, with all fixed points counterclockwise. St001481The minimal height of a peak of a Dyck path. St001499The number of indecomposable projective-injective modules of a magnitude 1 Nakayama algebra. St001554The number of distinct nonempty subtrees of a binary tree. St001566The length of the longest arithmetic progression in a permutation. St001652The length of a longest interval of consecutive numbers. St001654The monophonic hull number of a graph. St001655The general position number of a graph. St001656The monophonic position number of a graph. St001662The length of the longest factor of consecutive numbers in a permutation. St001672The restrained domination number of a graph. St001675The number of parts equal to the part in the reversed composition. St001717The largest size of an interval in a poset. St001721The degree of a binary word. St001725The harmonious chromatic number of a graph. St001809The index of the step at the first peak of maximal height in a Dyck path. St001910The height of the middle non-run of a Dyck path. St000004The major index of a permutation. St000021The number of descents of a permutation. St000024The number of double up and double down steps of a Dyck path. St000029The depth of a permutation. St000030The sum of the descent differences of a permutations. St000052The number of valleys of a Dyck path not on the x-axis. St000067The inversion number of the alternating sign matrix. St000068The number of minimal elements in a poset. St000070The number of antichains in a poset. St000071The number of maximal chains in a poset. St000080The rank of the poset. St000104The number of facets in the order polytope of this poset. St000133The "bounce" of a permutation. St000151The number of facets in the chain polytope of the poset. St000155The number of exceedances (also excedences) of a permutation. St000210Minimum over maximum difference of elements in cycles. St000214The number of adjacencies of a permutation. St000224The sorting index of a permutation. St000234The number of global ascents of a permutation. St000237The number of small exceedances. St000238The number of indices that are not small weak excedances. St000245The number of ascents of a permutation. St000292The number of ascents of a binary word. St000304The load of a permutation. St000312The number of leaves in a graph. St000329The number of evenly positioned ascents of the Dyck path, with the initial position equal to 1. St000334The maz index, the major index of a permutation after replacing fixed points by zeros. St000339The maf index of a permutation. St000340The number of non-final maximal constant sub-paths of length greater than one. St000410The tree factorial of an ordered tree. St000439The position of the first down step of a Dyck path. St000441The number of successions of a permutation. St000446The disorder of a permutation. St000519The largest length of a factor maximising the subword complexity. St000527The width of the poset. St000546The number of global descents of a permutation. St000651The maximal size of a rise in a permutation. St000662The staircase size of the code of a permutation. St000672The number of minimal elements in Bruhat order not less than the permutation. St000674The number of hills of a Dyck path. St000718The largest Laplacian eigenvalue of a graph if it is integral. St000724The label of the leaf of the path following the smaller label in the increasing binary tree associated to a permutation. St000783The side length of the largest staircase partition fitting into a partition. St000825The sum of the major and the inverse major index of a permutation. St000840The number of closers smaller than the largest opener in a perfect matching. St000864The number of circled entries of the shifted recording tableau of a permutation. St000868The aid statistic in the sense of Shareshian-Wachs. St000921The number of internal inversions of a binary word. St000979Half of MacMahon's equal index of a Dyck path. St001027Number of simple modules with projective dimension equal to injective 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. St001039The maximal height of a column in the parallelogram polyomino associated with a Dyck path. St001082The number of boxed occurrences of 123 in a permutation. St001161The major index north count of a Dyck path. St001172The number of 1-rises at odd height of a Dyck path. St001180Number of indecomposable injective modules with projective dimension at most 1. St001189The number of simple modules with dominant and codominant dimension equal to zero 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. St001213The number of indecomposable modules in the corresponding Nakayama algebra that have vanishing first Ext-group with the regular module. 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. St001233The number of indecomposable 2-dimensional modules with projective dimension one. St001259The vector space dimension of the double dual of D(A) in the corresponding Nakayama algebra. St001265The maximal i such that the i-th simple module has projective dimension equal to the global dimension in the corresponding Nakayama algebra. St001295Gives the vector space dimension of the homomorphism space between J^2 and J^2. St001298The number of repeated entries in the Lehmer code of a permutation. 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. St001391The disjunction number of a graph. St001405The number of bonds in a permutation. St001484The number of singletons of an integer partition. St001489The maximum of the number of descents and the number of inverse descents. 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. St001508The degree of the standard monomial associated to a Dyck path relative to the diagonal boundary. 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. St001631The number of simple modules $S$ with $dim Ext^1(S,A)=1$ in the incidence algebra $A$ of the poset. St001640The number of ascent tops in the permutation such that all smaller elements appear before. St001664The number of non-isomorphic subposets of a poset. St001723The differential of a graph. St001724The 2-packing differential of a graph. St001726The number of visible inversions of a permutation. St001759The Rajchgot index of a permutation. St001777The number of weak descents in an integer composition. St001782The order of rowmotion on the set of order ideals of a poset. St001925The minimal number of zeros in a row of an alternating sign matrix. St000806The semiperimeter of the associated bargraph. St001643The Frobenius dimension of the Nakayama algebra corresponding to the Dyck path. St000727The largest label of a leaf in the binary search tree associated with the permutation. St000844The size of the largest block in the direct sum decomposition of a permutation. St000653The last descent of a permutation. St000956The maximal displacement of a permutation. St001480The number of simple summands of the module J^2/J^3. St000225Difference between largest and smallest parts in a partition. St000799The number of occurrences of the vincular pattern |213 in a permutation. St000829The Ulam distance of a permutation to the identity permutation. St000837The number of ascents of distance 2 of a permutation. St000061The number of nodes on the left branch of a binary tree. St000064The number of one-box pattern of a permutation. St000247The number of singleton blocks of a set partition. 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. St000280The size of the preimage of the map 'to labelling permutation' from Parking functions to Permutations. St000294The number of distinct factors of a binary word. St000326The position of the first one in a binary word after appending a 1 at the end. St000438The position of the last up step in a Dyck path. St000444The length of the maximal rise of a Dyck path. St000461The rix statistic of a permutation. St000471The sum of the ascent tops of a permutation. St000485The length of the longest cycle of a permutation. St000487The length of the shortest cycle of a permutation. St000488The number of cycles of a permutation of length at most 2. St000489The number of cycles of a permutation of length at most 3. St000518The number of distinct subsequences in a binary word. St000625The sum of the minimal distances to a greater element. St000654The first descent of a permutation. St000656The number of cuts of a poset. St000673The number of non-fixed points of a permutation. St000675The number of centered multitunnels of a Dyck path. St000680The Grundy value for Hackendot on posets. St000702The number of weak deficiencies of a permutation. St000717The number of ordinal summands of a poset. St000729The minimal arc length of a set partition. St000873The aix statistic of a permutation. St000887The maximal number of nonzero entries on a diagonal of a permutation matrix. St000888The maximal sum of entries on a diagonal of an alternating sign matrix. St000890The number of nonzero entries in 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. St000906The length of the shortest maximal chain in 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. St000990The first ascent of a permutation. St001005The number of indices for a permutation that are either left-to-right maxima or right-to-left minima but not both. St001074The number of inversions of the cyclic embedding 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. St001118The acyclic chromatic index of a graph. St001959The product of the heights of the peaks of a Dyck path. St000060The greater neighbor of the maximum. St000083The number of left oriented leafs of a binary tree except the first one. St000197The number of entries equal to positive one in the alternating sign matrix. St000216The absolute length of a permutation. St000296The length of the symmetric border of a binary word. St000354The number of recoils of a permutation. St000385The number of vertices with out-degree 1 in a binary tree. St000414The binary logarithm of the number of binary trees with the same underlying unordered tree. St000442The maximal area to the right of an up step of a Dyck path. St000520The number of patterns in a permutation. St000530The number of permutations with the same descent word as the given permutation. St000541The number of indices greater than or equal to 2 of a permutation such that all smaller indices appear to its right. St000619The number of cyclic descents of a permutation. St000642The size of the smallest orbit of antichains under Panyushev complementation. St000643The size of the largest orbit of antichains under Panyushev complementation. St000652The maximal difference between successive positions of a permutation. St000794The mak of a permutation. St000795The mad of a permutation. St000809The reduced reflection length of the permutation. St000826The stopping time of the decimal representation of the binary word for the 3x+1 problem. St000831The number of indices that are either descents or recoils. St000874The position of the last double rise in a Dyck path. St000877The depth of the binary word interpreted as a path. St000898The number of maximal entries in the last diagonal of the monotone triangle. St000922The minimal number such that all substrings of this length are unique. St000957The number of Bruhat lower covers of a permutation. St000982The length of the longest constant subword. St000989The number of final rises of a permutation. St001061The number of indices that are both descents and recoils of a permutation. St001076The minimal length of a factorization of a permutation into transpositions that are cyclic shifts of (12). St001077The prefix exchange distance of a permutation. St001246The maximal difference between two consecutive entries of a permutation. 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. St001884The number of borders of a binary word. St000295The length of the border of a binary word. St000434The number of occurrences of the pattern 213 or of the pattern 312 in a permutation. St000800The number of occurrences of the vincular pattern |231 in a permutation. St000836The number of descents of distance 2 of a permutation. St000931The number of occurrences of the pattern UUU in a Dyck path. St001035The convexity degree of the parallelogram polyomino associated with the Dyck path. St001130The number of two successive successions in a permutation. St001280The number of parts of an integer partition that are at least two. St001880The number of 2-Gorenstein indecomposable injective modules in the incidence algebra of the lattice. 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. St001124The multiplicity of the standard representation in the Kronecker square corresponding to a partition. St000273The domination number of a graph. St000786The maximal number of occurrences of a colour in a proper colouring of a graph. St000916The packing number of a graph. St001286The annihilation number of a graph. St001322The size of a minimal independent dominating set in a graph. St001337The upper domination number of a graph. St001338The upper irredundance number of a graph. St001339The irredundance number of a graph. St001829The common independence number of a graph. St000259The diameter of a connected graph. St001340The cardinality of a minimal non-edge isolating set of a graph. St001917The order of toric promotion on the set of labellings of a graph. St001615The number of join prime elements of a lattice. St001617The dimension of the space of valuations of a lattice. St001820The size of the image of the pop stack sorting operator. St001720The minimal length of a chain of small intervals in a lattice. St000087The number of induced subgraphs. St000287The number of connected components of a graph. St000299The number of nonisomorphic vertex-induced subtrees. St000309The number of vertices with even degree. St000315The number of isolated vertices of a graph. St001828The Euler characteristic of a graph. St000550The number of modular elements of a lattice. St000551The number of left modular elements of a lattice. St001616The number of neutral elements in a lattice. St001623The number of doubly irreducible elements of a lattice. St001626The number of maximal proper sublattices of a lattice. St001649The length of a longest trail in a graph. St001846The number of elements which do not have a complement in the lattice. St001619The number of non-isomorphic sublattices of a lattice. St001666The number of non-isomorphic subposets of a lattice which are lattices. St001875The number of simple modules with projective dimension at most 1. St000097The order of the largest clique of the graph. St000098The chromatic number of a graph. St001570The minimal number of edges to add to make a graph Hamiltonian. St001645The pebbling number of a connected graph. St000454The largest eigenvalue of a graph if it is integral. St000246The number of non-inversions of a permutation. St001084The number of occurrences of the vincular pattern |1-23 in a permutation. St000744The length of the path to the largest entry in a standard Young tableau. St001029The size of the core of a graph. St001108The 2-dynamic chromatic number of a graph. St001494The Alon-Tarsi number of a graph. St000778The metric dimension of a graph. St001372The length of a longest cyclic run of ones of a binary word. St001644The dimension of a graph. St000332The positive inversions of an alternating sign matrix. St000547The number of even non-empty partial sums of an integer partition. St001048The number of leaves in the subtree containing 1 in the decreasing labelled binary unordered tree associated with the perfect matching. St001397Number of pairs of incomparable elements in a finite poset. St001428The number of B-inversions of a signed permutation. St000231Sum of the maximal elements of the blocks of a set partition. St000549The number of odd partial sums of an integer partition. 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. St000689The maximal n such that the minimal generator-cogenerator module in the LNakayama algebra of a Dyck path is n-rigid. St000949Gives the number of generalised tilting modules of the corresponding LNakayama algebra. St001003The number of indecomposable modules with projective dimension at most 1 in the Nakayama algebra corresponding to the Dyck path. St001468The smallest fixpoint of a permutation. St000134The size of the orbit of an alternating sign matrix under gyration. St000193The row of the unique '1' in the first column of the alternating sign matrix. St000305The inverse major index of a permutation. St000450The number of edges minus the number of vertices plus 2 of a graph. St000796The stat' of a permutation. St000797The stat`` of a permutation. St000798The makl of a permutation. St000833The comajor index of a permutation. St000988The orbit size of a permutation under Foata's bijection. St001045The number of leaves in the subtree not containing one in the decreasing labelled binary unordered tree associated with the perfect matching. St001132The number of leaves in the subtree whose sister has label 1 in the decreasing labelled binary unordered tree associated with the perfect matching. St001429The number of negative entries in a signed permutation. St001515The vector space dimension of the socle of the first syzygy module of the regular module (as a bimodule). St001526The Loewy length of the Auslander-Reiten translate of the regular module as a bimodule of the Nakayama algebra corresponding to the Dyck path. St001671Haglund's hag of a permutation. St000095The number of triangles of a graph. St000111The sum of the descent tops (or Genocchi descents) of a permutation. St000159The number of distinct parts of the integer partition. St000235The number of indices that are not cyclical small weak excedances. St000317The cycle descent number of a permutation. St000358The number of occurrences of the pattern 31-2. St000435The number of occurrences of the pattern 213 or of the pattern 231 in a permutation. St000691The number of changes of a binary word. St000732The number of double deficiencies of a permutation. St001134The largest label in the subtree rooted at the sister of 1 in the leaf labelled binary unordered tree associated with the perfect matching. St001229The vector space dimension of the first extension group between the Jacobson radical J and J^2. St001379The number of inversions plus the major index of a permutation. St001553The number of indecomposable summands of the square of the Jacobson radical as a bimodule in the Nakayama algebra corresponding to the Dyck path. St001684The reduced word complexity of a permutation. St001727The number of invisible inversions of a permutation. St001744The number of occurrences of the arrow pattern 1-2 with an arrow from 1 to 2 in a permutation. St001255The vector space dimension of the double dual of A/J when A is the corresponding Nakayama algebra with Jacobson radical J. St000474Dyson's crank of a partition. St001706The number of closed sets in a graph. St000327The number of cover relations in a poset. St001668The number of points of the poset minus the width of the poset. St000896The number of zeros on the main diagonal of an alternating sign matrix. St001431Half of the Loewy length minus one of a modified stable Auslander algebra of the Nakayama algebra corresponding to the Dyck path. St001432The order dimension of the partition. St001637The number of (upper) dissectors of a poset. St001948The number of augmented double ascents of a permutation. St001557The number of inversions of the second entry of a permutation. St001811The Castelnuovo-Mumford regularity of a permutation. St001960The number of descents of a permutation minus one if its first entry is not one. 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 $eA$. St001927Sparre Andersen's number of positives of a signed permutation. St001123The multiplicity of the dual of the standard representation in the Kronecker square corresponding to a partition. St001629The coefficient of the integer composition in the quasisymmetric expansion of the relabelling action of the symmetric group on cycles. St001834The number of non-isomorphic minors of a graph. St000822The Hadwiger number of the graph. St001316The domatic number of a graph. St000261The edge connectivity of a graph. St000262The vertex connectivity of a graph. St000310The minimal degree of a vertex of a graph. St000741The Colin de Verdière graph invariant. St001270The bandwidth of a graph. St001277The degeneracy of a graph. St001358The largest degree of a regular subgraph of a graph. St001962The proper pathwidth of a graph. St001817The number of flag weak exceedances of a signed permutation. St001892The flag excedance statistic of a signed permutation. St001434The number of negative sum pairs of a signed permutation. St000371The number of mid points of decreasing subsequences of length 3 in a permutation. St001603The number of colourings of a polygon such that the multiplicities of a colour are given by a partition. St001604The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on polygons. St001605The number of colourings of a cycle such that the multiplicities of colours are given by a partition. St000373The number of weak exceedences of a permutation that are also mid-points of a decreasing subsequence of length $3$. St001882The number of occurrences of a type-B 231 pattern in a signed permutation. St000692Babson and Steingrímsson's statistic of a permutation. St000356The number of occurrences of the pattern 13-2. St001136The largest label with larger sister in the leaf labelled binary unordered tree associated with the perfect matching. St000352The Elizalde-Pak rank of a permutation. St000381The largest part of an integer composition. St001330The hat guessing number of a graph. St001682The number of distinct positions of the pattern letter 1 in occurrences of 123 in a permutation. St001115The number of even descents of a permutation. St000820The number of compositions obtained by rotating the composition. St001214The aft of an integer partition. St001861The number of Bruhat lower covers of a permutation. St000780The size of the orbit under rotation of a perfect matching. St001555The order of a signed permutation. St001812The biclique partition number of a graph. St001182Number of indecomposable injective modules with codominant dimension at least two in the corresponding Nakayama algebra. St000044The number of vertices of the unicellular map given by a perfect matching. St000135The number of lucky cars of the parking function. 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. St000017The number of inversions of a standard tableau. St000035The number of left outer peaks of a permutation. St000186The sum of the first row in a Gelfand-Tsetlin pattern. St000742The number of big ascents of a permutation after prepending zero. St000808The number of up steps of the associated bargraph. St000884The number of isolated descents of a permutation. St001355Number of non-empty prefixes of a binary word that contain equally many 0's and 1's. St001413Half the length of the longest even length palindromic prefix of a binary word. St001419The length of the longest palindromic factor beginning with a one of a binary word. St001427The number of descents of a signed permutation. St001436The index of a given binary word in the lex-order among all its cyclic shifts. St001462The number of factors of a standard tableaux under concatenation. St001524The degree of symmetry of a binary word. St001855The number of signed permutations less than or equal to a signed permutation in left weak order. St001907The number of Bastidas - Hohlweg - Saliola excedances of a signed permutation. St000834The number of right outer peaks of a permutation. St000945The number of matchings in the dihedral orbit of a perfect matching. St001314The number of tilting modules of arbitrary projective dimension that have no simple modules as a direct summand in the corresponding Nakayama algebra. St001414Half the length of the longest odd length palindromic prefix of a binary word. St001424The number of distinct squares in a binary word. St001712The number of natural descents of a standard Young tableau. St001803The maximal overlap of the cylindrical tableau associated with a tableau. St001207The Lowey length of the algebra $A/T$ when $T$ is the 1-tilting module corresponding to the permutation in the Auslander algebra of $K[x]/(x^n)$. St000522The number of 1-protected nodes of a rooted tree. St001621The number of atoms of a lattice. St000521The number of distinct subtrees of an ordered tree. St001583The projective dimension of the simple module corresponding to the point in the poset of the symmetric group under bruhat order. St000264The girth of a graph, which is not a tree. St000490The intertwining number of a set partition. St000568The hook number of a binary tree. St000919The number of maximal left branches of a binary tree. St000502The number of successions of a set partitions. St001036The number of inner corners of the parallelogram polyomino associated with the Dyck path. St001926Sparre Andersen's position of the maximum of a signed permutation. St000848The balance constant multiplied with the number of linear extensions of a poset. St000849The number of 1/3-balanced pairs in a poset.