St001120The length of a longest path in a graph. St001176The size of a partition minus its first part. St001197The global dimension of $eAe$ for the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. St001506Half the projective dimension of the unique simple module with even projective dimension in a magnitude 1 Nakayama algebra. St001644The dimension of a graph. St001777The number of weak descents in an integer composition. St000010The length of the partition. St000011The number of touch points (or returns) of a Dyck path. St000097The order of the largest clique of the graph. St000098The chromatic number of a graph. St000172The Grundy number of a graph. St000288The number of ones in a binary word. St000297The number of leading ones in a binary word. St000363The number of minimal vertex covers of a graph. St000381The largest part of an integer composition. St000382The first part of an integer composition. St000383The last part of an integer composition. St000392The length of the longest run of ones in a binary word. St000684The global dimension of the LNakayama algebra associated to a Dyck path. St000686The finitistic dominant dimension of a Dyck path. St000808The number of up steps of the associated bargraph. St001029The size of the core of a graph. St001068Number of torsionless simple modules in the corresponding Nakayama algebra. St001108The 2-dynamic chromatic number of a graph. St001110The 3-dynamic chromatic number of a graph. St001116The game chromatic number of a graph. 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: St001372The length of a longest cyclic run of ones of a binary word. St001415The length of the longest palindromic prefix of a binary word. St001419The length of the longest palindromic factor beginning with a one of a binary word. St001494The Alon-Tarsi number of a graph. St001580The acyclic chromatic number of a graph. St001581The achromatic number of a graph. St001670The connected partition number of a graph. St001733The number of weak left to right maxima of a Dyck path. St001883The mutual visibility 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. St001505The number of elements generated by the Dyck path as a map in the full transformation monoid. St000008The major index of the composition. St000012The area of a Dyck path. St000018The number of inversions of a permutation. St000019The cardinality of the support of a permutation. St000024The number of double up and double down steps of a Dyck path. St000028The number of stack-sorts needed to sort a permutation. St000148The number of odd parts of a partition. St000157The number of descents of a standard tableau. St000160The multiplicity of the smallest part of a partition. St000228The size of a partition. St000234The number of global ascents of a permutation. St000237The number of small exceedances. St000245The number of ascents of a permutation. St000293The number of inversions of a binary word. St000319The spin of an integer partition. St000320The dinv adjustment of an integer partition. St000340The number of non-final maximal constant sub-paths of length greater than one. St000384The maximal part of the shifted composition of an integer partition. St000394The sum of the heights of the peaks of a Dyck path minus the number of peaks. St000459The hook length of the base cell of a partition. St000475The number of parts equal to 1 in a partition. St000519The largest length of a factor maximising the subword complexity. St000548The number of different non-empty partial sums of an integer partition. St000632The jump number of the poset. St000645The sum of the areas of the rectangles formed by two consecutive peaks and the valley in between. St000778The metric dimension of a graph. St000784The maximum of the length and the largest part of the integer partition. St000867The sum of the hook lengths in the first row of an integer partition. St000996The number of exclusive left-to-right maxima of a permutation. St001090The number of pop-stack-sorts needed to sort a permutation. St001127The sum of the squares of the parts of a partition. St001189The number of simple modules with dominant and codominant dimension equal to zero in the Nakayama algebra corresponding to the Dyck path. St001382The number of boxes in the diagram of a partition that do not lie in its Durfee square. St001436The index of a given binary word in the lex-order among all its cyclic shifts. St001759The Rajchgot index of a permutation. St001918The degree of the cyclic sieving polynomial corresponding to an integer partition. St001949The rigidity index of a graph. St000013The height of a Dyck path. St000025The number of initial rises of a Dyck path. St000026The position of the first return of a Dyck path. St000032The number of elements smaller than the given Dyck path in the Tamari Order. St000058The order of a permutation. St000063The number of linear extensions of a certain poset defined for an integer partition. St000068The number of minimal elements in a poset. St000071The number of maximal chains in a poset. St000093The cardinality of a maximal independent set of vertices of a graph. St000105The number of blocks in the set partition. St000108The number of partitions contained in the given partition. St000110The number of permutations less than or equal to a permutation in left weak order. St000147The largest part of an integer partition. St000167The number of leaves of an ordered tree. St000273The domination number of a graph. St000378The diagonal inversion number of an integer partition. St000395The sum of the heights of the peaks of a Dyck path. St000460The hook length of the last cell along the main diagonal of an integer partition. St000469The distinguishing number of a graph. St000527The width of the poset. St000528The height of a poset. St000532The total number of rook placements on a Ferrers board. St000544The cop number of a graph. St000722The number of different neighbourhoods in a graph. St000723The maximal cardinality of a set of vertices with the same neighbourhood in a graph. St000733The row containing the largest entry of a standard tableau. St000738The first entry in the last row of a standard tableau. 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. St000786The maximal number of occurrences of a colour in a proper colouring of a graph. St000839The largest opener of a set partition. St000870The product of the hook lengths of the diagonal cells in an integer partition. St000876The number of factors in the Catalan decomposition of a binary word. St000877The depth of the binary word interpreted as a path. St000885The number of critical steps in the Catalan decomposition of a binary word. St000909The number of maximal chains of maximal size in a poset. St000912The number of maximal antichains in a poset. St000916The packing number of a graph. St000982The length of the longest constant subword. St001007Number of simple 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. St001020Sum of the codominant dimensions of the non-projective indecomposable injective modules of the Nakayama algebra corresponding to the Dyck path. 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. St001135The projective dimension of the first simple module in the Nakayama algebra corresponding to the Dyck path. St001268The size of the largest ordinal summand in the poset. 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. St001330The hat guessing number of a graph. St001343The dimension of the reduced incidence algebra of a poset. St001348The bounce of the parallelogram polyomino associated with the Dyck path. St001389The number of partitions of the same length below the given integer partition. St001399The distinguishing number of a poset. St001400The total number of Littlewood-Richardson tableaux of given shape. St001672The restrained domination number of a graph. St001779The order of promotion on the set of linear extensions of a poset. St001809The index of the step at the first peak of maximal height in a Dyck path. St001829The common independence number of a graph. St000326The position of the first one in a binary word after appending a 1 at the end. St000439The position of the first down step of a Dyck path. 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. St000041The number of nestings of a perfect matching. St000059The inversion number of a standard tableau as defined by Haglund and Stevens. St000081The number of edges of a graph. St000141The maximum drop size of a permutation. St000211The rank of the set partition. St000214The number of adjacencies of a permutation. St000290The major index of a binary word. St000330The (standard) major index of a standard tableau. 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. St000377The dinv defect of an integer partition. St000441The number of successions of a permutation. St000442The maximal area to the right of an up step of a Dyck path. St000445The number of rises of length 1 of a Dyck path. St000533The minimum of the number of parts and the size of the first part of an integer partition. St000546The number of global descents of a permutation. St000662The staircase size of the code of a permutation. St000672The number of minimal elements in Bruhat order not less than the permutation. St000682The Grundy value of Welter's game on a binary word. St000691The number of changes of a binary word. St000692Babson and Steingrímsson's statistic of a permutation. St000703The number of deficiencies of a permutation. St000783The side length of the largest staircase partition fitting into a partition. St000835The minimal difference in size when partitioning the integer partition into two subpartitions. St000921The number of internal inversions of a binary word. St000992The alternating sum of the parts of an integer partition. St001034The area of the parallelogram polyomino associated with the Dyck path. St001036The number of inner corners of the parallelogram polyomino associated with the Dyck path. St001055The Grundy value for the game of removing cells of a row in an integer partition. St001119The length of a shortest maximal path in a graph. St001161The major index north count of a Dyck path. St001232The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2. St001245The cyclic maximal difference between two consecutive entries of a permutation. St001340The cardinality of a minimal non-edge isolating set of a graph. St001384The number of boxes in the diagram of a partition that do not lie in the largest triangle it contains. St001392The largest nonnegative integer which is not a part and is smaller than the largest part of the partition. St001479The number of bridges of a graph. St001484The number of singletons of an integer partition. St001485The modular major index of a binary word. St001641The number of ascent tops in the flattened set partition such that all smaller elements appear before. St001702The absolute value of the determinant of the adjacency matrix of a graph. St001826The maximal number of leaves on a vertex of a graph. St001955The number of natural descents for set-valued two row standard Young tableaux. St000007The number of saliances of the permutation. St000031The number of cycles in the cycle decomposition of a permutation. St000054The first entry of the permutation. St000069The number of maximal elements of a poset. St000153The number of adjacent cycles of a permutation. St000184The size of the centralizer of any permutation of given cycle type. St000203The number of external nodes of a binary tree. St000258The burning number of a graph. St000391The sum of the positions of the ones in a binary word. St000393The number of strictly increasing runs in a binary word. St000444The length of the maximal rise of a Dyck path. St000451The length of the longest pattern of the form k 1 2. St000468The Hosoya index of a graph. St000476The sum of the semi-lengths of tunnels before a valley of a Dyck path. St000479The Ramsey number of a graph. St000482The (zero)-forcing number of a graph. St000505The biggest entry in the block containing the 1. St000507The number of ascents of a standard tableau. St000531The leading coefficient of the rook polynomial of an integer partition. St000636The hull number of a graph. St000676The number of odd rises of a Dyck path. St000693The modular (standard) major index of a standard tableau. St000700The protection number of an ordered tree. 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. St000773The multiplicity of the largest Laplacian eigenvalue in a graph. St000774The maximal multiplicity of a Laplacian eigenvalue in a graph. St000775The multiplicity of the largest eigenvalue in a graph. St000776The maximal multiplicity of an eigenvalue in a graph. St000883The number of longest increasing subsequences of a permutation. St000908The length of the shortest maximal antichain in a poset. St000917The open packing number of a graph. St000918The 2-limited packing number of a graph. St000926The clique-coclique number of a graph. St000932The number of occurrences of the pattern UDU in a Dyck path. St000971The smallest closer of a set partition. St000975The length of the boundary minus the length of the trunk of an ordered tree. St000983The length of the longest alternating subword. St000986The multiplicity of the eigenvalue zero of the adjacency matrix of the graph. St001004The number of indices that are either left-to-right maxima or right-to-left minima. 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. St001070The absolute value of the derivative of the chromatic polynomial of the graph at 1. St001267The length of the Lyndon factorization of the binary word. St001286The annihilation number of a graph. St001313The number of Dyck paths above the lattice path given by a binary word. St001315The dissociation 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. St001342The number of vertices in the center of a graph. St001360The number of covering relations in Young's lattice below a partition. St001363The Euler characteristic of a graph according to Knill. St001366The maximal multiplicity of a degree of a vertex of a graph. St001368The number of vertices of maximal degree in a graph. St001373The logarithm of the number of winning configurations of the lights out game on a graph. St001416The length of a longest palindromic factor of a binary word. St001417The length of a longest palindromic subword of a binary word. St001437The flex of a binary word. St001441The number of non-empty connected induced subgraphs of a graph. St001462The number of factors of a standard tableaux under concatenation. St001463The number of distinct columns in the nullspace of a graph. St001523The degree of symmetry of a Dyck path. St001554The number of distinct nonempty subtrees of a binary tree. St001635The trace of the square of the Coxeter matrix of the incidence algebra of a poset. St001636The number of indecomposable injective modules with projective dimension at most one in the incidence algebra of the poset. St001645The pebbling number of a connected graph. St001654The monophonic hull number of a graph. St001655The general position number of a graph. St001656The monophonic position number of a graph. St001659The number of ways to place as many non-attacking rooks as possible on a Ferrers board. St001674The number of vertices of the largest induced star graph in the graph. St001691The number of kings in a graph. St001707The length of a longest path in a graph such that the remaining vertices can be partitioned into two sets of the same size without edges between them. St001721The degree of a binary word. St001725The harmonious chromatic number of a graph. St001746The coalition number of a graph. St001784The minimum of the smallest closer and the second element of the block containing 1 in a set partition. St001800The number of 3-Catalan paths having this Dyck path as first and last coordinate projections. St001814The number of partitions interlacing the given partition. St001844The maximal degree of a generator of the invariant ring of the automorphism group of a graph. St001933The largest multiplicity of a part in an integer partition. St000300The number of independent sets of vertices of a graph. St000380Half of the maximal perimeter of a rectangle fitting into the diagram of an integer partition. St000521The number of distinct subtrees of an ordered tree. St001365The number of lattice paths of the same length weakly above the path given by a binary word. St001664The number of non-isomorphic subposets of a poset. St000806The semiperimeter of the associated bargraph. St001643The Frobenius dimension of the Nakayama algebra corresponding to the Dyck path. St000306The bounce count of a Dyck path. St000874The position of the last double rise in a Dyck path. St000984The number of boxes below precisely one peak. St001418Half of the global dimension of the stable Auslander algebra of the Nakayama algebra corresponding to the Dyck path. St000144The pyramid weight of the Dyck path. St000617The number of global maxima of a Dyck path. St000668The least common multiple of the parts of the partition. St000675The number of centered multitunnels of a Dyck path. St000678The number of up steps after the last double rise of a Dyck path. St000708The product of the parts of an integer partition. St000925The number of topologically connected components of a set partition. St001018Sum of projective dimension of the indecomposable injective modules of the Nakayama algebra corresponding to the Dyck path. St001717The largest size of an interval in a poset. 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. St001190Number of simple modules with projective dimension at most 4 in the corresponding Nakayama algebra. St001240The number of indecomposable modules e_i J^2 that have injective dimension at most one in the corresponding Nakayama algebra St001650The order of Ringel's homological bijection associated to the linear Nakayama algebra corresponding to the Dyck path. St000967The value p(1) for the Coxeterpolynomial p of the corresponding LNakayama algebra. St001218Smallest index k greater than or equal to one such that the Coxeter matrix C of the corresponding Nakayama algebra has C^k=1. St000052The number of valleys of a Dyck path not on the x-axis. St000209Maximum difference of elements in cycles. St000261The edge connectivity of a graph. St000262The vertex connectivity of a graph. St000310The minimal degree of a vertex of a graph. St000419The number of Dyck paths that are weakly above the Dyck path, except for the path itself. St000446The disorder of a permutation. St000502The number of successions of a set partitions. St000503The maximal difference between two elements in a common block. St000674The number of hills of a Dyck path. St000728The dimension of a set partition. St000730The maximal arc length of a set partition. St000741The Colin de Verdière graph invariant. St000868The aid statistic in the sense of Shareshian-Wachs. St000946The sum of the skew hook positions in a Dyck path. St000947The major index east count of a Dyck path. St001033The normalized area of the parallelogram polyomino associated with the Dyck path. St001270The bandwidth of a graph. St001277The degeneracy of a graph. St001300The rank of the boundary operator in degree 1 of the chain complex of the order complex of the poset. St001357The maximal degree of a regular spanning subgraph of a graph. St001358The largest degree of a regular subgraph of a graph. St001391The disjunction number of a graph. 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. St001671Haglund's hag of a permutation. St001723The differential of a graph. St001724The 2-packing differential of a graph. St001726The number of visible inversions of a permutation. St001958The degree of the polynomial interpolating the values of a permutation. St001962The proper pathwidth of a graph. St000050The depth or height of a binary tree. St000087The number of induced subgraphs. St000189The number of elements in the poset. St000229Sum of the difference between the maximal and the minimal elements of the blocks plus the number of blocks of a set partition. St000286The number of connected components of the complement of a graph. St000287The number of connected components of a graph. St000309The number of vertices with even degree. St000315The number of isolated vertices of a graph. St000318The number of addable cells of the Ferrers diagram of an integer partition. St000336The leg major index of a standard tableau. St000420The number of Dyck paths that are weakly above a Dyck path. St000504The cardinality of the first block of a set partition. St000553The number of blocks of a graph. St000729The minimal arc length of a set partition. St000740The last entry of a permutation. St000822The Hadwiger number of the graph. St000823The number of unsplittable factors of the set partition. St000863The length of the first row of the shifted shape of a permutation. St000875The semilength of the longest Dyck word in the Catalan factorisation of a binary word. 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. St001062The maximal size of a block of a set partition. St001183The maximum of $projdim(S)+injdim(S)$ over all simple modules in the Nakayama algebra corresponding to the Dyck path. St001258Gives the maximum of injective plus projective dimension of an indecomposable module over the corresponding Nakayama algebra. St001302The number of minimally dominating sets of vertices of a graph. St001304The number of maximally independent sets of vertices of a graph. St001316The domatic number of a graph. St001461The number of topologically connected components of the chord diagram of a permutation. St001464The number of bases of the positroid corresponding to the permutation, with all fixed points counterclockwise. St001808The box weight or horizontal decoration of a Dyck path. St001828The Euler characteristic of a graph. St001963The tree-depth of a graph. St000180The number of chains of a poset. St000301The number of facets of the stable set polytope of a graph. St000718The largest Laplacian eigenvalue of a graph if it is integral. St001237The number of simple modules with injective dimension at most one or dominant dimension at least one. St001298The number of repeated entries in the Lehmer code of a permutation. St000717The number of ordinal summands of a poset. St000906The length of the shortest maximal chain in a poset. St001497The position of the largest weak excedence of a permutation. St000643The size of the largest orbit of antichains under Panyushev complementation. St000653The last descent of a permutation. St000794The mak of a permutation. St000797The stat`` of a permutation. St000798The makl of a permutation. St000809The reduced reflection length of the permutation. St000956The maximal displacement of a permutation. St000957The number of Bruhat lower covers of a permutation. St001076The minimal length of a factorization of a permutation into transpositions that are cyclic shifts of (12). St001489The maximum of the number of descents and the number of inverse descents. St001498The normalised height of a Nakayama algebra with magnitude 1. St001925The minimal number of zeros in a row of an alternating sign matrix. St000100The number of linear extensions of a poset. St000308The height of the tree associated to a permutation. St000470The number of runs in a permutation. St000485The length of the longest cycle of a permutation. St000654The first descent of a permutation. St000702The number of weak deficiencies of a permutation. St000844The size of the largest block in the direct sum decomposition of a permutation. St001786The number of total orderings of the north steps of a Dyck path such that steps after the k-th east step are not among the first k positions in the order. St001812The biclique partition number of a graph. St000727The largest label of a leaf in the binary search tree associated with the permutation. St000159The number of distinct parts of the integer partition. St000161The sum of the sizes of the right subtrees of a binary tree. St000354The number of recoils of a permutation. St000356The number of occurrences of the pattern 13-2. St000795The mad of a permutation. St000829The Ulam distance of a permutation to the identity permutation. St000831The number of indices that are either descents or recoils. St000833The comajor index of a permutation. St000989The number of final rises of a permutation. St001061The number of indices that are both descents and recoils of a permutation. St001083The number of boxed occurrences of 132 in a permutation. St001091The number of parts in an integer partition whose next smaller part has the same size. St000006The dinv of a Dyck path. St000029The depth of a permutation. St000030The sum of the descent differences of a permutations. St000181The number of connected components of the Hasse diagram for the poset. St000197The number of entries equal to positive one in the alternating sign matrix. St000210Minimum over maximum difference of elements in cycles. St000216The absolute length of a permutation. St000651The maximal size of a rise in a permutation. St000667The greatest common divisor of the parts of the partition. St000780The size of the orbit under rotation of a perfect matching. St000924The number of topologically connected components of a perfect matching. St001077The prefix exchange distance of a permutation. St001246The maximal difference between two consecutive entries of a permutation. St001480The number of simple summands of the module J^2/J^3. St000111The sum of the descent tops (or Genocchi descents) of a permutation. St000487The length of the shortest cycle of a permutation. St000501The size of the first part in the decomposition of a permutation. St000673The number of non-fixed points 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. St001834The number of non-isomorphic minors of a graph. St001468The smallest fixpoint of a permutation. St000246The number of non-inversions of a permutation. St000247The number of singleton blocks of a set partition. St000359The number of occurrences of the pattern 23-1. St000366The number of double descents of a permutation. St000371The number of mid points of decreasing subsequences of length 3 in a permutation. St000497The lcb statistic of a set partition. St000572The dimension exponent of a set partition. St000585The number of occurrences of the pattern {{1,3},{2}} such that 2 is maximal, (1,3) are consecutive in a block. St000594The number of occurrences of the pattern {{1,3},{2}} such that 1,2 are minimal, (1,3) are consecutive in a block. St000600The number of occurrences of the pattern {{1,3},{2}} such that 1 is minimal, (1,3) are consecutive in a block. St000731The number of double exceedences of a permutation. St000695The number of blocks in the first part of the atomic decomposition of a set partition. St000770The major index of an integer partition when read from bottom to top. St000914The sum of the values of the Möbius function of a poset. St000945The number of matchings in the dihedral orbit of a perfect matching. St000993The multiplicity of the largest part of an integer partition. St000065The number of entries equal to -1 in an alternating sign matrix. St000742The number of big ascents of a permutation after prepending zero. St001397Number of pairs of incomparable elements in a finite poset. St001584The area statistic between a Dyck path and its bounce path. St000292The number of ascents of a binary word. St000864The number of circled entries of the shifted recording tableau of a permutation. St000164The number of short pairs. St000291The number of descents of a binary word. St000390The number of runs of ones in a binary word. St000542The number of left-to-right-minima of a permutation. St000843The decomposition number of a perfect matching. 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. St000067The inversion number of the alternating sign matrix. St000332The positive inversions of an alternating sign matrix. St000369The dinv deficit of a Dyck path. St000648The number of 2-excedences of a permutation. St001046The maximal number of arcs nesting a given arc of a perfect matching. St001427The number of descents of a signed permutation. St001640The number of ascent tops in the permutation such that all smaller elements appear before. St001907The number of Bastidas - Hohlweg - Saliola excedances of a signed permutation. St000066The column of the unique '1' in the first row of the alternating sign matrix. St000213The number of weak exceedances (also weak excedences) of a permutation. St000314The number of left-to-right-maxima of a permutation. St000339The maf index of a permutation. St000628The balance of a binary word. St000720The size of the largest partition in the oscillating tableau corresponding to the perfect matching. St000744The length of the path to the largest entry in a standard Young tableau. St000838The number of terminal right-hand endpoints when the vertices are written in order. St001652The length of a longest interval of consecutive numbers. St001662The length of the longest factor of consecutive numbers in a permutation. St001778The largest greatest common divisor of an element and its image in a permutation. St000044The number of vertices of the unicellular map given by a perfect matching. St001291The number of indecomposable summands of the tensor product of two copies of the dual of the Nakayama algebra associated to a Dyck path. St001235The global dimension of the corresponding Comp-Nakayama algebra. St000331The number of upper interactions of a Dyck path. 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. St001199The dominant dimension of $eAe$ for the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. St001205The number of non-simple indecomposable projective-injective modules of the algebra $eAe$ in the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. St001223Number of indecomposable projective non-injective modules P such that the modules X and Y in a an Auslander-Reiten sequence ending at P are torsionless. St001225The vector space dimension of the first extension group between J and itself when J is the Jacobson radical of the corresponding Nakayama algebra. St001278The number of indecomposable modules that are fixed by $\tau \Omega^1$ composed with its inverse in the corresponding Nakayama algebra. St001294The maximal torsionfree index of a simple non-projective module in the corresponding Nakayama algebra. St001296The maximal torsionfree index of an indecomposable non-projective module in the corresponding Nakayama algebra. St001509The degree of the standard monomial associated to a Dyck path relative to the trivial lower boundary. St000015The number of peaks of a Dyck path. St000930The k-Gorenstein degree of the corresponding Nakayama algebra with linear quiver. St001024Maximum of dominant dimensions of the simple modules in the Nakayama 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. St001530The depth of a Dyck path. St001290The first natural number n such that the tensor product of n copies of D(A) is zero for the corresponding Nakayama algebra A. St000004The major index of a permutation. St000021The number of descents of a permutation. St000051The size of the left subtree of a binary tree. St000080The rank of the poset. St000155The number of exceedances (also excedences) of a permutation. St000224The sorting index of a permutation. St000316The number of non-left-to-right-maxima of a permutation. St000329The number of evenly positioned ascents of the Dyck path, with the initial position equal to 1. St000541The number of indices greater than or equal to 2 of a permutation such that all smaller indices appear to its right. St001233The number of indecomposable 2-dimensional modules with projective dimension one. 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. 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. St001508The degree of the standard monomial associated to a Dyck path relative to the diagonal boundary. St000056The decomposition (or block) number of a permutation. St000062The length of the longest increasing subsequence of the permutation. St000084The number of subtrees. St000239The number of small weak excedances. 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. St000443The number of long tunnels of a Dyck path. St000910The number of maximal chains of minimal length in a poset. 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. St001014Number of indecomposable injective modules with codominant dimension equal to the dominant dimension of the Nakayama algebra corresponding to the Dyck path. 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. 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. St001224Let X be the direct sum of all simple modules of 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. St001390The number of bumps occurring when Schensted-inserting the letter 1 of a permutation. St001481The minimal height of a peak of a Dyck path. St001499The number of indecomposable projective-injective modules of a magnitude 1 Nakayama algebra. St001714The number of subpartitions of an integer partition that do not dominate the conjugate subpartition. St001180Number of indecomposable injective modules with projective dimension at most 1. 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. St000656The number of cuts of a poset. St000005The bounce statistic of a Dyck path. St000057The Shynar inversion number of a standard tableau. St000076The rank of the alternating sign matrix in the alternating sign matrix poset. St000089The absolute variation of a composition. St000090The variation of a composition. St000091The descent variation of a composition. St000120The number of left tunnels of a Dyck path. St000133The "bounce" of a permutation. St000145The Dyson rank of a partition. St000154The sum of the descent bottoms of a permutation. St000156The Denert index of a permutation. St000168The number of internal nodes of an ordered tree. St000204The number of internal nodes of a binary tree. St000238The number of indices that are not small weak excedances. St000296The length of the symmetric border of a binary word. St000305The inverse major index of a permutation. St000333The dez statistic, the number of descents of a permutation after replacing fixed points by zeros. St000334The maz index, the major index of a permutation after replacing fixed points by zeros. 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. St000539The number of odd inversions of a permutation. St000627The exponent of a binary word. St000681The Grundy value of Chomp on Ferrers diagrams. St000688The global dimension minus the dominant dimension of the LNakayama algebra associated to a Dyck path. St000796The stat' of a permutation. St000834The number of right outer peaks of a permutation. St000871The number of very big ascents of a permutation. St000878The number of ones minus the number of zeros of a binary word. St000922The minimal number such that all substrings of this length are unique. St000931The number of occurrences of the pattern UUU in a Dyck path. St000970Number of peaks minus the dominant dimension of the corresponding LNakayama algebra. 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. St001066The number of simple reflexive modules in the corresponding Nakayama algebra. St001086The number of occurrences of the consecutive pattern 132 in a permutation. St001117The game chromatic index of a graph. St001118The acyclic chromatic index of a graph. St001126Number of simple module that are 1-regular in the corresponding Nakayama algebra. St001167The number of simple modules that appear as the top of an indecomposable non-projective modules that is reflexive in the corresponding Nakayama algebra. St001172The number of 1-rises at odd height of a Dyck path. St001185The number of indecomposable injective modules of grade at least 2 in the corresponding Nakayama algebra. St001192The maximal dimension of $Ext_A^2(S,A)$ for a simple module $S$ over the corresponding Nakayama algebra $A$. St001215Let X be the direct sum of all simple modules of the corresponding Nakayama algebra. St001216The number of indecomposable injective modules in the corresponding Nakayama algebra that have non-vanishing second Ext-group with the regular module. St001253The number of non-projective indecomposable reflexive modules in the corresponding Nakayama algebra. St001274The number of indecomposable injective modules with projective dimension equal to two. St001387Number of standard Young tableaux of the skew shape tracing the border of the given partition. St001428The number of B-inversions of a signed permutation. St001483The number of simple module modules that appear in the socle of the regular module but have no nontrivial selfextensions with the regular module. St001527The cyclic permutation representation number of an integer partition. St001571The Cartan determinant of the integer partition. St001660The number of ways to place as many non-attacking rooks as possible on a skew Ferrers board. St001781The interlacing number of a set partition. St001816Eigenvalues of the top-to-random operator acting on a simple module. St001841The number of inversions of a set partition. St001843The Z-index of a set partition. St001869The maximum cut size of a graph. St001884The number of borders of a binary word. St000035The number of left outer peaks of a permutation. St000086The number of subgraphs. St000166The depth minus 1 of an ordered tree. St000240The number of indices that are not small excedances. St000294The number of distinct factors of a binary word. St000295The length of the border of a binary word. St000299The number of nonisomorphic vertex-induced subtrees. St000376The bounce deficit of a Dyck path. St000389The number of runs of ones of odd length in a binary word. St000518The number of distinct subsequences in a binary word. St000529The number of permutations whose descent word is the given binary word. St000543The size of the conjugacy class of a binary word. St000625The sum of the minimal distances to a greater element. St000626The minimal period of a binary word. St000638The number of up-down runs of a permutation. St000639The number of relations in a poset. St000641The number of non-empty boolean intervals in a poset. St000724The label of the leaf of the path following the smaller label in the increasing binary tree associated to a permutation. St000771The largest multiplicity of a distance Laplacian eigenvalue in a connected graph. St000772The multiplicity of the largest distance Laplacian eigenvalue in a connected graph. St000837The number of ascents of distance 2 of a permutation. St000846The maximal number of elements covering an element of a poset. St000887The maximal number of nonzero entries on a diagonal of a permutation 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. St000990The first ascent of a permutation. St001074The number of inversions of the cyclic embedding of a permutation. St001102The number of words with multiplicities of the letters given by the composition, avoiding the consecutive pattern 132. St001211The number of simple modules in the corresponding Nakayama algebra that have vanishing second Ext-group with the regular module. 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. St001312Number of parabolic noncrossing partitions indexed by the composition. St001465The number of adjacent transpositions in the cycle decomposition of a permutation. St001492The number of simple modules that do not appear in the socle of the regular module or have no nontrivial selfextensions with the regular module in the corresponding Nakayama algebra. St001658The total number of rook placements on a Ferrers board. St001675The number of parts equal to the part in the reversed composition. St001693The excess length of a longest path consisting of elements and blocks of a set partition. St001803The maximal overlap of the cylindrical tableau associated with a tableau. St000094The depth of an ordered tree. St000438The position of the last up step in a 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. St001838The number of nonempty primitive factors of a binary word. St000083The number of left oriented leafs of a binary tree except the first one. St000061The number of nodes on the left branch of a binary tree. St001959The product of the heights of the peaks of a Dyck path. St000022The number of fixed points of a permutation. St000060The greater neighbor of the maximum. St000462The major index minus the number of excedences of a permutation. St000530The number of permutations with the same descent word as the given permutation. St000619The number of cyclic descents of a permutation. St000873The aix statistic of a permutation. 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. 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. St001331The size of the minimal feedback vertex set. St001336The minimal number of vertices in a graph whose complement is triangle-free. St001377The major index minus the number of inversions of a permutation. St001685The number of distinct positions of the pattern letter 1 in occurrences of 132 in a permutation. St001810The number of fixed points of a permutation smaller than its largest moved point. St001911A descent variant minus the number of inversions. St000014The number of parking functions supported by a Dyck path. St000082The number of elements smaller than a binary tree in Tamari order. St000225Difference between largest and smallest parts in a partition. St000280The size of the preimage of the map 'to labelling permutation' from Parking functions to Permutations. St001008Number of indecomposable injective modules with projective dimension 1 in the Nakayama algebra corresponding to the Dyck path. St001010Number of indecomposable injective modules with projective dimension g-1 when g is the global dimension of 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. St001164Number of indecomposable injective modules whose socle has projective dimension at most g-1 (g the global dimension) minus the number of indecomposable projective-injective modules. 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. St001264The smallest index i such that the i-th simple module has projective dimension equal to the global dimension of the corresponding Nakayama algebra. St001280The number of parts of an integer partition that are at least two. St001346The number of parking functions that give the same 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. St001019Sum of the projective dimensions of the simple modules in the Nakayama algebra corresponding to the Dyck path. St001458The rank of the adjacency matrix of a graph. St001459The number of zero columns in the nullspace of a graph. St001213The number of indecomposable modules in the corresponding Nakayama algebra that have vanishing first Ext-group with the regular module. St001259The vector space dimension of the double dual of D(A) in the corresponding Nakayama algebra. St001706The number of closed sets in a graph. St000840The number of closers smaller than the largest opener in a perfect matching. St001323The independence gap of a graph. St000890The number of nonzero entries in an alternating sign matrix. St000327The number of cover relations in a poset. St001000Number of indecomposable modules with projective dimension equal to the global dimension in the Nakayama algebra corresponding to the Dyck path. St001432The order dimension of the partition. St001491The number of indecomposable projective-injective modules in the algebra corresponding to a subset. St001515The vector space dimension of the socle of the first syzygy module of the regular module (as a bimodule). St000075The orbit size of a standard tableau under promotion. St000652The maximal difference between successive positions of a permutation. St000474Dyson's crank of a partition. 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. St000355The number of occurrences of the pattern 21-3. St000426The number of occurrences of the pattern 132 or of the pattern 312 in a permutation. St000437The number of occurrences of the pattern 312 or of the pattern 321 in a permutation. St000538The number of even inversions of a permutation. St000711The number of big exceedences of a permutation. St000799The number of occurrences of the vincular pattern |213 in a permutation. St000961The shifted major index of a permutation. 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. St000988The orbit size of a permutation under Foata's bijection. St000317The cycle descent number of a permutation. St000358The number of occurrences of the pattern 31-2. St000452The number of distinct eigenvalues of a graph. St000453The number of distinct Laplacian eigenvalues of a graph. St000732The number of double deficiencies of a permutation. St000777The number of distinct eigenvalues of the distance Laplacian of a connected graph. St001093The detour number of a graph. St001229The vector space dimension of the first extension group between the Jacobson radical J and J^2. St001431Half of the Loewy length minus one of a modified stable Auslander algebra of the Nakayama algebra corresponding to the Dyck path. St001684The reduced word complexity of a permutation. St001716The 1-improper chromatic number of a graph. St001727The number of invisible inversions of a permutation. St001742The difference of the maximal and the minimal degree in a graph. 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. St000259The diameter of a connected graph. St000260The radius of a connected graph. St001124The multiplicity of the standard representation in the Kronecker square corresponding to a partition. St001271The competition number of a graph. St001512The minimum rank of a graph. St001638The book thickness of a graph. St000039The number of crossings of a permutation. St000217The number of occurrences of the pattern 312 in a permutation. St000221The number of strong fixed points of a permutation. St000222The number of alignments in the permutation. St000338The number of pixed points of a permutation. St000430The number of occurrences of the pattern 123 or of the pattern 312 in a permutation. St000436The number of occurrences of the pattern 231 or of the pattern 321 in a permutation. St000477The weight of a partition according to Alladi. St000710The number of big deficiencies of a permutation. St000800The number of occurrences of the vincular pattern |231 in a permutation. St000801The number of occurrences of the vincular pattern |312 in a permutation. St000980The number of boxes weakly below the path and above the diagonal that lie below at least two peaks. St001021Sum of the differences between projective and codominant dimension of the non-projective indecomposable injective modules in the Nakayama algebra corresponding to the Dyck path. St001089Number of indecomposable projective non-injective modules minus the number of indecomposable projective non-injective modules with dominant dimension equal to the injective dimension in the corresponding Nakayama algebra. St001152The number of pairs with even minimum in a perfect matching. St001163The number of simple modules with dominant dimension at least three in the corresponding Nakayama algebra. St001219Number of simple modules S in the corresponding Nakayama algebra such that the Auslander-Reiten sequence ending at S has the property that all modules in the exact sequence are reflexive. St001231The number of simple modules that are non-projective and non-injective with the property that they have projective dimension equal to one and that also the Auslander-Reiten translates of the module and the inverse Auslander-Reiten translate of the module have the same projective dimension. St001234The number of indecomposable three dimensional modules with projective dimension one. St001238The number of simple modules S such that the Auslander-Reiten translate of S is isomorphic to the Nakayama functor applied to the second syzygy of S. St001642The Prague dimension of a graph. 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. St001744The number of occurrences of the arrow pattern 1-2 with an arrow from 1 to 2 in a permutation. St000193The row of the unique '1' in the first column of the alternating sign matrix. St000304The load of a permutation. St000714The number of semistandard Young tableau of given shape, with entries at most 2. St001037The number of inner corners of the upper path of the parallelogram polyomino associated with the Dyck path. St001555The order of a signed permutation. St001589The nesting number of a perfect matching. St000236The number of cyclical small weak excedances. St001032The number of horizontal steps in the bicoloured Motzkin path associated with the Dyck path. St001182Number of indecomposable injective modules with codominant dimension at least two in the corresponding Nakayama algebra. St001255The vector space dimension of the double dual of A/J when A is the corresponding Nakayama algebra with Jacobson radical J. St001668The number of points of the poset minus the width of the poset. St001948The number of augmented double ascents of a permutation. St001570The minimal number of edges to add to make a graph Hamiltonian. St000898The number of maximal entries in the last diagonal of the monotone triangle. St001060The distinguishing index of a graph. St001863The number of weak excedances of a signed permutation. St001889The size of the connectivity set of a signed permutation. St000466The Gutman (or modified Schultz) index of a connected graph. St001123The multiplicity of the dual of the standard representation in the Kronecker square corresponding to a partition. St001651The Frankl number of a lattice. St001592The maximal number of simple paths between any two different vertices of a graph. St001769The reflection length of a signed permutation. St001861The number of Bruhat lower covers of a permutation. St001864The number of excedances of a signed permutation. St001894The depth of a signed permutation. St001896The number of right descents of a signed permutations. St001855The number of signed permutations less than or equal to a signed permutation in left weak order. St001712The number of natural descents of a standard Young tableau. St001355Number of non-empty prefixes of a binary word that contain equally many 0's and 1's. St001188The number of simple modules $S$ with grade $\inf \{ i \geq 0 | Ext^i(S,A) \neq 0 \}$ at least two in the Nakayama algebra $A$ corresponding to the Dyck path. St001244The number of simple modules of projective dimension one that are not 1-regular for the Nakayama algebra associated to a Dyck path. St001314The number of tilting modules of arbitrary projective dimension that have no simple modules as a direct summand in the corresponding Nakayama algebra. St001557The number of inversions of the second entry of a permutation. St001804The minimal height of the rectangular inner shape in a cylindrical tableau associated to a tableau. St001811The Castelnuovo-Mumford regularity of a permutation. St001821The sorting index of a signed permutation. St001960The number of descents of a permutation minus one if its first entry is not one. St000670The reversal length of a permutation. St001514The dimension of the top of the Auslander-Reiten translate of the regular modules as a bimodule. St001773The number of minimal elements in Bruhat order not less than the signed permutation. St000937The number of positive values of the symmetric group character corresponding to the partition. St001526The Loewy length of the Auslander-Reiten translate of the regular module as a bimodule of the Nakayama algebra corresponding to the Dyck path. St001207The Lowey length of the algebra $A/T$ when $T$ is the 1-tilting module corresponding to the permutation in the Auslander algebra of $K[x]/(x^n)$. St001704The size of the largest multi-subset-intersection of the deck of a graph with the deck of another graph. St000455The second largest eigenvalue of a graph if it is integral. St001583The projective dimension of the simple module corresponding to the point in the poset of the symmetric group under bruhat order. St001096The size of the overlap set of a permutation. 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 $eA$. St000302The determinant of the distance matrix of a connected graph. St000467The hyper-Wiener index of a connected graph. St000023The number of inner peaks of a permutation. St000353The number of inner valleys of a permutation. St000486The number of cycles of length at least 3 of a permutation. St000646The number of big ascents of a permutation. St000663The number of right floats of a permutation. St000699The toughness times the least common multiple of 1,. St000866The number of admissible inversions of a permutation in the sense of Shareshian-Wachs. St001388The number of non-attacking neighbors of a permutation. St001469The holeyness of a permutation. St001470The cyclic holeyness of a permutation. St000092The number of outer peaks of a permutation. St000099The number of valleys of a permutation, including the boundary. St000456The monochromatic index of a connected graph. 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 $eA$. St001632The number of indecomposable injective modules $I$ with $dim Ext^1(I,A)=1$ for the incidence algebra A of a poset. St001665The number of pure excedances of a permutation. St001737The number of descents of type 2 in a permutation. St001859The number of factors of the Stanley symmetric function associated with a permutation. St000824The sum of the number of descents and the number of recoils of a permutation. St001630The global dimension of the incidence algebra of the lattice over the rational numbers. St001878The projective dimension of the simple modules corresponding to the minimum of L in the incidence algebra of the lattice L. 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. St001880The number of 2-Gorenstein indecomposable injective modules in the incidence algebra of the lattice. St001875The number of simple modules with projective dimension at most 1. St001877Number of indecomposable injective modules with projective dimension 2. St001545The second Elser number of a connected graph. St000464The Schultz index of a connected graph. St000782The indicator function of whether a given perfect matching is an L & P matching. St001582The grades of the simple modules corresponding to the points in the poset of the symmetric group under the Bruhat order. St001208The number of connected components of the quiver of $A/T$ when $T$ is the 1-tilting module corresponding to the permutation in the Auslander algebra $A$ of $K[x]/(x^n)$. St001722The number of minimal chains with small intervals between a binary word and the top element.