St000081The number of edges of a graph. 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. St000548The number of different non-empty partial sums of an integer partition. St000987The number of positive eigenvalues of the Laplacian matrix of the graph. St000998Number of indecomposable projective modules with injective dimension smaller than or equal to the dominant dimension in the Nakayama algebra corresponding to the Dyck path. St001012Number of simple modules with projective dimension at most 2 in the Nakayama algebra corresponding to the Dyck path. St001034The area of the parallelogram polyomino associated with the Dyck path. St001479The number of bridges of a graph. 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. St000007The number of saliances of the permutation. St000010The length of the partition. St000054The first entry of the permutation. St000215The number of adjacencies of a permutation, zero appended. St000293The number of inversions of a binary word. St000460The hook length of the last cell along the main diagonal of an integer partition. 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. St000883The number of longest increasing subsequences of a permutation. St001342The number of vertices in the center of a graph. St001527The cyclic permutation representation number of an integer partition. St001622The number of join-irreducible elements of a lattice. St001645The pebbling number of a connected 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. St001746The coalition number of a graph. St000019The cardinality of the support of a permutation. St000141The maximum drop size of a permutation. St000171The degree of the graph. St000214The number of adjacencies of a permutation. St000546The number of global descents of a permutation. St000645The sum of the areas of the rectangles formed by two consecutive peaks and the valley in between. St000662The staircase size of the code of a permutation. St001096The size of the overlap set of a permutation. St001120The length of a longest path in a graph. St001279The sum of the parts of an integer partition that are at least two. 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. St001641The number of ascent tops in the flattened set partition such that all smaller elements appear before. 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. 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. St000967The value p(1) for the Coxeterpolynomial p of the corresponding LNakayama algebra. St001018Sum of projective dimension of the indecomposable injective modules of the Nakayama algebra corresponding to the Dyck path. 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. St001218Smallest index k greater than or equal to one such that the Coxeter matrix C of the corresponding Nakayama algebra has C^k=1. St001291The number of indecomposable summands of the tensor product of two copies of the dual of the Nakayama algebra associated to a Dyck path. 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. St001958The degree of the polynomial interpolating the values of a permutation. St000167The number of leaves of an ordered tree. 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. 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. St001237The number of simple modules with injective dimension at most one or dominant dimension at least one. St000028The number of stack-sorts needed to sort a permutation. St000031The number of cycles in the cycle decomposition of a permutation. St000093The cardinality of a maximal independent set of vertices of a graph. 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. 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. St000703The number of deficiencies of a permutation. St000733The row containing the largest entry of a standard tableau. St000740The last entry of a permutation. St000743The number of entries in a standard Young tableau such that the next integer is a neighbour. 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. 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. St001052The length of the exterior of a permutation. 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. St001497The position of the largest weak excedence of a permutation. 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. St000051The size of the left subtree of a binary tree. St000209Maximum difference of elements in cycles. St000316The number of non-left-to-right-maxima of a permutation. St000533The minimum of the number of parts and the size of the first part of an integer partition. St001225The vector space dimension of the first extension group between J and itself when J is the Jacobson radical of the corresponding Nakayama algebra. 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. 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. St001827The number of two-component spanning forests of a graph. St001869The maximum cut size of a graph. St000068The number of minimal elements in a poset. St000071The number of maximal chains in a poset. St000294The number of distinct factors of a binary word. St000312The number of leaves in a graph. St000326The position of the first one in a binary word after appending a 1 at the end. St000452The number of distinct eigenvalues of a graph. St000518The number of distinct subsequences in a binary word. St000527The width of the poset. St000718The largest Laplacian eigenvalue of a graph if it is integral. St000050The depth or height of a binary tree. St000066The column of the unique '1' in the first row of the alternating sign matrix. St000240The number of indices that are not small excedances. St000271The chromatic index of a graph. St000296The length of the symmetric border of a binary word. St000381The largest part of an integer composition. St000382The first part of an integer composition. St000383The last part of an integer composition. St000393The number of strictly increasing runs in a binary word. St000476The sum of the semi-lengths of tunnels before a valley of a Dyck path. St000543The size of the conjugacy class of a binary word. St000547The number of even non-empty partial sums of an integer partition. St000549The number of odd partial sums of an integer partition. 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. St000657The smallest part of an integer composition. St000698The number of 2-rim hooks removed from an integer partition to obtain its associated 2-core. St000722The number of different neighbourhoods in a graph. St000728The dimension of a set partition. St000757The length of the longest weakly inreasing subsequence of parts of an integer composition. St000765The number of weak records in an integer composition. St000806The semiperimeter of the associated bargraph. St000808The number of up steps of the associated bargraph. St000826The stopping time of the decimal representation of the binary word for the 3x+1 problem. 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. St000877The depth of the binary word interpreted as a path. St000885The number of critical steps in the Catalan decomposition of a binary word. 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. St000922The minimal number such that all substrings of this length are unique. St000982The length of the longest constant subword. St001118The acyclic chromatic index of a graph. St001176The size of a partition minus its first part. St001235The global dimension of the corresponding Comp-Nakayama algebra. St001236The dominant dimension of the corresponding Comp-Nakayama algebra. St001249Sum of the odd parts of a partition. St001252Half the sum of the even parts of a partition. St001255The vector space dimension of the double dual of A/J when A is the corresponding Nakayama algebra with Jacobson radical J. St001267The length of the Lyndon factorization of the binary word. St001268The size of the largest ordinal summand in the poset. St001348The bounce of the parallelogram polyomino associated with the Dyck path. St001371The length of the longest Yamanouchi prefix of a binary word. St001415The length of the longest palindromic prefix of a binary word. St001416The length of a longest palindromic factor of a binary word. St001417The length of a longest palindromic subword of a binary word. St001437The flex of a binary word. St001523The degree of symmetry of a Dyck path. St001554The number of distinct nonempty subtrees of a binary tree. St001643The Frobenius dimension of the Nakayama algebra corresponding to the Dyck path. St001654The monophonic hull number of a graph. St001655The general position number of a graph. St001656The monophonic position number of a graph. St001672The restrained domination number of a graph. St001675The number of parts equal to the part in the reversed composition. St001725The harmonious chromatic 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. St001884The number of borders of a binary word. St000018The number of inversions of a permutation. 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. St000133The "bounce" of a permutation. St000210Minimum over maximum difference of elements in cycles. St000235The number of indices that are not cyclical small weak excedances. St000238The number of indices that are not small weak excedances. St000295The length of the border of a binary word. St000463The number of admissible inversions of a permutation. St000519The largest length of a factor maximising the subword complexity. St000651The maximal size of a rise in a permutation. St000921The number of internal inversions of a binary word. St001032The number of horizontal steps in the bicoloured Motzkin path associated with the Dyck path. St001090The number of pop-stack-sorts needed to sort a permutation. St001232The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2. 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. St001436The index of a given binary word in the lex-order among all its cyclic shifts. 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. St001721The degree of a binary word. St001723The differential of a graph. St001724The 2-packing differential of a graph. St001777The number of weak descents in an integer composition. St001925The minimal number of zeros in a row of an alternating sign matrix. St001955The number of natural descents for set-valued two row standard Young tableaux. St000250The number of blocks (St000105) plus the number of antisingletons (St000248) of a set partition. St000673The number of non-fixed points of a permutation. 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. St001005The number of indices for a permutation that are either left-to-right maxima or right-to-left minima but not both. 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. St000354The number of recoils of a permutation. 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. St000438The position of the last up step in a Dyck path. St000625The sum of the minimal distances to a greater element. St000656The number of cuts of a poset. St000770The major index of an integer partition when read from bottom to top. St000064The number of one-box pattern 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. St000724The label of the leaf of the path following the smaller label in the increasing binary tree associated to a permutation. St000794The mak of a permutation. St000874The position of the last double rise in a Dyck path. St000890The number of nonzero entries in an alternating sign matrix. St000924The number of topologically connected components of a perfect matching. St001074The number of inversions of the cyclic embedding of a permutation. St000060The greater neighbor of the maximum. St000197The number of entries equal to positive one in the alternating sign matrix. St000216The absolute length 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. St000619The number of cyclic descents of a permutation. St000652The maximal difference between successive positions of a permutation. St000672The number of minimal elements in Bruhat order not less than the permutation. St000726The normalized sum of the leaf labels of the increasing binary tree associated to a permutation. St000795The mad of a permutation. St000809The reduced reflection length of the permutation. St000831The number of indices that are either descents or recoils. St000840The number of closers smaller than the largest opener in a perfect matching. St000957The number of Bruhat lower covers of a permutation. St000961The shifted major index 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. St001516The number of cyclic bonds of a permutation. St000442The maximal area to the right of an up step of a Dyck path. St000730The maximal arc length of a set partition. St000800The number of occurrences of the vincular pattern |231 in a permutation. St000836The number of descents of distance 2 of a permutation. St001061The number of indices that are both descents and recoils of a permutation. St001082The number of boxed occurrences of 123 in a permutation. St001372The length of a longest cyclic run of ones of a binary word. St000878The number of ones minus the number of zeros of a binary word. St001557The number of inversions of the second entry of a permutation. St000308The height of the tree associated to a permutation. St000246The number of non-inversions of a permutation. St000245The number of ascents of a permutation. St001298The number of repeated entries in the Lehmer code of a permutation. 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. St000258The burning number of a graph. St000273The domination number of a graph. St000482The (zero)-forcing number of a graph. St000544The cop number of a graph. St000774The maximal multiplicity of a Laplacian eigenvalue in a graph. St000786The maximal number of occurrences of a colour in a proper colouring of a graph. St000916The packing number of a graph. St001093The detour 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. St001363The Euler characteristic of a graph according to Knill. St001373The logarithm of the number of winning configurations of the lights out game on a graph. St001463The number of distinct columns in the nullspace of a graph. St001829The common independence number of a graph. St000259The diameter of a connected graph. St000778The metric dimension of a graph. St001340The cardinality of a minimal non-edge isolating set of a graph. St001512The minimum rank of a graph. St001949The rigidity index of a graph. St000528The height of a poset. St000912The number of maximal antichains in a poset. St000643The size of the largest orbit of antichains under Panyushev complementation. St000680The Grundy value for Hackendot on posets. St000717The number of ordinal summands of a poset. St000906The length of the shortest maximal chain in a poset. St001917The order of toric promotion on the set of labellings of a graph. St001720The minimal length of a chain of small intervals in a lattice. St001820The size of the image of the pop stack sorting operator. St001615The number of join prime elements of a lattice. St001617The dimension of the space of valuations of a lattice. St000080The rank of the poset. St000172The Grundy number of a graph. St001029The size of the core of a graph. St001108The 2-dynamic chromatic number of a graph. St001110The 3-dynamic chromatic number of a graph. St001116The game chromatic number of a graph. 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. St001883The mutual visibility number of a graph. St000272The treewidth of a graph. St000362The size of a minimal vertex cover of a graph. St000536The pathwidth of a graph. St001644The dimension of a graph. St001782The order of rowmotion on the set of order ideals of a poset. St000287The number of connected components of a graph. St001828The Euler characteristic of a graph. 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. St000550The number of modular elements of a lattice. St000551The number of left modular elements of a lattice. St001626The number of maximal proper sublattices of a lattice. St001880The number of 2-Gorenstein indecomposable injective modules in the incidence algebra of the lattice. St001623The number of doubly irreducible elements of a 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. St001432The order dimension of the partition. St000286The number of connected components of the complement of a graph. St000822The Hadwiger number of the graph. 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. St001963The tree-depth 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. St001330The hat guessing number of a graph. St000454The largest eigenvalue of a graph if it is integral. St000907The number of maximal antichains of minimal length in a poset. St000911The number of maximal antichains of maximal size in a poset. St001343The dimension of the reduced incidence algebra of a poset. St001084The number of occurrences of the vincular pattern |1-23 in a permutation. St001397Number of pairs of incomparable elements in a finite poset. St000888The maximal sum of entries on a diagonal of an alternating sign matrix. St000892The maximal number of nonzero entries on a diagonal of an alternating sign matrix. St000015The number of peaks of a Dyck path. St000231Sum of the maximal elements of the blocks of a set partition. St000325The width of the tree associated to a permutation. St000470The number of runs in a permutation. St000542The number of left-to-right-minima of a permutation. 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. 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. St001390The number of bumps occurring when Schensted-inserting the letter 1 of a permutation. St001530The depth of a Dyck path. St001566The length of the longest arithmetic progression in a permutation. St000004The major index of a permutation. St000021The number of descents of a permutation. St000331The number of upper interactions of a Dyck path. St000332The positive inversions of an alternating sign matrix. St000864The number of circled entries of the shifted recording tableau of a permutation. St000868The aid statistic in the sense of Shareshian-Wachs. 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 $c_{n−1}$. St001117The game chromatic index of a graph. 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. 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. St001405The number of bonds in a permutation. St001428The number of B-inversions of a signed permutation. St001489The maximum of the number of descents and the number of inverse descents. St001509The degree of the standard monomial associated to a Dyck path relative to the trivial lower boundary. St001726The number of visible inversions of a permutation. St000949Gives the number of generalised tilting modules of the corresponding LNakayama algebra. 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. St000797The stat`` of a permutation. 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. St000689The maximal n such that the minimal generator-cogenerator module in the LNakayama algebra of a Dyck path is n-rigid. St000111The sum of the descent tops (or Genocchi descents) of a permutation. St000923The minimal number with no two order isomorphic substrings of this length in a permutation. St000990The first ascent of a permutation. St001040The depth of the decreasing labelled binary unordered tree associated with the perfect matching. St001134The largest label in the subtree rooted at the sister of 1 in the leaf labelled binary unordered tree associated with the perfect matching. St001379The number of inversions plus the major index of a permutation. St001464The number of bases of the positroid corresponding to the permutation, with all fixed points counterclockwise. St000062The length of the longest increasing subsequence of the permutation. St000134The size of the orbit of an alternating sign matrix under gyration. St000154The sum of the descent bottoms of a permutation. St000156The Denert index of a permutation. St000193The row of the unique '1' in the first column of the alternating sign matrix. St000305The inverse major index of a permutation. 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. St000373The number of weak exceedences of a permutation that are also mid-points of a decreasing subsequence of length $3$. St000450The number of edges minus the number of vertices plus 2 of a graph. 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. St000702The number of weak deficiencies of a permutation. St000780The size of the orbit under rotation of a perfect matching. St000796The stat' of a permutation. St000798The makl of a permutation. St000833The comajor index of a permutation. St000887The maximal number of nonzero entries on a diagonal of a permutation matrix. St000988The orbit size of a permutation under Foata's bijection. St000991The number of right-to-left minima of a permutation. 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. St001295Gives the vector space dimension of the homomorphism space between J^2 and J^2. St001345The Hamming dimension of a graph. St001429The number of negative entries in a signed permutation. St001508The degree of the standard monomial associated to a Dyck path relative to the diagonal boundary. 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. St001652The length of a longest interval of consecutive numbers. St001662The length of the longest factor of consecutive numbers in a permutation. St001671Haglund's hag of a permutation. St000039The number of crossings of a permutation. St000095The number of triangles of a graph. St000159The number of distinct parts of the integer partition. St000222The number of alignments in the permutation. St000317The cycle descent number of a permutation. St000358The number of occurrences of the pattern 31-2. St000434The number of occurrences of the pattern 213 or of the pattern 312 in a permutation. St000538The number of even inversions of a permutation. St000732The number of double deficiencies of a permutation. St000989The number of final rises of a permutation. St001229The vector space dimension of the first extension group between the Jacobson radical J and J^2. St001265The maximal i such that the i-th simple module has projective dimension equal to the global dimension in the corresponding Nakayama algebra. St001553The number of indecomposable summands of the square of the Jacobson radical as a bimodule in the Nakayama algebra corresponding to the Dyck path. St001640The number of ascent tops in the permutation such that all smaller elements appear before. St001684The reduced word complexity of a permutation. St001706The number of closed sets in a graph. 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. St000327The number of cover relations in a poset. 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 $eA$. St001668The number of points of the poset minus the width of the poset. St001520The number of strict 3-descents. St001556The number of inversions of the third entry of a permutation. 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. St001927Sparre Andersen's number of positives of a signed permutation. St001948The number of augmented double ascents of a permutation. St001123The multiplicity of the dual of the standard representation in the Kronecker square corresponding to a partition. St001207The Lowey length of the algebra $A/T$ when $T$ is the 1-tilting module corresponding to the permutation in the Auslander algebra of $K[x]/(x^n)$. St001960The number of descents of a permutation minus one if its first entry is not one. St000474Dyson's crank of a partition. St001834The number of non-isomorphic minors of a graph. St001629The coefficient of the integer composition in the quasisymmetric expansion of the relabelling action of the symmetric group on cycles. St001637The number of (upper) dissectors of a poset. St001812The biclique partition number of a graph. St000744The length of the path to the largest entry in a standard Young tableau. St001717The largest size of an interval in a poset. St000104The number of facets in the order polytope of this poset. St000151The number of facets in the chain polytope of the poset. St001664The number of non-isomorphic subposets of a poset. St000691The number of changes of a binary word. St000642The size of the smallest orbit of antichains under Panyushev complementation. St001817The number of flag weak exceedances of a signed permutation. St001892The flag excedance statistic of a signed permutation. St001882The number of occurrences of a type-B 231 pattern in a signed permutation. St001434The number of negative sum pairs of a signed 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. St001136The largest label with larger sister in the leaf labelled binary unordered tree associated with the perfect matching. St000157The number of descents of a standard tableau. St000507The number of ascents of a standard tableau. St000264The girth of a graph, which is not a tree. 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 $eA$. St001199The dominant dimension of $eAe$ for the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. St001498The normalised height of a Nakayama algebra with magnitude 1. St000203The number of external nodes of a binary tree. St000035The number of left outer peaks of a permutation. St000352The Elizalde-Pak rank of a permutation. St000742The number of big ascents of a permutation after prepending zero. St001693The excess length of a longest path consisting of elements and blocks of a set partition. St000356The number of occurrences of the pattern 13-2. St000834The number of right outer peaks of a permutation. St001632The number of indecomposable injective modules $I$ with $dim Ext^1(I,A)=1$ for the incidence algebra A of a poset. St000820The number of compositions obtained by rotating the composition. St001555The order of a signed permutation. St000494The number of inversions of distance at most 3 of a permutation. St000767The number of runs in an integer composition. St000371The number of mid points of decreasing subsequences of length 3 in a permutation. St000435The number of occurrences of the pattern 213 or of the pattern 231 in a permutation. St000884The number of isolated descents of a permutation. St000945The number of matchings in the dihedral orbit of a perfect matching. 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. St001214The aft of an integer partition. St001621The number of atoms of a lattice. St001682The number of distinct positions of the pattern letter 1 in occurrences of 123 in a permutation. St001086The number of occurrences of the consecutive pattern 132 in a permutation. St001596The number of two-by-two squares inside a skew partition. St000044The number of vertices of the unicellular map given by a perfect matching. St000135The number of lucky cars of the parking function. St001355Number of non-empty prefixes of a binary word that contain equally many 0's and 1's. 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. St001462The number of factors of a standard tableaux under concatenation. St000017The number of inversions of a standard tableau. St000389The number of runs of ones of odd length in a binary word. 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. St001811The Castelnuovo-Mumford regularity of a permutation. St000011The number of touch points (or returns) of a Dyck path. St001877Number of indecomposable injective modules with projective dimension 2. St000153The number of adjacent cycles of a permutation. St000186The sum of the first row in a Gelfand-Tsetlin pattern. St000237The number of small exceedances. St000390The number of runs of ones in a binary word. St000693The modular (standard) major index of a standard tableau. St001000Number of indecomposable modules with projective dimension equal to the global dimension in the Nakayama algebra corresponding to the Dyck path. 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. St001485The modular major index of a binary word. St001514The dimension of the top of the Auslander-Reiten translate of the regular modules as a bimodule. St001524The degree of symmetry of a binary word. St001697The shifted natural comajor index of a standard Young tableau. St001770The number of facets of a certain subword complex associated with the signed permutation. St001773The number of minimal elements in Bruhat order not less than the signed permutation. St001821The sorting index of a signed permutation. St001855The number of signed permutations less than or equal to a signed permutation in left weak order. St001861The number of Bruhat lower covers of a permutation. St001907The number of Bastidas - Hohlweg - Saliola excedances of a signed permutation. St000291The number of descents of a binary word. St000292The number of ascents of a binary word. St000628The balance of a binary word. St000647The number of big descents of a permutation. St000753The Grundy value for the game of Kayles on a binary word. St000871The number of very big ascents of a permutation. St001078The minimal number of occurrences of (12) in a factorization of a permutation into transpositions (12) and cycles (1,. St001083The number of boxed occurrences of 132 in a permutation. St001535The number of cyclic alignments of a permutation. St001769The reflection length of a signed permutation. St001803The maximal overlap of the cylindrical tableau associated with a tableau. St001864The number of excedances of a signed permutation. St001894The depth of a signed permutation. St001896The number of right descents of a signed permutations. St000668The least common multiple of the parts of the partition. St001280The number of parts of an integer partition that are at least two. St001571The Cartan determinant of the integer partition. St000319The spin of an integer partition. St000320The dinv adjustment of an integer partition. St000939The number of characters of the symmetric group whose value on the partition is positive. St001914The size of the orbit of an integer partition in Bulgarian solitaire. St001918The degree of the cyclic sieving polynomial corresponding to an integer partition. St000755The number of real roots of the characteristic polynomial of a linear recurrence associated with an integer partition. St001384The number of boxes in the diagram of a partition that do not lie in the largest triangle it contains. St001714The number of subpartitions of an integer partition that do not dominate the conjugate subpartition. St000137The Grundy value of an integer partition. St000512The number of invariant subsets of size 3 when acting with a permutation of given cycle type. St000941The number of characters of the symmetric group whose value on the partition is even. St001364The number of permutations whose cube equals a fixed permutation of given cycle type. St001383The BG-rank of an integer partition. St001442The number of standard Young tableaux whose major index is divisible by the size of a given integer partition. St001878The projective dimension of the simple modules corresponding to the minimum of L in the incidence algebra of the lattice L. St001876The number of 2-regular simple modules in the incidence algebra of the lattice.