St000395The sum of the heights of the peaks of a Dyck path. St000725The smallest label of a leaf of the increasing binary tree associated to a permutation. St000733The row containing the largest entry of a standard tableau. St001004The number of indices that are either left-to-right maxima or right-to-left minima. St001020Sum of the codominant dimensions of the non-projective indecomposable injective modules of the Nakayama algebra corresponding to the Dyck path. St001211The number of simple modules in the corresponding Nakayama algebra that have vanishing second Ext-group with the regular module. 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. St001237The number of simple modules with injective dimension at most one or dominant dimension at least one. St001348The bounce of the parallelogram polyomino associated with the Dyck path. St001554The number of distinct nonempty subtrees of a binary tree. St000157The number of descents of a standard tableau. St000784The maximum of the length and the largest part of the integer partition. St000806The semiperimeter of the associated bargraph. 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. St000003The number of standard Young tableaux of the partition. St000007The number of saliances of the permutation. St000050The depth or height of a binary tree. St000081The number of edges of a graph. St000144The pyramid weight of the Dyck path. St000246The number of non-inversions of a permutation. St000259The diameter of a connected graph. St000278The size of the preimage of the map 'to partition' from Integer compositions to Integer partitions. St000296The length of the symmetric border of a binary word. St000336The leg major index of a standard tableau. St000393The number of strictly increasing runs in a binary word. St000394The sum of the heights of the peaks of a Dyck path minus the number of peaks. St000476The sum of the semi-lengths of tunnels before a valley of a Dyck path. St000482The (zero)-forcing number 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. St000507The number of ascents of a standard tableau. St000529The number of permutations whose descent word is the given binary word. St000543The size of the conjugacy class of a binary word. St000553The number of blocks of a graph. St000626The minimal period of a binary word. St000627The exponent of a binary word. St000651The maximal size of a rise in a permutation. St000704The number of semistandard tableaux on a given integer partition with minimal maximal entry. St000724The label of the leaf of the path following the smaller label in the increasing binary tree associated to a permutation. St000728The dimension of a set partition. St000826The stopping time of the decimal representation of the binary word for the 3x+1 problem. St000844The size of the largest block in the direct sum decomposition of a permutation. St000863The length of the first row of the shifted shape of a permutation. St000875The semilength of the longest Dyck word in the Catalan factorisation of a binary word. St000876The number of factors in the Catalan decomposition of a binary word. St000877The depth of the binary word interpreted as a path. St000883The number of longest increasing subsequences of a permutation. St000885The number of critical steps in the Catalan decomposition of a binary word. St000922The minimal number such that all substrings of this length are unique. St000982The length of the longest constant subword. St000987The number of positive eigenvalues of the Laplacian matrix of the graph. St001018Sum of projective dimension of the indecomposable injective modules of the Nakayama algebra corresponding to the Dyck path. St001119The length of a shortest maximal path in a graph. St001120The length of a longest path in a graph. St001250The number of parts of a partition that are not congruent 0 modulo 3. St001267The length of the Lyndon factorization of the binary word. St001291The number of indecomposable summands of the tensor product of two copies of the dual of the Nakayama algebra associated to a Dyck path. St001332The number of steps on the non-negative side of the walk associated with the permutation. St001371The length of the longest Yamanouchi prefix of a binary word. St001382The number of boxes in the diagram of a partition that do not lie in its Durfee square. 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. St001479The number of bridges of a graph. St001512The minimum rank of a graph. St001541The Gini index of an integer partition. St001631The number of simple modules $S$ with $dim Ext^1(S,A)=1$ in the incidence algebra $A$ of the poset. St001641The number of ascent tops in the flattened set partition such that all smaller elements appear before. St001780The order of promotion on the set of standard tableaux of given shape. 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. St001884The number of borders of a binary word. St001908The number of semistandard tableaux of distinct weight whose maximal entry is the length of the partition. St001917The order of toric promotion on the set of labellings of a graph. St000019The cardinality of the support of a permutation. St000060The greater neighbor of the maximum. St000088The row sums of the character table of the symmetric group. St000141The maximum drop size of a permutation. St000148The number of odd parts of a partition. St000160The multiplicity of the smallest part of a partition. St000175Degree of the polynomial counting the number of semistandard Young tableaux when stretching the shape. St000203The number of external nodes of a binary tree. St000207Number of integral Gelfand-Tsetlin polytopes with prescribed top row and integer composition weight. St000209Maximum difference of elements in cycles. St000212The number of standard Young tableaux for an integer partition such that no two consecutive entries appear in the same row. St000214The number of adjacencies of a permutation. St000215The number of adjacencies of a permutation, zero appended. St000228The size of a partition. St000250The number of blocks (St000105) plus the number of antisingletons (St000248) of a set partition. St000293The number of inversions of a binary word. St000294The number of distinct factors of a binary word. St000295The length of the border of a binary word. St000313The number of degree 2 vertices of a graph. St000326The position of the first one in a binary word after appending a 1 at the end. St000356The number of occurrences of the pattern 13-2. St000381The largest part of an integer composition. St000382The first part of an integer composition. St000383The last part of an integer composition. St000448The number of pairs of vertices of a graph with distance 2. St000452The number of distinct eigenvalues of a graph. St000453The number of distinct Laplacian eigenvalues of a graph. St000459The hook length of the base cell of a partition. St000460The hook length of the last cell along the main diagonal of an integer partition. St000463The number of admissible inversions of a permutation. St000475The number of parts equal to 1 in a partition. St000505The biggest entry in the block containing the 1. St000518The number of distinct subsequences in a binary word. St000519The largest length of a factor maximising the subword complexity. St000528The height of a poset. St000531The leading coefficient of the rook polynomial of an integer partition. St000548The number of different non-empty partial sums of an integer partition. St000552The number of cut vertices of a graph. St000620The number of standard tableaux of shape equal to the given partition such that the minimal cyclic descent is odd. St000636The hull number of a graph. St000653The last descent of a permutation. St000657The smallest part of an integer composition. St000662The staircase size of the code of a permutation. St000718The largest Laplacian eigenvalue of a graph if it is integral. St000734The last entry in the first row of a standard tableau. St000738The first entry in the last row of a standard tableau. St000777The number of distinct eigenvalues of the distance Laplacian of a connected graph. St000808The number of up steps of the associated bargraph. St000815The number of semistandard Young tableaux of partition weight of given shape. St000839The largest opener of a set partition. St000870The product of the hook lengths of the diagonal cells in an integer partition. St000907The number of maximal antichains of minimal length in a poset. St000911The number of maximal antichains of maximal size in a poset. St000912The number of maximal antichains in a poset. St000956The maximal displacement of a permutation. St000957The number of Bruhat lower covers of a permutation. St001023Number of simple modules with projective dimension at most 3 in the Nakayama algebra corresponding to the Dyck path. St001034The area of the parallelogram polyomino associated with the Dyck path. St001082The number of boxed occurrences of 123 in a permutation. St001083The number of boxed occurrences of 132 in a permutation. St001084The number of occurrences of the vincular pattern |1-23 in a permutation. St001093The detour number of a graph. St001176The size of a partition minus its first part. St001190Number of simple modules with projective dimension at most 4 in the corresponding Nakayama algebra. St001225The vector space dimension of the first extension group between J and itself when J is the Jacobson radical of the corresponding Nakayama algebra. St001240The number of indecomposable modules e_i J^2 that have injective dimension at most one in the corresponding Nakayama algebra St001247The number of parts of a partition that are not congruent 2 modulo 3. St001249Sum of the odd 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. St001308The number of induced paths on three vertices in a graph. 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. St001342The number of vertices in the center of a graph. St001343The dimension of the reduced incidence algebra of a poset. St001368The number of vertices of maximal degree in a graph. St001436The index of a given binary word in the lex-order among all its cyclic shifts. St001480The number of simple summands of the module J^2/J^3. 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. 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. St001521Half the total irregularity of a graph. St001586The number of odd parts smaller than the largest even part in an integer partition. St001650The order of Ringel's homological bijection associated to the linear 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. St001659The number of ways to place as many non-attacking rooks as possible on a Ferrers board. St001692The number of vertices with higher degree than the average degree 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. St001838The number of nonempty primitive factors of a binary word. St001880The number of 2-Gorenstein indecomposable injective modules in the incidence algebra of the lattice. St001933The largest multiplicity of a part in an integer partition. St001958The degree of the polynomial interpolating the values of a permutation. St000070The number of antichains in a poset. St000245The number of ascents of a permutation. St000366The number of double descents of a permutation. St000371The number of mid points of decreasing subsequences of length 3 in a permutation. St000378The diagonal inversion number of an integer partition. St000447The number of pairs of vertices of a graph with distance 3. St000672The number of minimal elements in Bruhat order not less than the permutation. St000770The major index of an integer partition when read from bottom to top. St000867The sum of the hook lengths in the first row of an integer partition. St000921The number of internal inversions of a binary word. St000967The value p(1) for the Coxeterpolynomial p of the corresponding LNakayama algebra. St001012Number of simple modules with projective dimension at most 2 in the Nakayama algebra corresponding to the Dyck path. St001091The number of parts in an integer partition whose next smaller part has the same size. St001218Smallest index k greater than or equal to one such that the Coxeter matrix C of the corresponding Nakayama algebra has C^k=1. St001279The sum of the parts of an integer partition that are at least two. St001306The number of induced paths on four vertices in a graph. St001384The number of boxes in the diagram of a partition that do not lie in the largest triangle it contains. St001127The sum of the squares of the parts of a partition. St000171The degree of the graph. St001723The differential of a graph. St001724The 2-packing differential of a graph. St001746The coalition number of a graph. St000676The number of odd rises of a Dyck path. St001515The vector space dimension of the socle of the first syzygy module of the regular module (as a bimodule). St001039The maximal height of a column in the parallelogram polyomino associated with a Dyck path. St000372The number of mid points of increasing subsequences of length 3 in a permutation. St001268The size of the largest ordinal summand in the poset. St000329The number of evenly positioned ascents of the Dyck path, with the initial position equal to 1. St001300The rank of the boundary operator in degree 1 of the chain complex of the order complex of the poset. St001636The number of indecomposable injective modules with projective dimension at most one in the incidence algebra of the poset. St000656The number of cuts of a poset. St001068Number of torsionless simple modules in the corresponding Nakayama algebra. St000053The number of valleys of the Dyck path. St000012The area of a Dyck path. St000678The number of up steps after the last double rise of a Dyck path. St001622The number of join-irreducible elements of a lattice. St001499The number of indecomposable projective-injective modules of a magnitude 1 Nakayama algebra. St001777The number of weak descents in an integer composition. St000546The number of global descents of a permutation. St000744The length of the path to the largest entry in a standard Young tableau. St000924The number of topologically connected components of a perfect matching. St000727The largest label of a leaf in the binary search tree associated with the permutation. St000740The last entry of a permutation. St001497The position of the largest weak excedence of a permutation. St001778The largest greatest common divisor of an element and its image in a permutation. St000691The number of changes of a binary word. St001733The number of weak left to right maxima of a Dyck path. St000932The number of occurrences of the pattern UDU in a Dyck path. St000006The dinv of a Dyck path. St000013The height of a Dyck path. St000054The first entry of the permutation. St000757The length of the longest weakly inreasing subsequence of parts of an integer composition. St000765The number of weak records in an integer composition. St000445The number of rises of length 1 of a Dyck path. St000015The number of peaks of a Dyck path. St000442The maximal area to the right of an up step of a Dyck path. St001725The harmonious chromatic number of a graph. St000155The number of exceedances (also excedences) of a permutation. St000331The number of upper interactions of a Dyck path. St000809The reduced reflection length of the permutation. St001169Number of simple modules with projective dimension at least two in the corresponding Nakayama algebra. St001509The degree of the standard monomial associated to a Dyck path relative to the trivial lower boundary. St000011The number of touch points (or returns) of a Dyck path. St000439The position of the first down step of a Dyck path. St001430The number of positive entries in a signed permutation. St001462The number of factors of a standard tableaux under concatenation. St000216The absolute length of a permutation. St001484The number of singletons of an integer partition. St001245The cyclic maximal difference between two consecutive entries of a permutation. St000052The number of valleys of a Dyck path not on the x-axis. St001167The number of simple modules that appear as the top of an indecomposable non-projective modules that is reflexive in the corresponding Nakayama algebra. St000025The number of initial rises of a Dyck path. St000105The number of blocks in the set partition. St000444The length of the maximal rise of a Dyck path. St000925The number of topologically connected components of a set partition. St001007Number of simple modules with projective dimension 1 in the Nakayama algebra corresponding to the Dyck path. St001050The number of terminal closers of a set partition. St001088Number of indecomposable projective non-injective modules with dominant dimension equal to the injective dimension in the corresponding Nakayama algebra. 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: St001809The index of the step at the first peak of maximal height in a Dyck path. St000024The number of double up and double down steps of a Dyck path. St000211The rank of the set partition. St000340The number of non-final maximal constant sub-paths of length greater than one. St000625The sum of the minimal distances to a greater element. St000820The number of compositions obtained by rotating the composition. St000874The position of the last double rise in a Dyck path. St001028Number of simple modules with injective dimension equal to the dominant dimension in the Nakayama algebra corresponding to the Dyck path. St001066The number of simple reflexive modules in the corresponding Nakayama algebra. St001067The number of simple modules of dominant dimension at least two in the corresponding Nakayama algebra. St001074The number of inversions of the cyclic embedding of a permutation. St001189The number of simple modules with dominant and codominant dimension equal to zero in the Nakayama algebra corresponding to the Dyck path. St001197The global dimension of $eAe$ for the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. St001199The dominant dimension of $eAe$ for the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. St001506Half the projective dimension of the unique simple module with even projective dimension in a magnitude 1 Nakayama algebra. St000931The number of occurrences of the pattern UUU in a Dyck path. St001036The number of inner corners of the parallelogram polyomino associated with the Dyck path. St000189The number of elements in the poset. St000030The sum of the descent differences of a permutations. St000051The size of the left subtree of a binary tree. St000064The number of one-box pattern of a permutation. St000067The inversion number of the alternating sign matrix. St000080The rank of the poset. St000133The "bounce" of a permutation. St000204The number of internal nodes of a binary tree. St000213The number of weak exceedances (also weak excedences) of a permutation. St000276The size of the preimage of the map 'to graph' from Ordered trees to Graphs. St000304The load of a permutation. St000316The number of non-left-to-right-maxima of a permutation. St000325The width of the tree associated to a permutation. St000470The number of runs in a permutation. St000530The number of permutations with the same descent word as the given permutation. St000619The number of cyclic descents of a permutation. St000652The maximal difference between successive positions of a permutation. St000668The least common multiple of the parts of the partition. St000702The number of weak deficiencies of a permutation. St000708The product of the parts of an integer partition. St000745The index of the last row whose first entry is the row number in a standard Young tableau. St000795The mad of a permutation. St000923The minimal number with no two order isomorphic substrings of this length in a permutation. St001246The 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. St001295Gives the vector space dimension of the homomorphism space between J^2 and J^2. St001389The number of partitions of the same length below the given integer partition. St001391The disjunction number of a graph. St001516The number of cyclic bonds of a permutation. St001566The length of the longest arithmetic progression in a permutation. St001649The length of a longest trail in a graph. St001827The number of two-component spanning forests of a graph. St001869The maximum cut size of a graph. St000021The number of descents of a permutation. St000028The number of stack-sorts needed to sort a permutation. St000031The number of cycles in the cycle decomposition of a permutation. St000066The column of the unique '1' in the first row of the alternating sign matrix. St000083The number of left oriented leafs of a binary tree except the first one. St000111The sum of the descent tops (or Genocchi descents) of a permutation. St000226The convexity of a permutation. St000229Sum of the difference between the maximal and the minimal elements of the blocks plus the number of blocks of a set partition. St000235The number of indices that are not cyclical small weak excedances. St000238The number of indices that are not small weak excedances. St000240The number of indices that are not small excedances. St000242The number of indices that are not cyclical small weak excedances. St000280The size of the preimage of the map 'to labelling permutation' from Parking functions to Permutations. St000299The number of nonisomorphic vertex-induced subtrees. St000309The number of vertices with even degree. St000319The spin of an integer partition. St000320The dinv adjustment of an integer partition. St000337The lec statistic, the sum of the inversion numbers of the hook factors of a permutation. St000354The number of recoils of a permutation. St000374The number of exclusive right-to-left minima of a permutation. St000435The number of occurrences of the pattern 213 or of the pattern 231 in a permutation. St000471The sum of the ascent tops of a permutation. St000673The number of non-fixed points of a permutation. St000680The Grundy value for Hackendot on posets. St000692Babson and Steingrímsson's statistic of a permutation. St000703The number of deficiencies of a permutation. St000717The number of ordinal summands of a poset. St000829The Ulam distance of a permutation to the identity permutation. St000831The number of indices that are either descents or recoils. St000868The aid statistic in the sense of Shareshian-Wachs. St000906The length of the shortest maximal chain in a poset. 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. St001005The number of indices for a permutation that are either left-to-right maxima or right-to-left minima but not both. St001052The length of the exterior of a permutation. St001061The number of indices that are both descents and recoils of a permutation. St001096The size of the overlap set of a permutation. St001179Number of indecomposable injective modules with projective dimension at most 2 in the corresponding Nakayama algebra. St001298The number of repeated entries in the Lehmer code of a permutation. St001372The length of a longest cyclic run of ones of a binary word. St001377The major index minus the number of inversions of a permutation. St001405The number of bonds in a permutation. St001489The maximum of the number of descents and the number of inverse descents. St001519The pinnacle sum of a permutation. St001683The number of distinct positions of the pattern letter 3 in occurrences of 132 in a permutation. St001717The largest size of an interval in a poset. St001918The degree of the cyclic sieving polynomial corresponding to an integer partition. St000058The order of a permutation. St000094The depth of an ordered tree. St000104The number of facets in the order polytope of this poset. St000151The number of facets in the chain polytope of the poset. St000167The number of leaves of an ordered tree. St000451The length of the longest pattern of the form k 1 2. St000642The size of the smallest orbit of antichains under Panyushev complementation. St000643The size of the largest orbit of antichains under Panyushev complementation. St000836The number of descents of distance 2 of a permutation. St000864The number of circled entries of the shifted recording tableau of a permutation. St001065Number of indecomposable reflexive modules in the corresponding Nakayama algebra. St001468The smallest fixpoint of a permutation. St001664The number of non-isomorphic subposets of a poset. St001687The number of distinct positions of the pattern letter 2 in occurrences of 213 in a permutation. St001782The order of rowmotion on the set of order ideals of a poset. St000306The bounce count of a Dyck path. St000489The number of cycles of a permutation of length at most 3. St001461The number of topologically connected components of the chord diagram of a permutation. St000898The number of maximal entries in the last diagonal of the monotone triangle. St000018The number of inversions of a permutation. St000542The number of left-to-right-minima of a permutation. St001090The number of pop-stack-sorts needed to sort a permutation. St001390The number of bumps occurring when Schensted-inserting the letter 1 of a permutation. St001152The number of pairs with even minimum in a perfect matching. St000993The multiplicity of the largest part of an integer partition. St001925The minimal number of zeros in a row of an alternating sign matrix. St000446The disorder of a permutation. St000533The minimum of the number of parts and the size of the first part of an integer partition. St000783The side length of the largest staircase partition fitting into a partition. St000890The number of nonzero entries in an alternating sign matrix. 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. St000539The number of odd inversions of a permutation. St001965The number of decreasable positions in the corner sum matrix of an alternating sign matrix. St000541The number of indices greater than or equal to 2 of a permutation such that all smaller indices appear to its right. St001727The number of invisible inversions of a permutation. St000093The cardinality of a maximal independent set of vertices of a graph. St000786The maximal number of occurrences of a colour in a proper colouring of a graph. St001337The upper domination number of a graph. St001338The upper irredundance number of a graph. St000163The size of the orbit of the set partition under rotation. St000097The order of the largest clique of the graph. St000098The chromatic number of a graph. St000318The number of addable cells of the Ferrers diagram of an integer partition. St001804The minimal height of the rectangular inner shape in a cylindrical tableau associated to a tableau. St001698The comajor index of a standard tableau minus the weighted size of its shape. 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. St000061The number of nodes on the left branch of a binary tree. St000062The length of the longest increasing subsequence of the permutation. St000164The number of short pairs. St000236The number of cyclical small weak excedances. St000239The number of small weak excedances. St000291The number of descents of a binary word. St000314The number of left-to-right-maxima of a permutation. St000390The number of runs of ones in a binary word. St000443The number of long tunnels of a Dyck path. St000990The first ascent of a permutation. St001014Number of indecomposable injective modules with codominant dimension equal to the dominant dimension of the Nakayama algebra corresponding to the Dyck path. St001015Number of indecomposable injective modules with codominant dimension equal to one in the Nakayama algebra corresponding to the Dyck path. St001016Number of indecomposable injective modules with codominant dimension at most 1 in the Nakayama algebra corresponding to the Dyck path. St001180Number of indecomposable injective modules with projective dimension at most 1. 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. 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. 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. St001232The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2. St001235The global dimension of the corresponding Comp-Nakayama algebra. St001241The number of non-zero radicals of the indecomposable projective modules that have injective dimension and projective dimension at most one. 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. St001418Half of the global dimension of the stable Auslander algebra of the Nakayama algebra corresponding to the Dyck path. St001581The achromatic number of a graph. St000168The number of internal nodes of an ordered tree. St000292The number of ascents of a binary word. St001142The projective dimension of the socle of the regular module as a bimodule in the Nakayama algebra corresponding to the Dyck path. St001153The number of blocks with even minimum in a set partition. 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. St001226The number of integers i such that the radical of the i-th indecomposable projective module has vanishing first extension group with the Jacobson radical J in the corresponding Nakayama algebra. St001233The number of indecomposable 2-dimensional modules with projective dimension one. St001290The first natural number n such that the tensor product of n copies of D(A) is zero for the corresponding Nakayama algebra A. St001508The degree of the standard monomial associated to a Dyck path relative to the diagonal boundary. St001584The area statistic between a Dyck path and its bounce path. St001798The difference of the number of edges in a graph and the number of edges in the complement of the Turán graph. St001907The number of Bastidas - Hohlweg - Saliola excedances of a signed permutation. St000034The maximum defect over any reduced expression for a permutation and any subexpression. St000711The number of big exceedences of a permutation. St001124The multiplicity of the standard representation in the Kronecker square corresponding to a partition. 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. St000071The number of maximal chains in a poset. St000527The width of the poset. St001136The largest label with larger sister in the leaf labelled binary unordered tree associated with the perfect matching. St000068The number of minimal elements in a poset. St000069The number of maximal elements of a poset. St000504The cardinality of the first block of a set partition. St000823The number of unsplittable factors of the set partition. St000971The smallest closer of a set partition. St001062The maximal size of a block of a set partition. St000159The number of distinct parts of the integer partition. St000632The jump number of the poset. St001432The order dimension of the partition. St000481The number of upper covers of a partition in dominance order. St000172The Grundy number of a graph. St000249The number of singletons (St000247) plus the number of antisingletons (St000248) of a set partition. St000722The number of different neighbourhoods in a graph. St000746The number of pairs with odd minimum in a perfect matching. St001029The size of the core of a graph. St001108The 2-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. St001670The connected partition number of a graph. St000234The number of global ascents of a permutation. St000272The treewidth of a graph. St000362The size of a minimal vertex cover of a graph. St000536The pathwidth of a graph. St000771The largest multiplicity of a distance Laplacian eigenvalue in a connected graph. St000773The multiplicity of the largest Laplacian eigenvalue in a graph. St000774The maximal multiplicity of a Laplacian eigenvalue in a graph. St000778The metric dimension of a graph. St001051The depth of the label 1 in the decreasing labelled unordered tree associated with the set partition. St001087The number of occurrences of the vincular pattern |12-3 in a permutation. St001557The number of inversions of the second entry of a permutation. St001960The number of descents of a permutation minus one if its first entry is not one. St000840The number of closers smaller than the largest opener in a perfect matching. St001302The number of minimally dominating sets of vertices of a graph. St001304The number of maximally independent sets of vertices of a graph. St001498The normalised height of a Nakayama algebra with magnitude 1. St001963The tree-depth of a graph. St001270The bandwidth of a graph. St001277The degeneracy of a graph. St001358The largest degree of a regular subgraph of a graph. St001644The dimension of a graph. St001962The proper pathwidth of a graph. St001331The size of the minimal feedback vertex set. St001336The minimal number of vertices in a graph whose complement is triangle-free. St001514The dimension of the top of the Auslander-Reiten translate of the regular modules as a bimodule. St001002Number of indecomposable modules with projective and injective dimension at most 1 in the Nakayama algebra corresponding to the Dyck path. St000199The column of the unique '1' in the last row of the alternating sign matrix. St000308The height of the tree associated to a permutation. St000327The number of cover relations in a poset. St000434The number of occurrences of the pattern 213 or of the pattern 312 in a permutation. St000800The number of occurrences of the vincular pattern |231 in a permutation. St000908The length of the shortest maximal antichain in a poset. St000914The sum of the values of the Möbius function of 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 $eA$. St001229The vector space dimension of the first extension group between the Jacobson radical J and J^2. St001637The number of (upper) dissectors of a poset. St001668The number of points of the poset minus the width of the poset. St000029The depth of a permutation. St000044The number of vertices of the unicellular map given by a perfect matching. St000193The row of the unique '1' in the first column of the alternating sign matrix. St000197The number of entries equal to positive one in the alternating sign matrix. St000200The row of the unique '1' in the last column of the alternating sign matrix. St000210Minimum over maximum difference of elements in cycles. St000358The number of occurrences of the pattern 31-2. St001045The number of leaves in the subtree not containing one in the decreasing labelled binary unordered tree associated with the perfect matching. St001076The minimal length of a factorization of a permutation into transpositions that are cyclic shifts of (12). St001077The prefix exchange distance of a permutation. St001132The number of leaves in the subtree whose sister has label 1 in the decreasing labelled binary unordered tree associated with the perfect matching. St001207The Lowey length of the algebra $A/T$ when $T$ is the 1-tilting module corresponding to the permutation in the Auslander algebra of $K[x]/(x^n)$. St001511The minimal number of transpositions needed to sort a permutation in either direction. St001526The Loewy length of the Auslander-Reiten translate of the regular module as a bimodule of the Nakayama algebra corresponding to the Dyck path. St001558The number of transpositions that are smaller or equal to a permutation in Bruhat order. St001579The number of cyclically simple transpositions decreasing the number of cyclic descents needed to sort a permutation. St001811The Castelnuovo-Mumford regularity of a permutation. St000485The length of the longest cycle of a permutation. St000487The length of the shortest cycle of a permutation. St001134The largest label in the subtree rooted at the sister of 1 in the leaf labelled binary unordered tree associated with the perfect matching. St001520The number of strict 3-descents. St001556The number of inversions of the third entry of a permutation. St001948The number of augmented double ascents of a permutation. St000153The number of adjacent cycles of a permutation. St001316The domatic number of a graph. St001458The rank of the adjacency matrix of a graph. St000176The total number of tiles in the Gelfand-Tsetlin pattern. St001427The number of descents of a signed permutation. St000056The decomposition (or block) number of a permutation. St000286The number of connected components of the complement of a graph. St000822The Hadwiger number of the graph. St000887The maximal number of nonzero entries on a diagonal of a permutation matrix. St000991The number of right-to-left minima of a permutation. St001652The length of a longest interval of consecutive numbers. St001662The length of the longest factor of consecutive numbers in a permutation. St000787The number of flips required to make a perfect matching noncrossing. St000989The number of final rises of a permutation. St001640The number of ascent tops in the permutation such that all smaller elements appear before. St000039The number of crossings of a permutation. St000317The cycle descent number of a permutation. St000355The number of occurrences of the pattern 21-3. St000365The number of double ascents of a permutation. St000837The number of ascents of distance 2 of a permutation. St001130The number of two successive successions in a permutation. St001682The number of distinct positions of the pattern letter 1 in occurrences of 123 in a permutation. St001744The number of occurrences of the arrow pattern 1-2 with an arrow from 1 to 2 in a permutation. St000970Number of peaks minus the dominant dimension of the corresponding LNakayama algebra. St001185The number of indecomposable injective modules of grade at least 2 in the corresponding Nakayama algebra. St001215Let X be the direct sum of all simple modules of the corresponding Nakayama algebra. St000373The number of weak exceedences of a permutation that are also mid-points of a decreasing subsequence of length $3$. St000719The number of alignments in a perfect matching. St000741The Colin de Verdière graph invariant. 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. 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. St001239The largest vector space dimension of the double dual of a simple module 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. St001812The biclique partition number of a graph. St001431Half of the Loewy length minus one of a modified stable Auslander algebra of the Nakayama algebra corresponding to the Dyck path. St001330The hat guessing number of a graph. St000454The largest eigenvalue of a graph if it is integral. St001488The number of corners of a skew partition. St001645The pebbling number of a connected graph. St001720The minimal length of a chain of small intervals in a lattice. St000177The number of free tiles in the pattern. St000178Number of free entries. St000181The number of connected components of the Hasse diagram for the poset. St001769The reflection length of a signed permutation. St001864The number of excedances of a signed permutation. St001862The number of crossings of a signed permutation. St001882The number of occurrences of a type-B 231 pattern in a signed permutation. St001626The number of maximal proper sublattices of a lattice. St001684The reduced word complexity of a permutation. St000017The number of inversions of a standard tableau. St001314The number of tilting modules of arbitrary projective dimension that have no simple modules as a direct summand in the corresponding Nakayama algebra. 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. St001583The projective dimension of the simple module corresponding to the point in the poset of the symmetric group under bruhat order. St001773The number of minimal elements in Bruhat order not less than the signed permutation. St001803The maximal overlap of the cylindrical tableau associated with a tableau. St001861The number of Bruhat lower covers of a permutation. St000135The number of lucky cars of the parking function. St000522The number of 1-protected nodes of a rooted tree. St001419The length of the longest palindromic factor beginning with a one 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. St001642The Prague dimension of a graph. St001712The number of natural descents of a standard Young tableau. St001927Sparre Andersen's number of positives of a signed permutation. St001935The number of ascents in a parking function. St000521The number of distinct subtrees of an ordered tree. St000735The last entry on the main diagonal of a standard tableau. St000896The number of zeros on the main diagonal of an alternating sign matrix. 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. St001414Half the length of the longest odd length palindromic prefix of a binary word. St001423The number of distinct cubes in a binary word. St001491The number of indecomposable projective-injective modules in the algebra corresponding to a subset. St001555The order of a signed permutation.