St001717The largest size of an interval in a poset. St001880The number of 2-Gorenstein indecomposable injective modules in the incidence algebra of the lattice. St001300The rank of the boundary operator in degree 1 of the chain complex of the order complex of the poset. St000018The number of inversions of a permutation. St000030The sum of the descent differences of a permutations. St000224The sorting index of a permutation. St000228The size of a partition. St000476The sum of the semi-lengths of tunnels before a valley of a Dyck path. St000479The Ramsey number of a graph. St000645The sum of the areas of the rectangles formed by two consecutive peaks and the valley in between. St000728The dimension of a set partition. St000809The reduced reflection length of the permutation. St000915The Ore degree of a graph. St000957The number of Bruhat lower covers of a permutation. St001033The normalized area of the parallelogram polyomino associated with the Dyck path. St001076The minimal length of a factorization of a permutation into transpositions that are cyclic shifts of (12). St001278The number of indecomposable modules that are fixed by $\tau \Omega^1$ composed with its inverse in the corresponding Nakayama algebra. 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. St001579The number of cyclically simple transpositions decreasing the number of cyclic descents needed to sort a permutation. St001622The number of join-irreducible elements of a lattice. 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. St001726The number of visible inversions of a permutation. St001746The coalition number of a graph. St001869The maximum cut size of a graph. St000987The number of positive eigenvalues of the Laplacian matrix of the graph. St001120The length of a longest path in a graph. St000004The major index of a permutation. St000067The inversion number of the alternating sign matrix. St000081The number of edges of a graph. St000176The total number of tiles in the Gelfand-Tsetlin pattern. St000223The number of nestings in the permutation. St000246The number of non-inversions of a permutation. St000332The positive inversions of an alternating sign matrix. St000548The number of different non-empty partial sums of an integer partition. St000637The length of the longest cycle in a graph. St000718The largest Laplacian eigenvalue of a graph if it is integral. St000722The number of different neighbourhoods in a graph. St000794The mak of a permutation. St000795The mad of a permutation. St000874The position of the last double rise in a Dyck path. St000883The number of longest increasing subsequences of a permutation. 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. St001397Number of pairs of incomparable elements in a finite poset. St001428The number of B-inversions of a signed permutation. St001533The largest coefficient of the Poincare polynomial of the poset cone. St001725The harmonious chromatic number of a graph. St001727The number of invisible inversions of a permutation. St001861The number of Bruhat lower covers of a permutation. St001894The depth of a signed permutation. St001965The number of decreasable positions in the corner sum matrix of an alternating sign matrix. St000070The number of antichains in a poset. St000108The number of partitions contained in the given partition. St000171The degree of the graph. St000438The position of the last up step in a Dyck path. St000494The number of inversions of distance at most 3 of a permutation. St000625The sum of the minimal distances to a greater element. St001690The length of a longest path in a graph such that after removing the paths edges, every vertex of the path has distance two from some other vertex of the path. St000358The number of occurrences of the pattern 31-2. St000362The size of a minimal vertex cover of a graph. St001213The number of indecomposable modules in the corresponding Nakayama algebra that have vanishing first Ext-group with the regular module. St001282The number of graphs with the same chromatic polynomial. St001706The number of closed sets in a graph. St001723The differential of a graph. St001724The 2-packing differential of a graph. St001645The pebbling number of a connected graph. St001615The number of join prime elements of a lattice. St001617The dimension of the space of valuations of a lattice. St001875The number of simple modules with projective dimension at most 1. St001812The biclique partition number of a graph. St001626The number of maximal proper sublattices of a lattice. St000245The number of ascents of a permutation. St000672The number of minimal elements in Bruhat order not less than the permutation. St000031The number of cycles in the cycle decomposition of a permutation. St000670The reversal length of a permutation. St000680The Grundy value for Hackendot on posets. St001343The dimension of the reduced incidence algebra of a poset. St001330The hat guessing number of a graph. 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. St001554The number of distinct nonempty subtrees of a binary tree. St000327The number of cover relations in a poset. St001232The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2. St001637The number of (upper) dissectors of a poset. St001668The number of points of the poset minus the width of the poset. St001618The cardinality of the Frattini sublattice of a lattice. St000337The lec statistic, the sum of the inversion numbers of the hook factors of a permutation. St001087The number of occurrences of the vincular pattern |12-3 in a permutation. St001863The number of weak excedances of a signed permutation. St000371The number of mid points of decreasing subsequences of length 3 in a permutation. St001845The number of join irreducibles minus the rank of a lattice. St001644The dimension of a graph. St001491The number of indecomposable projective-injective modules in the algebra corresponding to a subset. St001625The Möbius invariant of a lattice. St000264The girth of a graph, which is not a tree. St000294The number of distinct factors of a binary word. St000518The number of distinct subsequences in a binary word. St000849The number of 1/3-balanced pairs in a poset. St000891The number of distinct diagonal sums of a permutation matrix. 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. St000308The height of the tree associated to a permutation. St000352The Elizalde-Pak rank of a permutation. St000550The number of modular elements of a lattice. St000725The smallest label of a leaf of the increasing binary tree associated to a permutation. St000834The number of right outer peaks of a permutation. St000994The number of cycle peaks and the number of cycle valleys of a permutation. St000871The number of very big ascents of a permutation. St001394The genus of a permutation. St000124The cardinality of the preimage of the Simion-Schmidt map. St001889The size of the connectivity set of a signed permutation. St000483The number of times a permutation switches from increasing to decreasing or decreasing to increasing. St000703The number of deficiencies of a permutation. St000717The number of ordinal summands of a poset. St001090The number of pop-stack-sorts needed to sort a permutation. St000035The number of left outer peaks of a permutation. St000074The number of special entries. St000243The number of cyclic valleys and cyclic peaks of a permutation. St000451The length of the longest pattern of the form k 1 2. St000647The number of big descents of a permutation. St000742The number of big ascents of a permutation after prepending zero. St000842The breadth of a permutation. St000884The number of isolated descents of a permutation. St001096The size of the overlap set of a permutation. St000036The evaluation at 1 of the Kazhdan-Lusztig polynomial with parameters given by the identity and the permutation. St001086The number of occurrences of the consecutive pattern 132 in a permutation. St000237The number of small exceedances. St000282The size of the preimage of the map 'to poset' from Ordered trees to Posets. St000546The number of global descents of a permutation. St000648The number of 2-excedences of a permutation. St000731The number of double exceedences of a permutation. St001084The number of occurrences of the vincular pattern |1-23 in a permutation. St001534The alternating sum of the coefficients of the Poincare polynomial of the poset cone. St001851The number of Hecke atoms of a signed permutation. St000393The number of strictly increasing runs in a binary word. St001722The number of minimal chains with small intervals between a binary word and the top element. St001285The number of primes in the column sums of the two line notation of a permutation. St001566The length of the longest arithmetic progression in a permutation. St000539The number of odd inversions of a permutation. St000624The normalized sum of the minimal distances to a greater element. St001515The vector space dimension of the socle of the first syzygy module of the regular module (as a bimodule). St001741The largest integer such that all patterns of this size are contained in the permutation. St001761The maximal multiplicity of a letter in a reduced word of a permutation. St001801Half the number of preimage-image pairs of different parity in a permutation. St001928The number of non-overlapping descents in a permutation. St000372The number of mid points of increasing subsequences of length 3 in a permutation. St000729The minimal arc length of a set partition. St000925The number of topologically connected components of a set partition. St001162The minimum jump of a permutation. St001236The dominant dimension of the corresponding Comp-Nakayama algebra. St001344The neighbouring number of a permutation. St001413Half the length of the longest even length palindromic prefix of a binary word. St001470The cyclic holeyness of a permutation. St000091The descent variation of a composition. St000217The number of occurrences of the pattern 312 in a permutation. St000338The number of pixed points of a permutation. St000562The number of internal points of a set partition. St000576The number of occurrences of the pattern {{1},{2}} such that 1 is a maximal and 2 a minimal element. St000590The number of occurrences of the pattern {{1},{2,3}} such that 2 is minimal, 1 is maximal, (2,3) are consecutive in a block. St000622The number of occurrences of the patterns 2143 or 4231 in a permutation. St000709The number of occurrences of 14-2-3 or 14-3-2. St000779The tier of a permutation. St001130The number of two successive successions in a permutation. St001174The Gorenstein dimension of the algebra $A/I$ when $I$ is the tilting module corresponding to the permutation in the Auslander algebra of $K[x]/(x^n)$. St001559The number of transpositions that are smaller or equal to a permutation in Bruhat order while not being inversions. St001705The number of occurrences of the pattern 2413 in a permutation. St001744The number of occurrences of the arrow pattern 1-2 with an arrow from 1 to 2 in a permutation. St001803The maximal overlap of the cylindrical tableau associated with a tableau. St001850The number of Hecke atoms of a permutation. St001857The number of edges in the reduced word graph of a signed permutation. St001866The nesting alignments of a signed permutation. St001867The number of alignments of type EN of a signed permutation. St001868The number of alignments of type NE of a signed permutation. St001906Half of the difference between the total displacement and the number of inversions and the reflection length of a permutation. St000039The number of crossings of a permutation. St000060The greater neighbor of the maximum. St000062The length of the longest increasing subsequence of the permutation. St000072The number of circled entries. St000155The number of exceedances (also excedences) of a permutation. St000213The number of weak exceedances (also weak excedences) of a permutation. St000216The absolute length of a permutation. St000230Sum of the minimal elements of the blocks of a set partition. St000236The number of cyclical small weak excedances. St000238The number of indices that are not small weak excedances. St000239The number of small weak excedances. St000242The number of indices that are not cyclical small weak excedances. St000291The number of descents of a binary word. St000316The number of non-left-to-right-maxima of a permutation. St000325The width of the tree associated to a permutation. St000331The number of upper interactions of a Dyck path. St000354The number of recoils of a permutation. St000390The number of runs of ones in a binary word. St000470The number of runs in a permutation. St000488The number of cycles of a permutation of length at most 2. St000489The number of cycles of a permutation of length at most 3. St000495The number of inversions of distance at most 2 of a permutation. St000538The number of even inversions of a permutation. St000572The dimension exponent of a set partition. St000584The number of occurrences of the pattern {{1},{2},{3}} such that 1 is minimal, 3 is maximal. St000605The number of occurrences of the pattern {{1},{2,3}} such that 3 is maximal, (2,3) are consecutive in a block. St000677The standardized bi-alternating inversion number of a permutation. St000686The finitistic dominant dimension of a Dyck path. St000702The number of weak deficiencies of a permutation. St000730The maximal arc length of a set partition. St000824The sum of the number of descents and the number of recoils of a permutation. St000829The Ulam distance of a permutation to the identity permutation. St000837The number of ascents of distance 2 of a permutation. St000864The number of circled entries of the shifted recording tableau of a permutation. St000963The 2-shifted major index of a permutation. St001108The 2-dynamic 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: St001246The maximal difference between two consecutive entries of a permutation. St001286The annihilation number of a graph. St001287The number of primes obtained by multiplying preimage and image of a permutation and subtracting one. St001288The number of primes obtained by multiplying preimage and image of a permutation and adding one. St001314The number of tilting modules of arbitrary projective dimension that have no simple modules as a direct summand in the corresponding Nakayama algebra. St001388The number of non-attacking neighbors of a permutation. St001405The number of bonds in a permutation. St001461The number of topologically connected components of the chord diagram of a permutation. St001471The magnitude of a Dyck path. St001489The maximum of the number of descents and the number of inverse descents. St001508The degree of the standard monomial associated to a Dyck path relative to the diagonal boundary. St001509The degree of the standard monomial associated to a Dyck path relative to the trivial lower boundary. St001526The Loewy length of the Auslander-Reiten translate of the regular module as a bimodule of the Nakayama algebra corresponding to the Dyck path. 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. St001798The difference of the number of edges in a graph and the number of edges in the complement of the Turán graph. St001806The upper middle entry of a permutation. St001821The sorting index of a signed permutation. St000021The number of descents of a permutation. St000058The order of a permutation. St000064The number of one-box pattern of a permutation. St000092The number of outer peaks of a permutation. St000099The number of valleys of a permutation, including the boundary. St000133The "bounce" of a permutation. St000162The number of nontrivial cycles in the cycle decomposition of a permutation. St000209Maximum difference of elements in cycles. St000211The rank of the set partition. St000240The number of indices that are not small excedances. St000241The number of cyclical small excedances. St000248The number of anti-singletons of a set partition. St000249The number of singletons (St000247) plus the number of antisingletons (St000248) of a set partition. St000251The number of nonsingleton blocks of a set partition. St000253The crossing number of a set partition. St000258The burning number of a graph. St000299The number of nonisomorphic vertex-induced subtrees. St000329The number of evenly positioned ascents of the Dyck path, with the initial position equal to 1. St000333The dez statistic, the number of descents of a permutation after replacing fixed points by zeros. St000374The number of exclusive right-to-left minima of a permutation. St000387The matching number of a graph. St000429The number of occurrences of the pattern 123 or of the pattern 321 in a permutation. St000430The number of occurrences of the pattern 123 or of the pattern 312 in a permutation. St000469The distinguishing number of a graph. St000482The (zero)-forcing number of a graph. St000485The length of the longest cycle of a permutation. St000487The length of the shortest cycle of a permutation. St000504The cardinality of the first block of a set partition. St000519The largest length of a factor maximising the subword complexity. St000542The number of left-to-right-minima of a permutation. St000556The number of occurrences of the pattern {{1},{2,3}} in a set partition. St000559The number of occurrences of the pattern {{1,3},{2,4}} in a set partition. St000599The number of occurrences of the pattern {{1},{2,3}} such that (2,3) 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. St000619The number of cyclic descents of a permutation. St000636The hull number of a graph. St000653The last descent of a permutation. St000662The staircase size of the code of a permutation. St000673The number of non-fixed points of a permutation. St000679The pruning number of an ordered tree. St000710The number of big deficiencies of a permutation. St000711The number of big exceedences of a permutation. St000758The length of the longest staircase fitting into an integer composition. St000831The number of indices that are either descents or recoils. St000839The largest opener of a set partition. St000862The number of parts of the shifted shape of a permutation. St000863The length of the first row of the shifted shape of a permutation. St000868The aid statistic in the sense of Shareshian-Wachs. St000887The maximal number of nonzero entries on a diagonal of a permutation matrix. St000906The length of the shortest maximal chain in a poset. St000922The minimal number such that all substrings of this length are unique. St000923The minimal number with no two order isomorphic substrings of this length in a permutation. St000942The number of critical left to right maxima of the parking functions. St000988The orbit size of a permutation under Foata's bijection. St001061The number of indices that are both descents and recoils of a permutation. St001062The maximal size of a block of a set partition. St001093The detour number of a graph. St001114The number of odd descents of a permutation. St001151The number of blocks with odd minimum. St001165Number of simple modules with even projective dimension in the corresponding Nakayama algebra. St001166Number of indecomposable projective non-injective modules with dominant dimension equal to the global dimension plus the number of indecomposable projective injective modules in the corresponding Nakayama algebra. St001197The global 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 $eA$. St001207The Lowey length of the algebra $A/T$ when $T$ is the 1-tilting module corresponding to the permutation in the Auslander algebra of $K[x]/(x^n)$. St001240The number of indecomposable modules e_i J^2 that have injective dimension at most one in the corresponding Nakayama algebra St001267The length of the Lyndon factorization of the binary word. St001269The sum of the minimum of the number of exceedances and deficiencies in each cycle of a permutation. St001277The degeneracy of a graph. St001298The number of repeated entries in the Lehmer code of a permutation. St001323The independence gap of a graph. St001350Half of the Albertson index of a graph. St001352The number of internal nodes in the modular decomposition of a graph. St001358The largest degree of a regular subgraph of a graph. St001366The maximal multiplicity of a degree of a vertex of a graph. St001390The number of bumps occurring when Schensted-inserting the letter 1 of a permutation. St001439The number of even weak deficiencies and of odd weak exceedences. St001466The number of transpositions swapping cyclically adjacent numbers in a 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. St001516The number of cyclic bonds of a permutation. St001517The length of a longest pair of twins in a permutation. St001565The number of arithmetic progressions of length 2 in a permutation. St001582The grades of the simple modules corresponding to the points in the poset of the symmetric group under the Bruhat order. St001623The number of doubly irreducible elements of a lattice. St001641The number of ascent tops in the flattened set partition such that all smaller elements appear before. St001654The monophonic hull number of a graph. St001662The length of the longest factor of consecutive numbers in a permutation. St001665The number of pure excedances of a permutation. St001672The restrained domination number of a graph. St001674The number of vertices of the largest induced star graph in the graph. St001682The number of distinct positions of the pattern letter 1 in occurrences of 123 in a permutation. St001683The number of distinct positions of the pattern letter 3 in occurrences of 132 in a permutation. St001713The difference of the first and last value in the first row of the Gelfand-Tsetlin pattern. St001729The number of visible descents of a permutation. St001737The number of descents of type 2 in a permutation. St001760The number of prefix or suffix reversals needed to sort a permutation. St001769The reflection length of a signed permutation. St001784The minimum of the smallest closer and the second element of the block containing 1 in a set partition. St001807The lower middle entry of a permutation. St001844The maximal degree of a generator of the invariant ring of the automorphism group of a graph. St001864The number of excedances of a signed permutation. St001873For a Nakayama algebra corresponding to a Dyck path, we define the matrix C with entries the Hom-spaces between $e_i J$ and $e_j J$ (the radical of the indecomposable projective modules). St001884The number of borders of a binary word. St001905The number of preferred parking spots in a parking function less than the index of the car. St001926Sparre Andersen's position of the maximum of a signed permutation. St001935The number of ascents in a parking function. St001962The proper pathwidth of a graph. St000023The number of inner peaks of a permutation. St000028The number of stack-sorts needed to sort a permutation. St000034The maximum defect over any reduced expression for a permutation and any subexpression. St000056The decomposition (or block) number of a permutation. St000078The number of alternating sign matrices whose left key is the permutation. St000118The number of occurrences of the contiguous pattern [.,[.,[.,.]]] in a binary tree. St000235The number of indices that are not cyclical small weak excedances. St000250The number of blocks (St000105) plus the number of antisingletons (St000248) of a set partition. St000252The number of nodes of degree 3 of a binary tree. St000254The nesting number of a set partition. St000255The number of reduced Kogan faces with the permutation as type. St000286The number of connected components of the complement of a graph. St000353The number of inner valleys of a permutation. St000357The number of occurrences of the pattern 12-3. St000461The rix statistic of a permutation. St000462The major index minus the number of excedences of a permutation. St000486The number of cycles of length at least 3 of a permutation. St000492The rob statistic of a set partition. St000496The rcs statistic of a set partition. St000535The rank-width of a graph. St000541The number of indices greater than or equal to 2 of a permutation such that all smaller indices appear to its right. St000554The number of occurrences of the pattern {{1,2},{3}} in a set partition. St000570The Edelman-Greene number of a permutation. St000577The number of occurrences of the pattern {{1},{2}} such that 1 is a maximal element. St000581The number of occurrences of the pattern {{1,3},{2}} such that 1 is minimal, 2 is maximal. St000597The number of occurrences of the pattern {{1},{2,3}} such that 2 is minimal, (2,3) are consecutive in a block. St000604The number of occurrences of the pattern {{1},{2},{3}} such that 3 is minimal, 2 is maximal. St000633The size of the automorphism group of a poset. St000638The number of up-down runs of a permutation. St000640The rank of the largest boolean interval in a poset. St000685The dominant dimension of the LNakayama algebra associated to a Dyck path. St000689The maximal n such that the minimal generator-cogenerator module in the LNakayama algebra of a Dyck path is n-rigid. St000694The number of affine bounded permutations that project to a given permutation. St000732The number of double deficiencies of a permutation. St000735The last entry on the main diagonal of a standard tableau. St000760The length of the longest strictly decreasing subsequence of parts of an integer composition. St000765The number of weak records in an integer composition. St000771The largest multiplicity of a distance Laplacian eigenvalue in a connected graph. St000774The maximal multiplicity of a Laplacian eigenvalue in a graph. St000805The number of peaks of the associated bargraph. St000832The number of permutations obtained by reversing blocks of three consecutive numbers. St000836The number of descents of distance 2 of a permutation. St000872The number of very big descents of a permutation. St000880The number of connected components of long braid edges in the graph of braid moves of a permutation. St000882The number of connected components of short braid edges in the graph of braid moves of a permutation. St000886The number of permutations with the same antidiagonal sums. St000900The minimal number of repetitions of a part in an integer composition. St000902 The minimal number of repetitions of an integer composition. St000914The sum of the values of the Möbius function of a poset. St000930The k-Gorenstein degree of the corresponding Nakayama algebra with linear quiver. 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 $c_{n−1}$. St000989The number of final rises of a permutation. St000990The first ascent of a permutation. St001006Number of simple modules with projective dimension equal to the global dimension of the Nakayama algebra corresponding to the Dyck path. St001011Number of simple modules of projective dimension 2 in the Nakayama algebra corresponding to the Dyck path. St001031The height of the bicoloured Motzkin path associated with the Dyck path. St001035The convexity degree of the parallelogram polyomino associated with the Dyck path. St001056The Grundy value for the game of deleting vertices of a graph until it has no edges. St001063Numbers of 3-torsionfree simple modules in the corresponding Nakayama algebra. St001064Number of simple modules in the corresponding Nakayama algebra that are 3-syzygy modules. St001075The minimal size of a block of a set partition. St001077The prefix exchange distance of a permutation. St001126Number of simple module that are 1-regular in the corresponding Nakayama algebra. St001160The number of proper blocks (or intervals) of a permutations. St001179Number of indecomposable injective modules with projective dimension at most 2 in the corresponding Nakayama algebra. St001194The injective dimension of $A/AfA$ in the corresponding Nakayama algebra $A$ when $Af$ is the minimal faithful projective-injective left $A$-module 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 $K[x]/(x^n)$. St001220The width of a permutation. 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. St001257The dominant dimension of the double dual of A/J when A is the corresponding Nakayama algebra with Jacobson radical J. St001274The number of indecomposable injective modules with projective dimension equal to two. St001327The minimal number of occurrences of the split-pattern in a linear ordering of the vertices of the graph. St001340The cardinality of a minimal non-edge isolating set of a graph. St001347The number of pairs of vertices of a graph having the same neighbourhood. St001359The number of permutations in the equivalence class of a permutation obtained by taking inverses of cycles. St001396Number of triples of incomparable elements in a finite poset. St001399The distinguishing number of a poset. St001414Half the length of the longest odd length palindromic prefix of a binary word. St001416The length of a longest palindromic factor of a binary word. St001423The number of distinct cubes in a binary word. St001431Half of the Loewy length minus one of a modified stable Auslander algebra of the Nakayama algebra corresponding to the Dyck path. St001462The number of factors of a standard tableaux under concatenation. St001481The minimal height of a peak of a Dyck path. 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. St001493The number of simple modules with maximal even projective dimension in the corresponding Nakayama algebra. St001499The number of indecomposable projective-injective modules of a magnitude 1 Nakayama algebra. St001501The dominant dimension of magnitude 1 Nakayama algebras. St001503The largest distance of a vertex to a vertex in a cycle in the resolution quiver of the corresponding Nakayama algebra. St001507The sum of projective dimension of simple modules with even projective dimension divided by 2 in the LNakayama algebra corresponding to Dyck paths. St001518The number of graphs with the same ordinary spectrum as the given graph. St001520The number of strict 3-descents. St001553The number of indecomposable summands of the square of the Jacobson radical as a bimodule in the Nakayama algebra corresponding to the Dyck path. St001578The minimal number of edges to add or remove to make a graph a line graph. St001591The number of graphs with the given composition of multiplicities of Laplacian eigenvalues. St001640The number of ascent tops in the permutation such that all smaller elements appear before. St001652The length of a longest interval of consecutive numbers. St001661Half the permanent of the Identity matrix plus the permutation matrix associated to the permutation. St001693The excess length of a longest path consisting of elements and blocks of a set partition. St001728The number of invisible descents of a permutation. St001735The number of permutations with the same set of runs. St001743The discrepancy of a graph. St001768The number of reduced words of a signed permutation. St001774The degree of the minimal polynomial of the smallest eigenvalue of a graph. St001775The degree of the minimal polynomial of the largest eigenvalue of a graph. St001822The number of alignments of a signed permutation. St001839The number of excedances of a set partition. St001859The number of factors of the Stanley symmetric function associated with a permutation. St001860The number of factors of the Stanley symmetric function associated with a signed permutation. St001882The number of occurrences of a type-B 231 pattern in a signed permutation. St001896The number of right descents of a signed permutations. St001904The length of the initial strictly increasing segment of a parking function. St001937The size of the center of a parking function. St001941The evaluation at 1 of the modified Kazhdan--Lusztig R polynomial (as in [1, Section 5. St001942The number of loops of the quiver corresponding to the reduced incidence algebra of a poset. St001946The number of descents in a parking function. St001949The rigidity index of a graph. St000017The number of inversions of a standard tableau. St000090The variation of a composition. St000122The number of occurrences of the contiguous pattern [.,[.,[[.,.],.]]] in a binary tree. St000125The number of occurrences of the contiguous pattern [.,[[[.,.],.],. St000130The number of occurrences of the contiguous pattern [.,[[.,.],[[.,.],.]]] in a binary tree. St000131The number of occurrences of the contiguous pattern [.,[[[[.,.],.],.],. St000132The number of occurrences of the contiguous pattern [[.,.],[.,[[.,.],.]]] in a binary tree. St000154The sum of the descent bottoms of a permutation. St000210Minimum over maximum difference of elements in cycles. St000219The number of occurrences of the pattern 231 in a permutation. St000221The number of strong fixed points of a permutation. St000233The number of nestings of a set partition. St000234The number of global ascents of a permutation. St000274The number of perfect matchings of a graph. St000317The cycle descent number of a permutation. St000322The skewness of a graph. St000323The minimal crossing number of a graph. St000355The number of occurrences of the pattern 21-3. St000360The number of occurrences of the pattern 32-1. St000365The number of double ascents of a permutation. St000367The number of simsun double descents of a permutation. St000370The genus of a graph. St000375The number of non weak exceedences of a permutation that are mid-points of a decreasing subsequence of length $3$. St000405The number of occurrences of the pattern 1324 in a permutation. St000406The number of occurrences of the pattern 3241 in a permutation. St000407The number of occurrences of the pattern 2143 in a permutation. St000423The number of occurrences of the pattern 123 or of the pattern 132 in a permutation. St000426The number of occurrences of the pattern 132 or of the pattern 312 in a permutation. St000472The sum of the ascent bottoms of a permutation. St000500Eigenvalues of the random-to-random operator acting on the regular representation. St000516The number of stretching pairs of a permutation. St000560The number of occurrences of the pattern {{1,2},{3,4}} in a set partition. St000589The number of occurrences of the pattern {{1},{2,3}} such that 1 is maximal, (2,3) are consecutive in a block. St000606The number of occurrences of the pattern {{1},{2,3}} such that 1,3 are maximal, (2,3) are consecutive in a block. St000611The number of occurrences of the pattern {{1},{2,3}} such that 1 is maximal. St000613The number of occurrences of the pattern {{1,3},{2}} such that 2 is minimal, 3 is maximal, (1,3) are consecutive in a block. St000623The number of occurrences of the pattern 52341 in a permutation. St000649The number of 3-excedences of a permutation. St000650The number of 3-rises of a permutation. St000664The number of right ropes of a permutation. St000666The number of right tethers of a permutation. St000687The dimension of $Hom(I,P)$ for the LNakayama algebra of a Dyck path. St000750The number of occurrences of the pattern 4213 in a permutation. St000751The number of occurrences of either of the pattern 2143 or 2143 in a permutation. St000766The number of inversions of an integer composition. St000768The number of peaks in an integer composition. St000796The stat' of a permutation. St000797The stat`` of a permutation. St000799The number of occurrences of the vincular pattern |213 in 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. St000802The number of occurrences of the vincular pattern |321 in a permutation. St000803The number of occurrences of the vincular pattern |132 in a permutation. St000804The number of occurrences of the vincular pattern |123 in a permutation. St000806The semiperimeter of the associated bargraph. St000807The sum of the heights of the valleys of the associated bargraph. St000873The aix statistic of a permutation. St000879The number of long braid edges in the graph of braid moves of a permutation. St000881The number of short braid edges in the graph of braid moves of a permutation. St000954Number of times the corresponding LNakayama algebra has $Ext^i(D(A),A)=0$ for $i>0$. St000962The 3-shifted major index of a permutation. St000966Number of peaks minus the global dimension of the corresponding LNakayama algebra. St001001The number of indecomposable modules with projective and injective dimension equal to the global dimension of 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. St001013Number of indecomposable injective modules with codominant dimension equal to the global dimension in the Nakayama algebra corresponding to the Dyck path. St001025Number of simple modules with projective dimension 4 in the Nakayama algebra corresponding to the Dyck path. St001059Number of occurrences of the patterns 41352,42351,51342,52341 in a permutation. St001065Number of indecomposable reflexive modules in the corresponding Nakayama algebra. St001082The number of boxed occurrences of 123 in a permutation. St001085The number of occurrences of the vincular pattern |21-3 in a permutation. St001113Number of indecomposable projective non-injective modules with reflexive Auslander-Reiten sequences in the corresponding Nakayama algebra. St001140Number of indecomposable modules with projective and injective dimension at least two in the corresponding Nakayama algebra. St001153The number of blocks with even minimum in a set partition. St001159Number of simple modules with dominant dimension equal to the global dimension in the corresponding Nakayama algebra. St001163The number of simple modules with dominant dimension at least three in the corresponding Nakayama algebra. St001171The vector space dimension of $Ext_A^1(I_o,A)$ when $I_o$ is the tilting module corresponding to the permutation $o$ in the Auslander algebra $A$ of $K[x]/(x^n)$. St001181Number of indecomposable injective modules with grade at least 3 in the corresponding Nakayama algebra. St001186Number of simple modules with grade at least 3 in the corresponding Nakayama algebra. St001191Number of simple modules $S$ with $Ext_A^i(S,A)=0$ for all $i=0,1,...,g-1$ in the corresponding Nakayama algebra $A$ with global dimension $g$. St001193The dimension of $Ext_A^1(A/AeA,A)$ in the corresponding Nakayama algebra $A$ such that $eA$ is a minimal faithful projective-injective module. St001195The global dimension of the algebra $A/AfA$ of the corresponding Nakayama algebra $A$ with minimal left faithful projective-injective module $Af$. 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. St001221The number of simple modules in the corresponding LNakayama algebra that have 2 dimensional second Extension group with the regular module. 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. St001260The permanent of an alternating sign matrix. St001264The smallest index i such that the i-th simple module has projective dimension equal to the global dimension of the corresponding Nakayama algebra. St001266The largest vector space dimension of an indecomposable non-projective module that is reflexive in the corresponding Nakayama algebra. St001292The injective dimension of the tensor product of two copies of the dual of the Nakayama algebra associated to a Dyck path. St001309The number of four-cliques in a graph. St001329The minimal number of occurrences of the outerplanar pattern in a linear ordering of the vertices of the graph. St001334The minimal number of occurrences of the 3-colorable pattern in a linear ordering of the vertices of the graph. St001353The number of prime nodes in the modular decomposition of a graph. St001354The number of series nodes in the modular decomposition of a graph. St001357The maximal degree of a regular spanning subgraph of a graph. St001381The fertility of a permutation. St001402The number of separators in a permutation. St001403The number of vertical separators in a permutation. St001411The number of patterns 321 or 3412 in a permutation. St001417The length of a longest palindromic subword 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. St001465The number of adjacent transpositions in the cycle decomposition of a permutation. St001510The number of self-evacuating linear extensions of a finite poset. St001511The minimal number of transpositions needed to sort a permutation in either direction. St001513The number of nested exceedences of a permutation. St001535The number of cyclic alignments of a permutation. St001537The number of cyclic crossings of a permutation. St001549The number of restricted non-inversions between exceedances. St001550The number of inversions between exceedances where the greater exceedance is linked. St001551The number of restricted non-inversions between exceedances where the rightmost exceedance is linked. St001552The number of inversions between excedances and fixed points of a permutation. St001577The minimal number of edges to add or remove to make a graph a cograph. St001633The number of simple modules with projective dimension two in the incidence algebra of the poset. St001663The number of occurrences of the Hertzsprung pattern 132 in a permutation. St001684The reduced word complexity of a permutation. St001685The number of distinct positions of the pattern letter 1 in occurrences of 132 in a permutation. St001687The number of distinct positions of the pattern letter 2 in occurrences of 213 in a permutation. St001691The number of kings in a graph. St001702The absolute value of the determinant of the adjacency matrix of a graph. St001715The number of non-records in a permutation. St001745The number of occurrences of the arrow pattern 13 with an arrow from 1 to 2 in a permutation. St001781The interlacing number of a set partition. St001797The number of overfull subgraphs of a graph. St001810The number of fixed points of a permutation smaller than its largest moved point. St001811The Castelnuovo-Mumford regularity of a permutation. St001816Eigenvalues of the top-to-random operator acting on a simple module. St001847The number of occurrences of the pattern 1432 in a permutation. St001856The number of edges in the reduced word graph of a permutation. St001862The number of crossings of a signed permutation. St001871The number of triconnected components of a graph. St001874Lusztig's a-function for the symmetric group. St001903The number of fixed points of a parking function. St001948The number of augmented double ascents of a permutation. St001957The number of Hasse diagrams with a given underlying undirected graph. St001960The number of descents of a permutation minus one if its first entry is not one. St001854The size of the left Kazhdan-Lusztig cell, St000301The number of facets of the stable set polytope of a graph. St000376The bounce deficit of a Dyck path. St000798The makl of a permutation. St001671Haglund's hag of a permutation. St001759The Rajchgot index of a permutation. St000564The number of occurrences of the pattern {{1},{2}} in a set partition. St001858The number of covering elements of a signed permutation in absolute order. St001168The vector space dimension of the tilting module corresponding to the permutation in the Auslander algebra of $K[x]/(x^n)$. St001528The number of permutations such that the product with the permutation has the same number of fixed points. St000080The rank of the poset. St000422The energy of a graph, if it is integral. St000632The jump number of the 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 $eA$. St001621The number of atoms of a lattice. St001754The number of tolerances of a finite lattice. St001820The size of the image of the pop stack sorting operator. St001876The number of 2-regular simple modules in the incidence algebra of the lattice. St000524The number of posets with the same order polynomial. St000526The number of posets with combinatorially isomorphic order polytopes. St000910The number of maximal chains of minimal length in a poset. St001105The number of greedy linear extensions of a poset. St001106The number of supergreedy linear extensions of a poset. St001902The number of potential covers of a poset. St000307The number of rowmotion orbits of a poset.