St001405The number of bonds in a permutation. St000058The order of a permutation. St000062The length of the longest increasing subsequence of the permutation. St000134The size of the orbit of an alternating sign matrix under gyration. St000184The size of the centralizer of any permutation of given cycle type. St000236The number of cyclical small weak excedances. St000258The burning number of a graph. St000308The height of the tree associated to a permutation. St000384The maximal part of the shifted composition of an integer partition. St000469The distinguishing number of a graph. St000485The length of the longest cycle of a permutation. St000495The number of inversions of distance at most 2 of a permutation. St000619The number of cyclic descents of a permutation. St000662The staircase size of the code of a permutation. St000675The number of centered multitunnels of a Dyck path. St000784The maximum of the length and the largest part of the integer partition. St000793The length of the longest partition in the vacillating tableau corresponding to a set partition. St000822The Hadwiger number of the graph. St000829The Ulam distance of a permutation to the identity permutation. St000907The number of maximal antichains of minimal length in a poset. St000983The length of the longest alternating subword. St000991The number of right-to-left minima of a permutation. St001052The length of the exterior of a permutation. St001116The game chromatic number of a graph. St001245The cyclic maximal difference between two consecutive entries of a permutation. St001246The maximal difference between two consecutive entries of a permutation. St001330The hat guessing number of a graph. St001366The maximal multiplicity of a degree of a vertex of a graph. St001486The number of corners of the ribbon associated with an integer composition. St001580The acyclic chromatic number of a graph. St001642The Prague dimension of a graph. St001670The connected partition number of a graph. St001741The largest integer such that all patterns of this size are contained in the permutation. St001746The coalition number of a graph. St001760The number of prefix or suffix reversals needed to sort a permutation. St001761The maximal multiplicity of a letter in a reduced word of a permutation. St001806The upper middle entry of a permutation. St001844The maximal degree of a generator of the invariant ring of the automorphism group of a graph. St001883The mutual visibility number of a graph. St001884The number of borders of a binary word. St001899The total number of irreducible representations contained in the higher Lie character for an integer partition. St001900The number of distinct irreducible representations contained in the higher Lie character for an integer partition. St001914The size of the orbit of an integer partition in Bulgarian solitaire. St001963The tree-depth of a graph. St000028The number of stack-sorts needed to sort a permutation. St000035The number of left outer peaks of a permutation. St000162The number of nontrivial cycles in the cycle decomposition of a permutation. St000245The number of ascents of a permutation. St000260The radius of a connected graph. St000261The edge connectivity of a graph. St000262The vertex connectivity of a graph. St000272The treewidth of a graph. St000290The major index of a binary word. St000310The minimal degree of a vertex of a graph. 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. St000337The lec statistic, the sum of the inversion numbers of the hook factors of a permutation. St000354The number of recoils of a permutation. St000362The size of a minimal vertex cover of a graph. St000374The number of exclusive right-to-left minima of a permutation. St000380Half of the maximal perimeter of a rectangle fitting into the diagram of an integer partition. St000387The matching number of a graph. St000483The number of times a permutation switches from increasing to decreasing or decreasing to increasing. St000536The pathwidth of a graph. St000537The cutwidth of a graph. St000646The number of big ascents of a permutation. St000651The maximal size of a rise in a permutation. St000659The number of rises of length at least 2 of a Dyck path. St000691The number of changes of a binary word. St000703The number of deficiencies of a permutation. St000710The number of big deficiencies of a permutation. St000711The number of big exceedences of a permutation. St000743The number of entries in a standard Young tableau such that the next integer is a neighbour. St000778The metric dimension of a graph. 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. St000923The minimal number with no two order isomorphic substrings of this length in a permutation. St000938The number of zeros of the symmetric group character corresponding to the partition. St000941The number of characters of the symmetric group whose value on the partition is even. St000994The number of cycle peaks and the number of cycle valleys of a permutation. St001035The convexity degree of the parallelogram polyomino associated with the Dyck path. St001036The number of inner corners of the parallelogram polyomino associated with the Dyck path. St001078The minimal number of occurrences of (12) in a factorization of a permutation into transpositions (12) and cycles (1,. St001090The number of pop-stack-sorts needed to sort a permutation. 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. St001214The aft of an integer partition. St001269The sum of the minimum of the number of exceedances and deficiencies in each cycle of a permutation. St001270The bandwidth of a graph. St001271The competition number of a graph. St001277The degeneracy of a graph. St001287The number of primes obtained by multiplying preimage and image of a permutation and subtracting one. St001340The cardinality of a minimal non-edge isolating set of a graph. St001358The largest degree of a regular subgraph of a graph. St001388The number of non-attacking neighbors of a permutation. St001421Half the length of a longest factor which is its own reverse-complement and begins with a one of a binary word. St001485The modular major index of a binary word. St001508The degree of the standard monomial associated to a Dyck path relative to the diagonal boundary. St001511The minimal number of transpositions needed to sort a permutation in either direction. St001553The number of indecomposable summands of the square of the Jacobson radical as a bimodule in the Nakayama algebra corresponding to the Dyck path. St001644The dimension of a graph. St001665The number of pure excedances of a permutation. St001729The number of visible descents of a permutation. St001737The number of descents of type 2 in a permutation. St001792The arboricity of a graph. St001807The lower middle entry of a permutation. St001859The number of factors of the Stanley symmetric function associated with a 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). St001928The number of non-overlapping descents in a permutation. St001949The rigidity index of a graph. St001958The degree of the polynomial interpolating the values of a permutation. St001962The proper pathwidth of a graph. St001023Number of simple modules with projective dimension at most 3 in the Nakayama algebra corresponding to the Dyck path. St000007The number of saliances of the permutation. St000010The length of the partition. St000013The height of a Dyck path. St000015The number of peaks of a Dyck path. St000021The number of descents of a permutation. St000031The number of cycles in the cycle decomposition of a permutation. St000054The first entry of the permutation. St000060The greater neighbor of the maximum. St000092The number of outer peaks of a permutation. St000093The cardinality of a maximal independent set of vertices of a graph. St000097The order of the largest clique of the graph. St000098The chromatic number of a graph. St000099The number of valleys of a permutation, including the boundary. St000141The maximum drop size of a permutation. St000147The largest part of an integer partition. St000155The number of exceedances (also excedences) of a permutation. St000171The degree of the graph. St000213The number of weak exceedances (also weak excedences) of a permutation. St000216The absolute length of a permutation. St000238The number of indices that are not small weak excedances. St000243The number of cyclic valleys and cyclic peaks of a permutation. St000271The chromatic index of a graph. St000288The number of ones in a binary word. St000299The number of nonisomorphic vertex-induced subtrees. St000306The bounce count of a Dyck path. St000314The number of left-to-right-maxima of a permutation. St000316The number of non-left-to-right-maxima of a permutation. St000325The width of the tree associated to a permutation. St000326The position of the first one in a binary word after appending a 1 at the end. St000340The number of non-final maximal constant sub-paths of length greater than one. St000378The diagonal inversion number of an integer partition. St000381The largest part of an integer composition. St000390The number of runs of ones in a binary word. St000393The number of strictly increasing runs in a binary word. St000443The number of long tunnels of a Dyck path. St000444The length of the maximal rise of a Dyck path. St000451The length of the longest pattern of the form k 1 2. St000453The number of distinct Laplacian eigenvalues of a graph. St000470The number of runs in a permutation. St000482The (zero)-forcing number of a graph. St000488The number of cycles of a permutation of length at most 2. St000489The number of cycles of a permutation of length at most 3. St000507The number of ascents of a standard tableau. St000527The width of the poset. St000542The number of left-to-right-minima of a permutation. St000626The minimal period of a binary word. St000628The balance of a binary word. St000638The number of up-down runs of a permutation. St000645The sum of the areas of the rectangles formed by two consecutive peaks and the valley in between. St000652The maximal difference between successive positions of a permutation. St000668The least common multiple of the parts of the partition. St000670The reversal length of a permutation. St000672The number of minimal elements in Bruhat order not less than the permutation. St000676The number of odd rises of a Dyck path. St000684The global dimension of the LNakayama algebra associated to a Dyck path. St000686The finitistic dominant dimension of a Dyck path. St000702The number of weak deficiencies of a permutation. St000725The smallest label of a leaf of the increasing binary tree associated to a permutation. St000741The Colin de Verdière graph invariant. St000742The number of big ascents of a permutation after prepending zero. St000744The length of the path to the largest entry in a standard Young tableau. St000757The length of the longest weakly inreasing subsequence of parts of an integer composition. St000758The length of the longest staircase fitting into an integer composition. St000759The smallest missing part in an integer partition. St000767The number of runs 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. St000777The number of distinct eigenvalues of the distance Laplacian of a connected graph. St000780The size of the orbit under rotation of a perfect matching. St000786The maximal number of occurrences of a colour in a proper colouring of a graph. St000796The stat' of a permutation. St000808The number of up steps of the associated bargraph. St000831The number of indices that are either descents or recoils. St000862The number of parts of the shifted shape of a permutation. St000876The number of factors in the Catalan decomposition of a binary word. St000887The maximal number of nonzero entries on a diagonal of a permutation matrix. St000903The number of different parts of an integer composition. St000904The maximal number of repetitions of an integer composition. St000918The 2-limited packing number of a graph. St000922The minimal number such that all substrings of this length are unique. St000937The number of positive values of the symmetric group character corresponding to the partition. St000939The number of characters of the symmetric group whose value on the partition is positive. St000945The number of matchings in the dihedral orbit of a perfect matching. St000956The maximal displacement of a permutation. St000982The length of the longest constant subword. St000988The orbit size of a permutation under Foata's bijection. St001004The number of indices that are either left-to-right maxima or right-to-left minima. St001007Number of simple modules with projective dimension 1 in the Nakayama algebra corresponding to the Dyck path. St001029The size of the core of a graph. St001038The minimal height of a column in the parallelogram polyomino associated with the Dyck path. St001039The maximal height of a column in the parallelogram polyomino associated with a Dyck path. St001068Number of torsionless simple modules in the corresponding Nakayama algebra. St001075The minimal size of a block of a set partition. St001093The detour number of a graph. St001112The 3-weak dynamic number of a graph. St001117The game chromatic index of a graph. St001118The acyclic chromatic index of a graph. St001128The exponens consonantiae of a partition. St001165Number of simple modules with even projective dimension in the corresponding Nakayama algebra. St001176The size of a partition minus its first part. St001183The maximum of $projdim(S)+injdim(S)$ over all simple modules in the Nakayama algebra corresponding to the Dyck path. St001184Number of indecomposable injective modules with grade at least 1 in the corresponding Nakayama algebra. St001187The number of simple modules with grade at least one in the corresponding Nakayama algebra. St001197The global dimension of $eAe$ for the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. 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: 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 $K[x]/(x^n)$. St001224Let X be the direct sum of all simple modules of the corresponding Nakayama algebra. St001235The global dimension of the corresponding Comp-Nakayama algebra. St001239The largest vector space dimension of the double dual of a simple module in the corresponding Nakayama algebra. St001250The number of parts of a partition that are not congruent 0 modulo 3. St001258Gives the maximum of injective plus projective dimension of an indecomposable module over the corresponding Nakayama algebra. St001267The length of the Lyndon factorization of the binary word. St001285The number of primes in the column sums of the two line notation of a permutation. St001286The annihilation number of a graph. St001298The number of repeated entries in the Lehmer code of a permutation. St001315The dissociation number of 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. St001337The upper domination number of a graph. St001338The upper irredundance number of a graph. St001346The number of parking functions that give the same permutation. St001355Number of non-empty prefixes of a binary word that contain equally many 0's and 1's. St001357The maximal degree of a regular spanning subgraph of a graph. St001372The length of a longest cyclic run of ones of a binary word. St001375The pancake length of a permutation. St001390The number of bumps occurring when Schensted-inserting the letter 1 of a permutation. St001415The length of the longest palindromic prefix of a binary word. St001416The length of a longest palindromic factor of a binary word. St001417The length of a longest palindromic subword of a binary word. St001420Half the length of a longest factor which is its own reverse-complement of a binary word. St001437The flex of a binary word. St001439The number of even weak deficiencies and of odd weak exceedences. St001461The number of topologically connected components of the chord diagram of a permutation. St001464The number of bases of the positroid corresponding to the permutation, with all fixed points counterclockwise. St001466The number of transpositions swapping cyclically adjacent numbers in a permutation. St001471The magnitude of a Dyck path. St001483The number of simple module modules that appear in the socle of the regular module but have no nontrivial selfextensions with the regular module. St001488The number of corners of a skew partition. St001489The maximum of the number of descents and the number of inverse descents. St001494The Alon-Tarsi number of a graph. St001497The position of the largest weak excedence of a permutation. St001499The number of indecomposable projective-injective modules of a magnitude 1 Nakayama algebra. St001514The dimension of the top of the Auslander-Reiten translate of the regular modules as a bimodule. St001515The vector space dimension of the socle of the first syzygy module of the regular module (as a bimodule). St001517The length of a longest pair of twins in a permutation. St001530The depth of a Dyck path. St001555The order of a signed permutation. St001615The number of join prime elements of a lattice. St001617The dimension of the space of valuations of a lattice. St001622The number of join-irreducible elements of a lattice. St001637The number of (upper) dissectors of a poset. St001662The length of the longest factor of consecutive numbers in a permutation. St001674The number of vertices of the largest induced star graph in the graph. St001723The differential of a graph. St001785The number of ways to obtain a partition as the multiset of antidiagonal lengths of the Ferrers diagram of a partition. St001814The number of partitions interlacing the given partition. St001907The number of Bastidas - Hohlweg - Saliola excedances of a signed permutation. St000023The number of inner peaks of a permutation. St000024The number of double up and double down steps of a Dyck path. St000050The depth or height of a binary tree. St000053The number of valleys of the Dyck path. St000057The Shynar inversion number of a standard tableau. St000083The number of left oriented leafs of a binary tree except the first one. St000091The descent variation of a composition. St000120The number of left tunnels of a Dyck path. St000144The pyramid weight of the Dyck path. St000153The number of adjacent cycles of a permutation. St000157The number of descents of a standard tableau. St000203The number of external nodes of a binary tree. St000222The number of alignments in the permutation. St000225Difference between largest and smallest parts in a partition. St000239The number of small weak excedances. St000242The number of indices that are not cyclical small weak excedances. St000251The number of nonsingleton blocks of a set partition. St000253The crossing number of a set partition. St000259The diameter of a connected graph. St000291The number of descents of a binary word. St000292The number of ascents of a binary word. St000293The number of inversions of a binary word. St000295The length of the border of a binary word. St000319The spin of an integer partition. St000320The dinv adjustment of an integer partition. St000331The number of upper interactions of a Dyck path. St000334The maz index, the major index of a permutation after replacing fixed points by zeros. St000352The Elizalde-Pak rank of a permutation. St000353The number of inner valleys of a permutation. St000356The number of occurrences of the pattern 13-2. St000372The number of mid points of increasing subsequences of length 3 in a permutation. St000373The number of weak exceedences of a permutation that are also mid-points of a decreasing subsequence of length $3$. St000392The length of the longest run of ones in a binary word. St000395The sum of the heights of the peaks of a Dyck path. St000430The number of occurrences of the pattern 123 or of the pattern 312 in a permutation. St000442The maximal area to the right of an up step of a Dyck path. St000446The disorder of a permutation. St000452The number of distinct eigenvalues of a graph. St000461The rix statistic of a permutation. St000462The major index minus the number of excedences of a permutation. St000480The number of lower covers of a partition in dominance order. St000481The number of upper covers of a partition in dominance order. St000486The number of cycles of length at least 3 of a permutation. St000512The number of invariant subsets of size 3 when acting with a permutation of given cycle type. St000534The number of 2-rises of a permutation. St000538The number of even inversions of a permutation. St000539The number of odd inversions of a permutation. St000541The number of indices greater than or equal to 2 of a permutation such that all smaller indices appear to its right. St000546The number of global descents of a permutation. St000547The number of even non-empty partial sums of an integer partition. St000565The major index of a set partition. 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. St000624The normalized sum of the minimal distances to a greater element. St000632The jump number of the poset. St000640The rank of the largest boolean interval in a poset. St000663The number of right floats of a permutation. St000665The number of rafts of a permutation. St000677The standardized bi-alternating inversion number of a permutation. St000682The Grundy value of Welter's game on a binary word. St000688The global dimension minus the dominant dimension of the LNakayama algebra associated to a Dyck path. St000692Babson and Steingrímsson's statistic of a permutation. St000717The number of ordinal summands of a poset. St000724The label of the leaf of the path following the smaller label in the increasing binary tree associated to a permutation. St000761The number of ascents in an integer composition. St000779The tier of a permutation. St000809The reduced reflection length of the permutation. St000824The sum of the number of descents and the number of recoils of a permutation. St000836The number of descents of distance 2 of a permutation. St000837The number of ascents of distance 2 of a permutation. St000850The number of 1/2-balanced pairs in a poset. St000864The number of circled entries of the shifted recording tableau of a permutation. St000868The aid statistic in the sense of Shareshian-Wachs. St000871The number of very big ascents of a permutation. St000872The number of very big descents of a permutation. St000873The aix statistic of a permutation. St000877The depth of the binary word interpreted as a path. St000883The number of longest increasing subsequences of a permutation. St000884The number of isolated descents of a permutation. St000906The length of the shortest maximal chain in a poset. St000919The number of maximal left branches of a binary tree. St000921The number of internal inversions of a binary word. St000940The number of characters of the symmetric group whose value on the partition is zero. St000970Number of peaks minus the dominant dimension of the corresponding LNakayama algebra. 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. St001011Number of simple modules of projective dimension 2 in the Nakayama algebra corresponding to the Dyck path. St001012Number of simple modules with projective dimension at most 2 in the Nakayama algebra corresponding to the Dyck path. St001017Number of indecomposable injective modules with projective dimension equal to the codominant dimension in the Nakayama algebra corresponding to the Dyck path. St001018Sum of projective dimension of the indecomposable injective modules of the Nakayama algebra corresponding to the Dyck path. St001020Sum of the codominant dimensions of the non-projective indecomposable injective modules of the Nakayama algebra corresponding to the Dyck path. St001026The maximum of the projective dimensions of the indecomposable non-projective injective modules minus the minimum in the Nakayama algebra corresponding to the Dyck path. St001027Number of simple modules with projective dimension equal to injective dimension in the Nakayama algebra corresponding to the Dyck path. St001028Number of simple modules with injective dimension equal to the dominant dimension in the Nakayama algebra corresponding to the Dyck path. St001031The height of the bicoloured Motzkin path 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. St001085The number of occurrences of the vincular pattern |21-3 in a permutation. St001087The number of occurrences of the vincular pattern |12-3 in a permutation. St001104The number of descents of the invariant in a tensor power of the adjoint representation of the rank two general linear group. St001108The 2-dynamic chromatic number of a graph. St001110The 3-dynamic chromatic number of a graph. St001114The number of odd descents of a permutation. St001119The length of a shortest maximal path in a graph. St001126Number of simple module that are 1-regular in the corresponding Nakayama algebra. St001140Number of indecomposable modules with projective and injective dimension at least two in the corresponding Nakayama algebra. St001142The projective dimension of the socle of the regular module as a bimodule in the Nakayama algebra corresponding to the Dyck path. St001152The number of pairs with even minimum in a perfect matching. St001164Number of indecomposable injective modules whose socle has projective dimension at most g-1 (g the global dimension) minus the number of indecomposable projective-injective modules. St001169Number of simple modules with projective dimension at least two in the corresponding Nakayama algebra. St001170Number of indecomposable injective modules whose socle has projective dimension at most g-1 when g denotes the global dimension in the corresponding Nakayama algebra. St001179Number of indecomposable injective modules with projective dimension at most 2 in the corresponding Nakayama algebra. St001180Number of indecomposable injective modules with projective dimension at most 1. St001188The number of simple modules $S$ with grade $\inf \{ i \geq 0 | Ext^i(S,A) \neq 0 \}$ at least two in the Nakayama algebra $A$ corresponding to the Dyck path. St001192The maximal dimension of $Ext_A^2(S,A)$ for a simple module $S$ over the corresponding Nakayama algebra $A$. St001194The injective dimension of $A/AfA$ in the corresponding Nakayama algebra $A$ when $Af$ is the minimal faithful projective-injective left $A$-module St001211The number of simple modules in the corresponding Nakayama algebra that have vanishing second Ext-group with the regular module. St001212The number of simple modules in the corresponding Nakayama algebra that have non-zero second Ext-group with the regular module. St001215Let X be the direct sum of all simple modules of the corresponding Nakayama algebra. St001222Number of simple modules in the corresponding LNakayama algebra that have a unique 2-extension with the regular module. St001244The number of simple modules of projective dimension one that are not 1-regular for the Nakayama algebra associated to a Dyck path. St001251The number of parts of a partition that are not congruent 1 modulo 3. St001266The largest vector space dimension of an indecomposable non-projective module that is reflexive in the corresponding Nakayama algebra. St001273The projective dimension of the first term in an injective coresolution of the regular module. St001276The number of 2-regular indecomposable modules in the corresponding Nakayama algebra. St001280The number of parts of an integer partition that are at least two. St001294The maximal torsionfree index of a simple non-projective module in the corresponding Nakayama algebra. St001296The maximal torsionfree index of an indecomposable non-projective module in the corresponding Nakayama algebra. St001331The size of the minimal feedback vertex set. St001349The number of different graphs obtained from the given graph by removing an edge. St001394The genus of a permutation. St001403The number of vertical separators in a permutation. St001418Half of the global dimension of the stable Auslander algebra of the Nakayama algebra corresponding to the Dyck path. St001424The number of distinct squares 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. St001436The index of a given binary word in the lex-order among all its cyclic shifts. St001469The holeyness of a permutation. St001470The cyclic holeyness of a permutation. St001484The number of singletons of an integer partition. 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. St001505The number of elements generated by the Dyck path as a map in the full transformation monoid. St001506Half the projective dimension of the unique simple module with even projective dimension in a magnitude 1 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. St001509The degree of the standard monomial associated to a Dyck path relative to the trivial lower boundary. St001512The minimum rank of a graph. St001520The number of strict 3-descents. St001537The number of cyclic crossings of a permutation. St001554The number of distinct nonempty subtrees of a binary tree. St001557The number of inversions of the second entry of a permutation. St001565The number of arithmetic progressions of length 2 in a permutation. St001569The maximal modular displacement of a permutation. St001579The number of cyclically simple transpositions decreasing the number of cyclic descents needed to sort a permutation. St001582The grades of the simple modules corresponding to the points in the poset of the symmetric group under the Bruhat order. St001601The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on trees. St001633The number of simple modules with projective dimension two in the incidence algebra of the poset. St001638The book thickness of a graph. St001655The general position number of a graph. St001656The monophonic position number of a graph. St001671Haglund's hag of a permutation. St001673The degree of asymmetry of an integer composition. 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. St001685The number of distinct positions of the pattern letter 1 in occurrences of 132 in a permutation. St001693The excess length of a longest path consisting of elements and blocks of a set partition. St001724The 2-packing differential of a graph. St001725The harmonious chromatic number of a graph. St001726The number of visible inversions of a permutation. St001727The number of invisible inversions of a permutation. St001742The difference of the maximal and the minimal degree in a graph. St001744The number of occurrences of the arrow pattern 1-2 with an arrow from 1 to 2 in a permutation. St001777The number of weak descents in an integer composition. St001798The difference of the number of edges in a graph and the number of edges in the complement of the Turán graph. St001801Half the number of preimage-image pairs of different parity in a permutation. St001810The number of fixed points of a permutation smaller than its largest moved point. St001811The Castelnuovo-Mumford regularity of a permutation. St001839The number of excedances of a set partition. St001842The major index of a set partition. St001864The number of excedances of a signed permutation. St001874Lusztig's a-function for the symmetric group. St001896The number of right descents of a signed permutations. St001911A descent variant minus the number of inversions. St001918The degree of the cyclic sieving polynomial corresponding to an integer partition. St001935The number of ascents in a parking function. St001942The number of loops of the quiver corresponding to the reduced incidence algebra of a poset. St001955The number of natural descents for set-valued two row standard Young tableaux. St001960The number of descents of a permutation minus one if its first entry is not one. St000351The determinant of the adjacency matrix of a graph. St000998Number of indecomposable projective modules with injective dimension smaller than or equal to the dominant dimension in the Nakayama algebra corresponding to the Dyck path. St001190Number of simple modules with projective dimension at most 4 in the corresponding Nakayama algebra. St001240The number of indecomposable modules e_i J^2 that have injective dimension at most one in the corresponding Nakayama algebra St001650The order of Ringel's homological bijection associated to the linear Nakayama algebra corresponding to the Dyck path. St000967The value p(1) for the Coxeterpolynomial p of the corresponding LNakayama algebra. St001218Smallest index k greater than or equal to one such that the Coxeter matrix C of the corresponding Nakayama algebra has C^k=1. St000369The dinv deficit of a Dyck path. St000376The bounce deficit of a Dyck path. St000661The number of rises of length 3 of a Dyck path. St000791The number of pairs of left tunnels, one strictly containing the other, of a Dyck path. St000931The number of occurrences of the pattern UUU in a Dyck path. St001141The number of occurrences of hills of size 3 in a Dyck path. St000064The number of one-box pattern of a permutation. St000893The number of distinct diagonal sums of an alternating sign matrix. St000100The number of linear extensions of a poset. St000633The size of the automorphism group of a poset. St000695The number of blocks in the first part of the atomic decomposition of a set partition. St000832The number of permutations obtained by reversing blocks of three consecutive numbers. St000910The number of maximal chains of minimal length in a poset. St001081The number of minimal length factorizations of a permutation into star transpositions. St001105The number of greedy linear extensions of a poset. St001106The number of supergreedy linear extensions of a poset. St001220The width of a permutation. St001632The number of indecomposable injective modules $I$ with $dim Ext^1(I,A)=1$ for the incidence algebra A of a poset. St000432The number of occurrences of the pattern 231 or of the pattern 312 in a permutation. St000434The number of occurrences of the pattern 213 or of the pattern 312 in a permutation. St000436The number of occurrences of the pattern 231 or of the pattern 321 in a permutation. St000437The number of occurrences of the pattern 312 or of the pattern 321 in a permutation. St000491The number of inversions of a set partition. St000497The lcb statistic of a set partition. St000554The number of occurrences of the pattern {{1,2},{3}} in a set partition. St000555The number of occurrences of the pattern {{1,3},{2}} in a set partition. St000556The number of occurrences of the pattern {{1},{2,3}} in a set partition. St000557The number of occurrences of the pattern {{1},{2},{3}} in a set partition. St000561The number of occurrences of the pattern {{1,2,3}} in a set partition. St000572The dimension exponent of a set partition. St000580The number of occurrences of the pattern {{1},{2},{3}} such that 2 is minimal, 3 is maximal. St000582The number of occurrences of the pattern {{1,3},{2}} such that 1 is minimal, 3 is maximal, (1,3) are consecutive in a block. St000584The number of occurrences of the pattern {{1},{2},{3}} such that 1 is minimal, 3 is maximal. St000585The number of occurrences of the pattern {{1,3},{2}} such that 2 is maximal, (1,3) are consecutive in a block. St000586The number of occurrences of the pattern {{1},{2,3}} such that 2 is minimal. St000587The number of occurrences of the pattern {{1},{2},{3}} such that 1 is minimal. St000588The number of occurrences of the pattern {{1},{2},{3}} such that 1,3 are minimal, 2 is maximal. St000589The number of occurrences of the pattern {{1},{2,3}} such that 1 is maximal, (2,3) are consecutive in a block. 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. St000591The number of occurrences of the pattern {{1},{2},{3}} such that 2 is maximal. St000592The number of occurrences of the pattern {{1},{2},{3}} such that 1 is maximal. St000593The number of occurrences of the pattern {{1},{2},{3}} such that 1,2 are minimal. St000594The number of occurrences of the pattern {{1,3},{2}} such that 1,2 are minimal, (1,3) are consecutive in a block. St000595The number of occurrences of the pattern {{1},{2,3}} such that 1 is minimal. St000596The number of occurrences of the pattern {{1},{2},{3}} such that 3 is minimal, 1 is maximal. St000598The number of occurrences of the pattern {{1},{2,3}} such that 1,2 are minimal, 3 is maximal, (2,3) are consecutive in a block. 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. St000601The number of occurrences of the pattern {{1},{2,3}} such that 1,2 are minimal, (2,3) are consecutive in a block. St000602The number of occurrences of the pattern {{1,3},{2}} such that 1 is minimal. St000603The number of occurrences of the pattern {{1},{2},{3}} such that 2,3 are minimal. St000604The number of occurrences of the pattern {{1},{2},{3}} such that 3 is minimal, 2 is maximal. St000605The number of occurrences of the pattern {{1},{2,3}} such that 3 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. St000607The number of occurrences of the pattern {{1},{2,3}} such that 2 is minimal, 3 is maximal, (2,3) are consecutive in a block. St000608The number of occurrences of the pattern {{1},{2},{3}} such that 1,2 are minimal, 3 is maximal. St000609The number of occurrences of the pattern {{1},{2,3}} such that 1,2 are minimal. St000610The number of occurrences of the pattern {{1,3},{2}} such that 2 is maximal. St000611The number of occurrences of the pattern {{1},{2,3}} such that 1 is maximal. St000612The number of occurrences of the pattern {{1},{2,3}} such that 1 is minimal, (2,3) are consecutive in a block. 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. St000614The number of occurrences of the pattern {{1},{2,3}} such that 1 is minimal, 3 is maximal, (2,3) are consecutive in a block. St000615The number of occurrences of the pattern {{1},{2},{3}} such that 1,3 are maximal. St000732The number of double deficiencies 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. St000848The balance constant multiplied with the number of linear extensions of a poset. St000849The number of 1/3-balanced pairs in a poset. St000866The number of admissible inversions of a permutation in the sense of Shareshian-Wachs. 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 $K[x]/(x^n)$. St001552The number of inversions between excedances and fixed points of a permutation. St001731The factorization defect of a permutation. St000515The number of invariant set partitions when acting with a permutation of given cycle type. St001704The size of the largest multi-subset-intersection of the deck of a graph with the deck of another graph. St000045The number of linear extensions of a binary tree. St000402Half the size of the symmetry class of a permutation. St000456The monochromatic index of a connected graph. St000524The number of posets with the same order polynomial. St000525The number of posets with the same zeta polynomial. St000526The number of posets with combinatorially isomorphic order polytopes. St000529The number of permutations whose descent word is the given binary word. St000530The number of permutations with the same descent word as the given permutation. St000543The size of the conjugacy class of a binary word. St000568The hook number of a binary tree. St000627The exponent of a binary word. St000630The length of the shortest palindromic decomposition of a binary word. St000631The number of distinct palindromic decompositions of a binary word. St000698The number of 2-rim hooks removed from an integer partition to obtain its associated 2-core. St000704The number of semistandard tableaux on a given integer partition with minimal maximal entry. St000844The size of the largest block in the direct sum decomposition of a permutation. St001281The normalized isoperimetric number of a graph. St001313The number of Dyck paths above the lattice path given by a binary word. St001592The maximal number of simple paths between any two different vertices of a graph. St000219The number of occurrences of the pattern 231 in a permutation. St000347The inversion sum of a binary word. St000348The non-inversion sum of a binary word. St000379The number of Hamiltonian cycles in a graph. St000435The number of occurrences of the pattern 213 or of the pattern 231 in a permutation. St000494The number of inversions of distance at most 3 of a permutation. St000747A variant of the major index of a set partition. St000795The mad of a permutation. St000833The comajor index of a permutation. St000936The number of even values of the symmetric group character corresponding to the partition. St000957The number of Bruhat lower covers of a permutation. St000961The shifted major index of a permutation. St001061The number of indices that are both descents and recoils of a permutation. St001076The minimal length of a factorization of a permutation into transpositions that are cyclic shifts of (12). St001101The coefficient times the product of the factorials of the parts of the monomial symmetric function indexed by the partition in the formal group law for increasing trees. St001124The multiplicity of the standard representation in the Kronecker square corresponding to a partition. St001195The global dimension of the algebra $A/AfA$ of the corresponding Nakayama algebra $A$ with minimal left faithful projective-injective module $Af$. St001413Half the length of the longest even length palindromic prefix of a binary word. St001502The global dimension minus the dominant dimension of magnitude 1 Nakayama algebras. St001524The degree of symmetry of a binary word. St001604The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on polygons. St001876The number of 2-regular simple modules in the incidence algebra of the lattice. St001877Number of indecomposable injective modules with projective dimension 2. St000249The number of singletons (St000247) plus the number of antisingletons (St000248) of a set partition. St000673The number of non-fixed points of a permutation. St000842The breadth of a permutation. St001060The distinguishing index of a graph. St001198The number of simple modules in the algebra $eAe$ with projective dimension at most 1 in the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. 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 $eA$. St001206The maximal dimension of an indecomposable projective $eAe$-module (that is the height of the corresponding Dyck path) of the corresponding Nakayama algebra with minimal faithful projective-injective module $eA$. St000020The rank of the permutation. St000033The number of permutations greater than or equal to the given permutation in (strong) Bruhat order. St000040The number of regions of the inversion arrangement of a permutation. St000056The decomposition (or block) number of a permutation. St000109The number of elements less than or equal to the given element in Bruhat order. St000110The number of permutations less than or equal to a permutation in left weak order. St000207Number of integral Gelfand-Tsetlin polytopes with prescribed top row and integer composition weight. St000208Number of integral Gelfand-Tsetlin polytopes with prescribed top row and integer partition weight. St000240The number of indices that are not small excedances. St000264The girth of a graph, which is not a tree. St000280The size of the preimage of the map 'to labelling permutation' from Parking functions to Permutations. St000382The first part of an integer composition. St000383The last part of an integer composition. St000418The number of Dyck paths that are weakly below a Dyck path. St000501The size of the first part in the decomposition of a permutation. St000545The number of parabolic double cosets with minimal element being the given permutation. St000620The number of standard tableaux of shape equal to the given partition such that the minimal cyclic descent is odd. St000654The first descent of a permutation. St000657The smallest part of an integer composition. St000667The greatest common divisor of the parts of the partition. St000690The size of the conjugacy class of a permutation. St000694The number of affine bounded permutations that project to a given permutation. St000706The product of the factorials of the multiplicities of an integer partition. St000707The product of the factorials of the parts. St000708The product of the parts of an integer partition. St000727The largest label of a leaf in the binary search tree associated with the permutation. St000740The last entry of a permutation. St000753The Grundy value for the game of Kayles on a binary word. St000755The number of real roots of the characteristic polynomial of a linear recurrence associated with an integer partition. St000765The number of weak records in an integer composition. St000817The sum of the entries in the column specified by the composition of the change of basis matrix from dual immaculate quasisymmetric functions to monomial quasisymmetric functions. St000818The sum of the entries in the column specified by the composition of the change of basis matrix from quasisymmetric Schur functions to monomial quasisymmetric functions. St000899The maximal number of repetitions of an integer composition. St000900The minimal number of repetitions of a part in an integer composition. St000902 The minimal number of repetitions of an integer composition. St000933The number of multipartitions of sizes given by an integer partition. St000990The first ascent of a permutation. St000993The multiplicity of the largest part of an integer partition. St001062The maximal size of a block of a set partition. St001077The prefix exchange distance of a permutation. St001080The minimal length of a factorization of a permutation using the transposition (12) and the cycle (1,. St001162The minimum jump of a permutation. St001199The dominant dimension of $eAe$ for the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. St001236The dominant dimension of the corresponding Comp-Nakayama algebra. St001312Number of parabolic noncrossing partitions indexed by the composition. St001344The neighbouring number of a permutation. St001365The number of lattice paths of the same length weakly above the path given by a binary word. St001389The number of partitions of the same length below the given integer partition. St001419The length of the longest palindromic factor beginning with a one of a binary word. St001482The product of the prefix sums of a permutation. St001491The number of indecomposable projective-injective modules in the algebra corresponding to a subset. St001527The cyclic permutation representation number of an integer partition. St001531Number of partial orders contained in the poset determined by the Dyck path. St001568The smallest positive integer that does not appear twice in the partition. St001570The minimal number of edges to add to make a graph Hamiltonian. St001571The Cartan determinant of the integer partition. St001603The number of colourings of a polygon such that the multiplicities of a colour are given by a partition. St001605The number of colourings of a cycle such that the multiplicities of colours are given by a partition. St001652The length of a longest interval of consecutive numbers. St001661Half the permanent of the Identity matrix plus the permutation matrix associated to the permutation. St001675The number of parts equal to the part in the reversed composition. St001778The largest greatest common divisor of an element and its image in a permutation. St001875The number of simple modules with projective dimension at most 1. St001878The projective dimension of the simple modules corresponding to the minimum of L in the incidence algebra of the lattice L. St001915The size of the component corresponding to a necklace in Bulgarian solitaire. St001959The product of the heights of the peaks of a Dyck path. St000008The major index of the composition. St000019The cardinality of the support of a permutation. St000029The depth of a permutation. St000030The sum of the descent differences of a permutations. St000055The inversion sum of a permutation. St000133The "bounce" of a permutation. St000154The sum of the descent bottoms of a permutation. St000156The Denert index of a permutation. St000209Maximum difference of elements in cycles. St000210Minimum over maximum difference of elements in cycles. St000224The sorting index of a permutation. St000234The number of global ascents of a permutation. St000248The number of anti-singletons of a set partition. St000254The nesting number of a set partition. St000289The decimal representation of a binary word. St000304The load of a permutation. St000305The inverse major index of a permutation. St000339The maf index of a permutation. St000341The non-inversion sum of a permutation. St000389The number of runs of ones of odd length in a binary word. St000421The number of Dyck paths that are weakly below a Dyck path, except for the path itself. St000455The second largest eigenvalue of a graph if it is integral. St000472The sum of the ascent bottoms of a permutation. St000478Another weight of a partition according to Alladi. St000502The number of successions of a set partitions. St000503The maximal difference between two elements in a common block. St000558The number of occurrences of the pattern {{1,2}} in a set partition. St000566The number of ways to select a row of a Ferrers shape and two cells in this row. St000621The number of standard tableaux of shape equal to the given partition such that the minimal cyclic descent is even. St000622The number of occurrences of the patterns 2143 or 4231 in a permutation. St000649The number of 3-excedences of a permutation. St000650The number of 3-rises of a permutation. St000653The last descent of a permutation. St000658The number of rises of length 2 of a Dyck path. St000683The number of points below the Dyck path such that the diagonal to the north-east hits the path between two down steps, and the diagonal to the north-west hits the path between two up steps. St000699The toughness times the least common multiple of 1,. St000709The number of occurrences of 14-2-3 or 14-3-2. St000728The dimension of a set partition. St000730The maximal arc length of a set partition. St000794The mak of a permutation. St000797The stat`` of a permutation. St000798The makl of a permutation. St000934The 2-degree of an integer partition. St000984The number of boxes below precisely one peak. St000989The number of final rises of a permutation. St001097The coefficient of the monomial symmetric function indexed by the partition in the formal group law for linear orders. St001139The number of occurrences of hills of size 2 in a Dyck path. 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 $K[x]/(x^n)$. St001332The number of steps on the non-negative side of the walk associated with the permutation. St001392The largest nonnegative integer which is not a part and is smaller than the largest part of the partition. St001412Number of minimal entries in the Bruhat order matrix of a permutation. St001465The number of adjacent transpositions in the cycle decomposition of a permutation. St001480The number of simple summands of the module J^2/J^3. St001541The Gini index of an integer partition. St001558The number of transpositions that are smaller or equal to a permutation in Bruhat order. St001583The projective dimension of the simple module corresponding to the point in the poset of the symmetric group under bruhat order. St001587Half of the largest even part of an integer partition. St001640The number of ascent tops in the permutation such that all smaller elements appear before. St001657The number of twos in an integer partition. St001684The reduced word complexity of a permutation. St001721The degree of a binary word. St001759The Rajchgot index of a permutation. St001860The number of factors of the Stanley symmetric function associated with a signed permutation. St001930The weak major index of a binary word. St001931The weak major index of an integer composition regarded as a word. St001948The number of augmented double ascents of a permutation. St000298The order dimension or Dushnik-Miller dimension of a poset. St000307The number of rowmotion orbits of a poset. St001880The number of 2-Gorenstein indecomposable injective modules in the incidence algebra of the lattice. St000318The number of addable cells of the Ferrers diagram of an integer partition. St000439The position of the first down step of a Dyck path. St000930The k-Gorenstein degree of the corresponding Nakayama algebra with linear quiver. 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. St001629The coefficient of the integer composition in the quasisymmetric expansion of the relabelling action of the symmetric group on cycles. St000011The number of touch points (or returns) of a Dyck path. St000032The number of elements smaller than the given Dyck path in the Tamari Order. St000061The number of nodes on the left branch of a binary tree. St000084The number of subtrees. St000105The number of blocks in the set partition. St000164The number of short pairs. St000167The number of leaves of an ordered tree. St000235The number of indices that are not cyclical small weak excedances. St000328The maximum number of child nodes in a tree. St000335The difference of lower and upper interactions. St000397The Strahler number of a rooted tree. St000454The largest eigenvalue of a graph if it is integral. St000464The Schultz index of a connected graph. St000514The number of invariant simple graphs when acting with a permutation of given cycle type. St000678The number of up steps after the last double rise of a Dyck path. St000733The row containing the largest entry of a standard tableau. St000738The first entry in the last row of a standard tableau. St000746The number of pairs with odd minimum in a perfect matching. St000843The decomposition number of a perfect matching. 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. St000925The number of topologically connected components of a set partition. St000953The largest degree of an irreducible factor of the Coxeter polynomial of the Dyck path over the rational numbers. St000969We make a CNakayama algebra out of the LNakayama algebra (corresponding to the Dyck path) $[c_0,c_1,...,c_{n-1}]$ by adding $c_0$ to $c_{n-1}$. 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. St001041The depth of the label 1 in the decreasing labelled binary unordered tree associated with the perfect matching. St001042The size of the automorphism group of the leaf labelled binary unordered tree associated with the perfect matching. St001048The number of leaves in the subtree containing 1 in the decreasing labelled binary unordered tree associated with the perfect matching. St001051The depth of the label 1 in the decreasing labelled unordered tree associated with the set partition. St001058The breadth of the ordered tree. St001088Number of indecomposable projective non-injective modules with dominant dimension equal to the injective dimension in the corresponding Nakayama algebra. St001133The smallest label in the subtree rooted at the sister of 1 in the decreasing labelled binary unordered tree associated with the perfect matching. St001134The largest label in the subtree rooted at the sister of 1 in the leaf labelled binary unordered tree associated with the perfect matching. St001135The projective dimension of the first simple module in the Nakayama algebra corresponding to the Dyck path. St001201The grade of the simple module $S_0$ in the special CNakayama algebra corresponding to the Dyck path. 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. 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. St001241The number of non-zero radicals of the indecomposable projective modules that have injective dimension and projective dimension at most one. St001275The projective dimension of the second term in a minimal injective coresolution of the regular module. St001290The first natural number n such that the tensor product of n copies of D(A) is zero for the corresponding Nakayama algebra A. St001291The number of indecomposable summands of the tensor product of two copies of the dual of the Nakayama algebra associated to a Dyck path. St001297The number of indecomposable non-injective projective modules minus the number of indecomposable non-injective projective modules that have reflexive Auslander-Reiten sequences in the corresponding Nakayama algebra. St001299The product of all non-zero projective dimensions of simple modules of the corresponding Nakayama algebra. St001432The order dimension of the partition. St001462The number of factors of a standard tableaux under concatenation. St001500The global dimension of magnitude 1 Nakayama algebras. 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. St001516The number of cyclic bonds of a permutation. St001545The second Elser number of a connected graph. St001804The minimal height of the rectangular inner shape in a cylindrical tableau associated to a tableau. St001809The index of the step at the first peak of maximal height in a Dyck path. St001933The largest multiplicity of a part in an integer partition. St000285The size of the preimage of the map 'to inverse des composition' from Parking functions to Integer compositions. St000487The length of the shortest cycle of a permutation. St000772The multiplicity of the largest distance Laplacian eigenvalue in a connected graph. St001498The normalised height of a Nakayama algebra with magnitude 1. St001168The vector space dimension of the tilting module corresponding to the permutation in the Auslander algebra of $K[x]/(x^n)$. 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. St000656The number of cuts of a poset. St000680The Grundy value for Hackendot on posets. St001232The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2. St001630The global dimension of the incidence algebra of the lattice over the rational numbers. St001668The number of points of the poset minus the width of the poset. St000718The largest Laplacian eigenvalue of a graph if it is integral. St001621The number of atoms of a lattice. St001623The number of doubly irreducible elements of a lattice. St001626The number of maximal proper sublattices of a lattice. St000550The number of modular elements of a lattice. St000551The number of left modular elements of a lattice. St000739The first entry in the last row of a semistandard tableau. St001401The number of distinct entries in a semistandard tableau. St001686The order of promotion on a Gelfand-Tsetlin pattern. St000101The cocharge of a semistandard tableau. St001556The number of inversions of the third entry of a permutation. St001856The number of edges in the reduced word graph of a permutation. St001926Sparre Andersen's position of the maximum of a signed permutation. St000080The rank of the poset. St000116The major index of a semistandard tableau obtained by standardizing. St000168The number of internal nodes of an ordered tree. St000173The segment statistic of a semistandard tableau. St000174The flush statistic of a semistandard tableau. St000199The column of the unique '1' in the last row of the alternating sign matrix. St000338The number of pixed points of a permutation. St000358The number of occurrences of the pattern 31-2. St000371The number of mid points of decreasing subsequences of length 3 in a permutation. St000375The number of non weak exceedences of a permutation that are mid-points of a decreasing subsequence of length $3$. St000411The tree factorial of a binary tree. St000625The sum of the minimal distances to a greater element. St000736The last entry in the first row of a semistandard tableau. St000880The number of connected components of long braid edges in the graph of braid moves of a permutation. St000890The number of nonzero entries in an alternating sign matrix. St000942The number of critical left to right maxima of the parking functions. St000958The number of Bruhat factorizations of a permutation. St001074The number of inversions of the cyclic embedding of a permutation. St001225The vector space dimension of the first extension group between J and itself when J is the Jacobson radical of the corresponding Nakayama algebra. St001278The number of indecomposable modules that are fixed by $\tau \Omega^1$ composed with its inverse in the corresponding Nakayama algebra. St001487The number of inner corners of a skew partition. St001591The number of graphs with the given composition of multiplicities of Laplacian eigenvalues. St001596The number of two-by-two squares inside a skew partition. St001645The pebbling number of a connected graph. St001768The number of reduced words of a signed permutation. St001769The reflection length of a signed permutation. St001773The number of minimal elements in Bruhat order not less than the signed permutation. St001812The biclique partition number of a graph. St001863The number of weak excedances of a signed permutation. St001885The number of binary words with the same proper border set. St001904The length of the initial strictly increasing segment of a parking function. St001905The number of preferred parking spots in a parking function less than the index of the car. St001946The number of descents in a parking function. St000002The number of occurrences of the pattern 123 in a permutation. St000004The major index of a permutation. St000075The orbit size of a standard tableau under promotion. St000095The number of triangles of a graph. St000102The charge of a semistandard tableau. St000166The depth minus 1 of an ordered tree. St000211The rank of the set partition. St000357The number of occurrences of the pattern 12-3. St000493The los statistic of a set partition. St000499The rcb statistic of a set partition. St000504The cardinality of the first block of a set partition. St000522The number of 1-protected nodes of a rooted tree. St000553The number of blocks of a graph. St000823The number of unsplittable factors of the set partition. 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. St000963The 2-shifted major index of a permutation. St001084The number of occurrences of the vincular pattern |1-23 in a permutation. St001314The number of tilting modules of arbitrary projective dimension that have no simple modules as a direct summand in the corresponding Nakayama algebra. St001435The number of missing boxes in the first row. St001438The number of missing boxes of a skew partition. St001572The minimal number of edges to remove to make a graph bipartite. St001573The minimal number of edges to remove to make a graph triangle-free. St001575The minimal number of edges to add or remove to make a graph edge transitive. St001577The minimal number of edges to add or remove to make a graph a cograph. St001578The minimal number of edges to add or remove to make a graph a line graph. St001649The length of a longest trail in a graph. St001667The maximal size of a pair of weak twins for a permutation. St001722The number of minimal chains with small intervals between a binary word and the top element. St001738The minimal order of a graph which is not an induced subgraph of the given graph. St001745The number of occurrences of the arrow pattern 13 with an arrow from 1 to 2 in a permutation. St001857The number of edges in the reduced word graph of a signed permutation. St001861The number of Bruhat lower covers of a permutation. St001882The number of occurrences of a type-B 231 pattern in a signed permutation. St001964The interval resolution global dimension of a poset. St000094The depth of an ordered tree. St000135The number of lucky cars of the parking function. St000521The number of distinct subtrees of an ordered tree. St000973The length of the boundary of an ordered tree. St000975The length of the boundary minus the length of the trunk of an ordered tree. St001002Number of indecomposable modules with projective and injective dimension at most 1 in the Nakayama algebra corresponding to the Dyck path. St001927Sparre Andersen's number of positives of a signed permutation. St000044The number of vertices of the unicellular map given by a perfect matching. St000735The last entry on the main diagonal of a standard tableau.