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 $eA$. 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. St000007The number of saliances of the permutation. St000011The number of touch points (or returns) of a Dyck path. St000013The height of a Dyck path. St000062The length of the longest increasing subsequence of the permutation. St000071The number of maximal chains in a poset. St000105The number of blocks in the set partition. St000157The number of descents of a standard tableau. St000164The number of short pairs. St000167The number of leaves of an ordered tree. St000213The number of weak exceedances (also weak excedences) of a permutation. St000236The number of cyclical small weak excedances. St000239The number of small weak excedances. St000259The diameter of a connected graph. St000291The number of descents of a binary word. St000314The number of left-to-right-maxima of a permutation. St000318The number of addable cells of the Ferrers diagram of an integer partition. St000325The width of the tree associated to a permutation. St000374The number of exclusive right-to-left minima of a permutation. St000390The number of runs of ones in a binary word. St000443The number of long tunnels of a Dyck path. St000451The length of the longest pattern of the form k 1 2. St000470The number of runs in a permutation. St000542The number of left-to-right-minima of a permutation. St000636The hull number of a graph. St000670The reversal length of a permutation. 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. St000703The number of deficiencies of a permutation. St000767The number of runs in an integer composition. St000991The number of right-to-left minima of a permutation. St001007Number of simple modules with projective dimension 1 in the Nakayama algebra corresponding to the Dyck path. St001187The number of simple modules with grade at least one in the corresponding Nakayama algebra. St001202Call a CNakayama algebra (a Nakayama algebra with a cyclic quiver) with Kupisch series $L=[c_0,c_1,...,c_{n−1}]$ such that $n=c_0 < c_i$ for all $i > 0$ a special CNakayama algebra. St001224Let X be the direct sum of all simple modules of the corresponding Nakayama algebra. 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. St001304The number of maximally independent sets of vertices of a graph. St001315The dissociation number of a graph. St001390The number of bumps occurring when Schensted-inserting the letter 1 of a permutation. St001486The number of corners of the ribbon associated with an integer composition. St001488The number of corners of a skew partition. St001499The number of indecomposable projective-injective modules of a magnitude 1 Nakayama algebra. St001512The minimum rank of a graph. St001654The monophonic hull number of a graph. St001655The general position number of a graph. St001656The monophonic position number of a graph. St001883The mutual visibility number of a graph. St000021The number of descents of a permutation. St000024The number of double up and double down steps of a Dyck path. St000028The number of stack-sorts needed to sort a permutation. St000052The number of valleys of a Dyck path not on the x-axis. St000155The number of exceedances (also excedences) of a permutation. St000159The number of distinct parts of the integer partition. St000245The number of ascents of a permutation. St000292The number of ascents of a binary word. St000316The number of non-left-to-right-maxima of a permutation. St000317The cycle descent number of a permutation. 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. St000358The number of occurrences of the pattern 31-2. St000662The staircase size of the code of a permutation. St000672The number of minimal elements in Bruhat order not less than the permutation. St000742The number of big ascents of a permutation after prepending zero. St000761The number of ascents in an integer composition. St000778The metric dimension of a graph. St000834The number of right outer peaks of a permutation. St000846The maximal number of elements covering an element of a poset. St000864The number of circled entries of the shifted recording tableau of a permutation. St000970Number of peaks minus the dominant dimension of the corresponding LNakayama algebra. St000996The number of exclusive left-to-right maxima of a permutation. St001036The number of inner corners of the parallelogram polyomino associated with the Dyck path. St001093The detour number of a graph. St001104The number of descents of the invariant in a tensor power of the adjoint representation of the rank two general linear group. 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. St001180Number of indecomposable injective modules with projective dimension at most 1. St001215Let X be the direct sum of all simple modules of the corresponding Nakayama algebra. St001225The vector space dimension of the first extension group between J and itself when J is the Jacobson radical of the corresponding Nakayama algebra. St001278The number of indecomposable modules that are fixed by $\tau \Omega^1$ composed with its inverse in the corresponding Nakayama algebra. St001290The first natural number n such that the tensor product of n copies of D(A) is zero for the corresponding Nakayama algebra A. St001296The maximal torsionfree index of an indecomposable non-projective module in the corresponding Nakayama algebra. St001298The number of repeated entries in the Lehmer code of a permutation. St001354The number of series nodes in the modular decomposition of a graph. 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. St001553The number of indecomposable summands of the square of the Jacobson radical as a bimodule in the Nakayama algebra corresponding to the Dyck path. St001726The number of visible inversions of a permutation. St001729The number of visible descents of a permutation. St001761The maximal multiplicity of a letter in a reduced word of a permutation. St001514The dimension of the top of the Auslander-Reiten translate of the regular modules as a bimodule. St000789The number of crossing-similar perfect matchings of a perfect matching. St000824The sum of the number of descents and the number of recoils of a permutation. St000354The number of recoils of a permutation. St000413The number of ordered trees with the same underlying unordered tree. St000619The number of cyclic descents of a permutation. St000691The number of changes of a binary word. St000889The number of alternating sign matrices with the same antidiagonal sums. St001052The length of the exterior of a permutation. St001199The dominant dimension of $eAe$ for the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. St001355Number of non-empty prefixes of a binary word that contain equally many 0's and 1's. St000222The number of alignments in the permutation. St000225Difference between largest and smallest parts in a partition. St000538The number of even inversions of a permutation. 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. St000646The number of big ascents of a permutation. St000647The number of big descents of a permutation. St000663The number of right floats of a permutation. St000779The tier of a permutation. St000836The number of descents of distance 2 of a permutation. St000837The number of ascents of distance 2 of a permutation. St000871The number of very big ascents of a permutation. St001035The convexity degree of the parallelogram polyomino associated with the Dyck path. St001085The number of occurrences of the vincular pattern |21-3 in a permutation. 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. St001730The number of times the path corresponding to a binary word crosses the base line. St000925The number of topologically connected components of a set partition. St001005The number of indices for a permutation that are either left-to-right maxima or right-to-left minima but not both. St001105The number of greedy linear extensions of a poset. St001106The number of supergreedy linear extensions of a poset. St001183The maximum of $projdim(S)+injdim(S)$ over all simple modules in the Nakayama algebra corresponding to the Dyck path. St001637The number of (upper) dissectors of a poset. St000035The number of left outer peaks of a permutation. St000083The number of left oriented leafs of a binary tree except the first one. St000282The size of the preimage of the map 'to poset' from Ordered trees to Posets. St000388The number of orbits of vertices of a graph under automorphisms. St000442The maximal area to the right of an up step of a Dyck path. St000495The number of inversions of distance at most 2 of a permutation. St000527The width of the poset. St000541The number of indices greater than or equal to 2 of a permutation such that all smaller indices appear to its right. St000568The hook number of a binary tree. St000638The number of up-down runs of a permutation. St000668The least common multiple of the parts of the partition. St000820The number of compositions obtained by rotating the composition. St000829The Ulam distance of a permutation to the identity permutation. St000886The number of permutations with the same antidiagonal sums. St000955Number of times one has $Ext^i(D(A),A)>0$ for $i>0$ for the corresponding LNakayama algebra. St001112The 3-weak dynamic number of a graph. St001128The exponens consonantiae of a partition. St001235The global dimension of the corresponding Comp-Nakayama algebra. St001352The number of internal nodes in the modular decomposition of a graph. St001418Half of the global dimension of the stable Auslander algebra of the Nakayama algebra corresponding to the Dyck path. St001896The number of right descents of a signed permutations. St001951The number of factors in the disjoint direct product decomposition of the automorphism group of a graph. St000089The absolute variation of a composition. St000175Degree of the polynomial counting the number of semistandard Young tableaux when stretching the shape. St000204The number of internal nodes of a binary tree. St000242The number of indices that are not cyclical small weak excedances. St000353The number of inner valleys of a permutation. St000359The number of occurrences of the pattern 23-1. St000392The length of the longest run of ones in a binary word. St000446The disorder of a permutation. St000473The number of parts of a partition that are strictly bigger than the number of ones. St000480The number of lower covers of a partition in dominance order. St000483The number of times a permutation switches from increasing to decreasing or decreasing to increasing. St000534The number of 2-rises of a permutation. St000547The number of even non-empty partial sums of an integer partition. St000552The number of cut vertices of a graph. St000595The number of occurrences of the pattern {{1},{2,3}} such that 1 is minimal. St000612The number of occurrences of the pattern {{1},{2,3}} such that 1 is minimal, (2,3) are consecutive in a block. St000624The normalized sum of the minimal distances to a greater element. St000628The balance of a binary word. St000632The jump number of the poset. 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. St000710The number of big deficiencies of a permutation. St000711The number of big exceedences of a permutation. St000872The number of very big descents of a permutation. St000875The semilength of the longest Dyck word in the Catalan factorisation of a binary word. 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. St001061The number of indices that are both descents and recoils of a permutation. St001078The minimal number of occurrences of (12) in a factorization of a permutation into transpositions (12) and cycles (1,. St001083The number of boxed occurrences of 132 in a permutation. St001194The injective dimension of $A/AfA$ in the corresponding Nakayama algebra $A$ when $Af$ is the minimal faithful projective-injective left $A$-module St001214The aft of an integer partition. St001251The number of parts of a partition that are not congruent 1 modulo 3. St001281The normalized isoperimetric number of a graph. St001331The size of the minimal feedback vertex set. St001336The minimal number of vertices in a graph whose complement is triangle-free. St001372The length of a longest cyclic run of ones of a binary word. St001384The number of boxes in the diagram of a partition that do not lie in the largest triangle it contains. St001388The number of non-attacking neighbors of a permutation. St001403The number of vertical separators in a permutation. St001421Half the length of a longest factor which is its own reverse-complement and begins with a one of a binary word. St001520The number of strict 3-descents. St001557The number of inversions of the second entry of a permutation. St001565The number of arithmetic progressions of length 2 in a permutation. 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. St001584The area statistic between a Dyck path and its bounce path. St001638The book thickness of a graph. St001647The number of edges that can be added without increasing the clique number. St001648The number of edges that can be added without increasing the chromatic number. 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. St001687The number of distinct positions of the pattern letter 2 in occurrences of 213 in a permutation. St001689The number of celebrities in a graph. St001723The differential of a graph. St001724The 2-packing differential of a graph. St001727The number of invisible inversions of a permutation. St001744The number of occurrences of the arrow pattern 1-2 with an arrow from 1 to 2 in a permutation. St001798The difference of the number of edges in a graph and the number of edges in the complement of the Turán graph. St001810The number of fixed points of a permutation smaller than its largest moved point. St001811The Castelnuovo-Mumford regularity of a permutation. St001822The number of alignments of a signed permutation. St001842The major index of a set partition. St001931The weak major index of an integer composition regarded as a word. St001960The number of descents of a permutation minus one if its first entry is not one. St000524The number of posets with the same order polynomial. St000526The number of posets with combinatorially isomorphic order polytopes. St000983The length of the longest alternating subword. St000249The number of singletons (St000247) plus the number of antisingletons (St000248) of a set partition. St000307The number of rowmotion orbits of a poset. St000525The number of posets with the same zeta polynomial. St000982The length of the longest constant subword. St000988The orbit size of a permutation under Foata's bijection. St001267The length of the Lyndon factorization of the binary word. St001437The flex of a binary word. St001570The minimal number of edges to add to make a graph Hamiltonian. St000141The maximum drop size of a permutation. St000238The number of indices that are not small weak excedances. St000289The decimal representation of a binary word. St000293The number of inversions of a binary word. St000472The sum of the ascent bottoms of a permutation. St000565The major index of a set partition. St000800The number of occurrences of the vincular pattern |231 in a permutation. St000848The balance constant multiplied with the number of linear extensions of a poset. St000868The aid statistic in the sense of Shareshian-Wachs. St000938The number of zeros of the symmetric group character corresponding to the partition. St000961The shifted major index of a permutation. St001097The coefficient of the monomial symmetric function indexed by the partition in the formal group law for linear orders. St001124The multiplicity of the standard representation in the Kronecker square corresponding to a partition. St001436The index of a given binary word in the lex-order among all its cyclic shifts. St000626The minimal period of a binary word. St001012Number of simple modules with projective dimension at most 2 in the Nakayama algebra corresponding to the Dyck path. St001118The acyclic chromatic index of a graph. St001632The number of indecomposable injective modules $I$ with $dim Ext^1(I,A)=1$ for the incidence algebra A of a poset. St000506The number of standard desarrangement tableaux of shape equal to the given partition. St000885The number of critical steps in the Catalan decomposition of a binary word. St000454The largest eigenvalue of a graph if it is integral. St000539The number of odd inversions of a permutation. St000659The number of rises of length at least 2 of a Dyck path. St001424The number of distinct squares in a binary word. 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). St000050The depth or height of a binary tree. St000144The pyramid weight of the Dyck path. St000831The number of indices that are either descents or recoils. St001258Gives the maximum of injective plus projective dimension of an indecomposable module over the corresponding Nakayama algebra. St001554The number of distinct nonempty subtrees of a binary tree. St000075The orbit size of a standard tableau under promotion. St000519The largest length of a factor maximising the subword complexity. St000676The number of odd rises of a Dyck path. St000780The size of the orbit under rotation of a perfect matching. St000945The number of matchings in the dihedral orbit of a perfect matching. 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. St001039The maximal height of a column in the parallelogram polyomino associated with a Dyck path. St001065Number of indecomposable reflexive modules in the corresponding Nakayama algebra. St001165Number of simple modules with even projective dimension in the corresponding Nakayama algebra. St001179Number of indecomposable injective modules with projective dimension at most 2 in the corresponding Nakayama algebra. St001237The number of simple modules with injective dimension at most one or dominant dimension at least one. St001240The number of indecomposable modules e_i J^2 that have injective dimension at most one in the corresponding Nakayama algebra St001245The cyclic maximal difference between two consecutive entries of a permutation. St001375The pancake length of a permutation. St001471The magnitude of a Dyck path. St001498The normalised height of a Nakayama algebra with magnitude 1. St001526The Loewy length of the Auslander-Reiten translate of the regular module as a bimodule of the Nakayama algebra corresponding to the Dyck path. St001566The length of the longest arithmetic progression in a permutation. St000162The number of nontrivial cycles in the cycle decomposition of a permutation. St000216The absolute length of a permutation. St000223The number of nestings in the permutation. St000251The number of nonsingleton blocks of a set partition. St000331The number of upper interactions of a Dyck path. St000371The number of mid points of decreasing 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 $3$. St000809The reduced reflection length of the permutation. St000845The maximal number of elements covered by an element in a poset. St000919The number of maximal left branches of a binary tree. St001011Number of simple modules of projective dimension 2 in the Nakayama algebra corresponding to the Dyck path. St001152The number of pairs with even minimum in a perfect matching. 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. St001212The number of simple modules in the corresponding Nakayama algebra that have non-zero second Ext-group with the regular module. 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. St001269The sum of the minimum of the number of exceedances and deficiencies in each cycle of a permutation. 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. St001405The number of bonds in a permutation. 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. St001517The length of a longest pair of twins in a permutation. St001639The number of alternating subsets such that applying the permutation does not yield an alternating subset. St001665The number of pure excedances of a permutation. St001667The maximal size of a pair of weak twins for a permutation. St001693The excess length of a longest path consisting of elements and blocks of a set partition. St001737The number of descents of type 2 in a permutation. St001760The number of prefix or suffix reversals needed to sort a permutation. St001801Half the number of preimage-image pairs of different parity in a permutation. St001859The number of factors of the Stanley symmetric function associated with a permutation. St001874Lusztig's a-function for the symmetric group. St001928The number of non-overlapping descents in a permutation. St000232The number of crossings of a set partition. St000562The number of internal points of a set partition. St000563The number of overlapping pairs of blocks of a set partition. St000648The number of 2-excedences of a permutation. St000698The number of 2-rim hooks removed from an integer partition to obtain its associated 2-core. St000455The second largest eigenvalue of a graph if it is integral. St000630The length of the shortest palindromic decomposition of a binary word. St001330The hat guessing number of a graph. St001431Half of the Loewy length minus one of a modified stable Auslander algebra of the Nakayama algebra corresponding to the Dyck path. St001462The number of factors of a standard tableaux under concatenation. St000243The number of cyclic valleys and cyclic peaks of a permutation. St001712The number of natural descents of a standard Young tableau. St001864The number of excedances of a signed permutation. 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. St000731The number of double exceedences of a permutation. St001084The number of occurrences of the vincular pattern |1-23 in a permutation. St001115The number of even descents of a permutation. St001394The genus of a permutation. St000233The number of nestings of a set partition. St000596The number of occurrences of the pattern {{1},{2},{3}} such that 3 is minimal, 1 is maximal. St000650The number of 3-rises of a permutation. St000661The number of rises of length 3 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. St000241The number of cyclical small excedances. St000248The number of anti-singletons of a set partition. St000891The number of distinct diagonal sums of a permutation matrix. St001126Number of simple module that are 1-regular in the corresponding Nakayama algebra. 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 $eA$. St001439The number of even weak deficiencies and of odd weak exceedences. St001642The Prague dimension of a graph. St001672The restrained domination number of a graph. St000064The number of one-box pattern of a permutation. St000706The product of the factorials of the multiplicities of an integer partition. St000771The largest multiplicity of a distance Laplacian eigenvalue in a connected graph. St000772The multiplicity of the largest distance Laplacian eigenvalue in a connected graph. St000785The number of distinct colouring schemes of a graph. St000923The minimal number with no two order isomorphic substrings of this length in a permutation. St000959The number of strong Bruhat factorizations of a permutation. St000965The sum of the dimension of Ext^i(D(A),A) for i=1,. St000985The number of positive eigenvalues of the adjacency matrix of the graph. St000993The multiplicity of the largest part of an integer partition. St001060The distinguishing index of a graph. St001064Number of simple modules in the corresponding Nakayama algebra that are 3-syzygy modules. St001198The number of simple modules in the algebra $eAe$ with projective dimension at most 1 in the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. St001206The maximal dimension of an indecomposable projective $eAe$-module (that is the height of the corresponding Dyck path) of the corresponding Nakayama algebra with minimal faithful projective-injective module $eA$. St001207The Lowey length of the algebra $A/T$ when $T$ is the 1-tilting module corresponding to the permutation in the Auslander algebra of $K[x]/(x^n)$. St001272The number of graphs with the same degree sequence. St001359The number of permutations in the equivalence class of a permutation obtained by taking inverses of cycles. St001483The number of simple module modules that appear in the socle of the regular module but have no nontrivial selfextensions with the regular module. St001493The number of simple modules with maximal even projective dimension in the corresponding Nakayama algebra. St001496The number of graphs with the same Laplacian spectrum as the given graph. St001516The number of cyclic bonds of a permutation. St001518The number of graphs with the same ordinary spectrum as the given graph. St001582The grades of the simple modules corresponding to the points in the poset of the symmetric group under the Bruhat order. St001722The number of minimal chains with small intervals between a binary word and the top element. St001768The number of reduced words of a signed permutation. St001875The number of simple modules with projective dimension at most 1. St000039The number of crossings of a permutation. St000091The descent variation of a composition. St000100The number of linear extensions of a poset. St000365The number of double ascents of a permutation. St000372The number of mid points of increasing subsequences of length 3 in a permutation. St000432The number of occurrences of the pattern 231 or of the pattern 312 in a permutation. St000456The monochromatic index of a connected graph. St000486The number of cycles of length at least 3 of a permutation. St000516The number of stretching pairs of a permutation. St000633The size of the automorphism group of a poset. St000640The rank of the largest boolean interval in a poset. St000649The number of 3-excedences of a permutation. St000664The number of right ropes of a permutation. St000732The number of double deficiencies of a permutation. St000804The number of occurrences of the vincular pattern |123 in a permutation. St000832The number of permutations obtained by reversing blocks of three consecutive numbers. St000847The number of standard Young tableaux whose descent set is the binary word. St000880The number of connected components of long braid edges in the graph of braid moves of a permutation. St000910The number of maximal chains of minimal length in a poset. St000966Number of peaks minus the global dimension of the corresponding LNakayama algebra. St001174The Gorenstein dimension of the algebra $A/I$ when $I$ is the tilting module corresponding to the permutation in the Auslander algebra of $K[x]/(x^n)$. St001220The width of a permutation. St001313The number of Dyck paths above the lattice path given by a binary word. St001470The cyclic holeyness of a permutation. St001513The number of nested exceedences of a permutation. St001535The number of cyclic alignments of a permutation. St001537The number of cyclic crossings of a permutation. St001551The number of restricted non-inversions between exceedances where the rightmost exceedance is linked. St001686The order of promotion on a Gelfand-Tsetlin pattern. St001715The number of non-records in a permutation. St001728The number of invisible descents of a permutation. St001731The factorization defect of a permutation. St001857The number of edges in the reduced word graph of a signed permutation. St000347The inversion sum of a binary word. St000348The non-inversion sum of a binary word. St000369The dinv deficit of a Dyck path. St000376The bounce deficit of a Dyck path. St000434The number of occurrences of the pattern 213 or of the pattern 312 in a permutation. St000437The number of occurrences of the pattern 312 or of the pattern 321 in a permutation. St000560The number of occurrences of the pattern {{1,2},{3,4}} in a set partition. St000561The number of occurrences of the pattern {{1,2,3}} 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. 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. 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. St000601The number of occurrences of the pattern {{1},{2,3}} such that 1,2 are minimal, (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. St000609The number of occurrences of the pattern {{1},{2,3}} such that 1,2 are minimal. St000611The number of occurrences of the pattern {{1},{2,3}} such that 1 is maximal. St000622The number of occurrences of the patterns 2143 or 4231 in a permutation. St000747A variant of the major index of a set partition. St000791The number of pairs of left tunnels, one strictly containing the other, of a Dyck path. St000801The number of occurrences of the vincular pattern |312 in a permutation. St000802The number of occurrences of the vincular pattern |321 in a permutation. St000849The number of 1/3-balanced pairs in a poset. St000850The number of 1/2-balanced pairs in a poset. St000881The number of short braid edges in the graph of braid moves of a permutation. St001082The number of boxed occurrences of 123 in a permutation. St001130The number of two successive successions in a permutation. St001414Half the length of the longest odd length palindromic prefix of a binary word. St001420Half the length of a longest factor which is its own reverse-complement of a binary word. St001502The global dimension minus the dominant dimension of magnitude 1 Nakayama algebras. St001552The number of inversions between excedances and fixed points of a permutation. St001629The coefficient of the integer composition in the quasisymmetric expansion of the relabelling action of the symmetric group on cycles. St000907The number of maximal antichains of minimal length in a poset. St000914The sum of the values of the Möbius function of a poset. St001624The breadth of a lattice. St001630The global dimension of the incidence algebra of the lattice over the rational numbers. St001878The projective dimension of the simple modules corresponding to the minimum of L in the incidence algebra of the lattice L. St001491The number of indecomposable projective-injective modules in the algebra corresponding to a subset. St001603The number of colourings of a polygon such that the multiplicities of a colour are given by a partition. St001876The number of 2-regular simple modules in the incidence algebra of the lattice. St001877Number of indecomposable injective modules with projective dimension 2. St001890The maximum magnitude of the Möbius function of a poset. St000510The number of invariant oriented cycles when acting with a permutation of given cycle type. St000681The Grundy value of Chomp on Ferrers diagrams. 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. St000667The greatest common divisor of the parts of the partition. St000755The number of real roots of the characteristic polynomial of a linear recurrence associated with an integer partition. St000782The indicator function of whether a given perfect matching is an L & P matching. St001389The number of partitions of the same length below the given integer partition. St001527The cyclic permutation representation number of an integer partition. St001571The Cartan determinant of the integer partition. St000319The spin of an integer partition. St000320The dinv adjustment of an integer partition. St001392The largest nonnegative integer which is not a part and is smaller than the largest part of the partition. St001541The Gini index of an integer partition. St001587Half of the largest even part of an integer partition. St001657The number of twos in an integer partition. St001918The degree of the cyclic sieving polynomial corresponding to an integer partition. St000092The number of outer peaks of a permutation. St000099The number of valleys of a permutation, including the boundary. St000264The girth of a graph, which is not a tree. St000402Half the size of the symmetry class of a permutation. St000679The pruning number of an ordered tree. St000806The semiperimeter of the associated bargraph. St000893The number of distinct diagonal sums of an alternating sign matrix. St001239The largest vector space dimension of the double dual of a simple module in the corresponding Nakayama algebra. St001597The Frobenius rank of a skew partition. St001621The number of atoms of a lattice. St001644The dimension of a graph. St001720The minimal length of a chain of small intervals in a lattice. St001734The lettericity of a graph. St001741The largest integer such that all patterns of this size are contained in the permutation. St001784The minimum of the smallest closer and the second element of the block containing 1 in a set partition. St000023The number of inner peaks of a permutation. St000254The nesting number of a set partition. St000260The radius of a connected graph. St000439The position of the first down step of a Dyck path. St000460The hook length of the last cell along the main diagonal of an integer partition. St000464The Schultz index of a connected graph. 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. St000870The product of the hook lengths of the diagonal cells in an integer partition. St000939The number of characters of the symmetric group whose value on the partition is positive. 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 $c_{n-1}$. St001192The maximal dimension of $Ext_A^2(S,A)$ for a simple module $S$ over 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. St001360The number of covering relations in Young's lattice below a partition. St001378The product of the cohook lengths of the integer partition. St001380The number of monomer-dimer tilings of a Ferrers diagram. St001545The second Elser number of a connected graph. St001568The smallest positive integer that does not appear twice in the partition. St001607The number of coloured graphs such that the multiplicities of colours are given by a partition. St001611The number of multiset partitions such that the multiplicities of elements are given by a partition. St001719The number of shortest chains of small intervals from the bottom to the top in a lattice. St001814The number of partitions interlacing the given partition. St001914The size of the orbit of an integer partition in Bulgarian solitaire. St000005The bounce statistic of a Dyck path. St000006The dinv of a Dyck path. St000010The length of the partition. St000014The number of parking functions supported by a Dyck path. St000026The position of the first return of a Dyck path. St000046The largest eigenvalue of the random to random operator acting on the simple module corresponding to the given partition. St000048The multinomial of the parts of a partition. St000120The number of left tunnels of a Dyck path. St000137The Grundy value of an integer partition. St000147The largest part of an integer partition. St000160The multiplicity of the smallest part of a partition. St000285The size of the preimage of the map 'to inverse des composition' from Parking functions to Integer compositions. St000321The number of integer partitions of n that are dominated by an integer partition. St000326The position of the first one in a binary word after appending a 1 at the end. St000345The number of refinements of a partition. St000346The number of coarsenings of a partition. St000378The diagonal inversion number of an integer partition. St000476The sum of the semi-lengths of tunnels before a valley of a Dyck path. St000548The number of different non-empty partial sums of an integer partition. St000618The number of self-evacuating tableaux of given shape. St000685The dominant dimension of the LNakayama algebra associated to a Dyck path. St000734The last entry in the first row of a standard tableau. St000762The sum of the positions of the weak records of an integer composition. St000781The number of proper colouring schemes of a Ferrers diagram. St000814The sum of the entries in the column specified by the partition of the change of basis matrix from elementary symmetric functions to Schur symmetric functions. St000929The constant term of the character polynomial of an integer partition. St000930The k-Gorenstein degree of the corresponding Nakayama algebra with linear quiver. St000935The number of ordered refinements of an integer partition. St000947The major index east count of a Dyck path. St001024Maximum of dominant dimensions of the simple modules in the Nakayama algebra corresponding to the Dyck path. St001103The number of words with multiplicities of the letters given by the partition, avoiding the consecutive pattern 123. St001122The multiplicity of the sign representation in the Kronecker square corresponding to a partition. St001135The projective dimension of the first simple module in the Nakayama algebra corresponding to the Dyck path. St001161The major index north count of a Dyck path. St001170Number of indecomposable injective modules whose socle has projective dimension at most g-1 when g denotes the global dimension in the corresponding Nakayama algebra. 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. St001232The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2. St001247The number of parts of a partition that are not congruent 2 modulo 3. St001249Sum of the odd parts of a partition. St001250The number of parts of a partition that are not congruent 0 modulo 3. St001257The dominant dimension of the double dual of A/J when A is the corresponding Nakayama algebra with Jacobson radical J. St001262The dimension of the maximal parabolic seaweed algebra corresponding to the partition. St001283The number of finite solvable groups that are realised by the given partition over the complex numbers. St001284The number of finite groups that are realised by the given partition over the complex numbers. St001299The product of all non-zero projective dimensions of simple modules of the corresponding Nakayama algebra. St001364The number of permutations whose cube equals a fixed permutation of given cycle type. St001365The number of lattice paths of the same length weakly above the path given by a binary word. St001383The BG-rank of an integer partition. St001387Number of standard Young tableaux of the skew shape tracing the border of the given partition. St001432The order dimension of the partition. St001442The number of standard Young tableaux whose major index is divisible by the size of a given integer partition. St001525The number of symmetric hooks on the diagonal of a partition. St001529The number of monomials in the expansion of the nabla operator applied to the power-sum symmetric function indexed by the partition. St001530The depth of a Dyck path. St001561The value of the elementary symmetric function evaluated at 1. St001562The value of the complete homogeneous symmetric function evaluated at 1. St001563The value of the power-sum symmetric function evaluated at 1. St001564The value of the forgotten symmetric functions when all variables set to 1. St001593This is the number of standard Young tableaux of the given shifted shape. St001599The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on rooted trees. St001600The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on simple graphs. St001601The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on trees. St001602The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on endofunctions. St001606The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on set partitions. St001608The number of coloured rooted trees such that the multiplicities of colours are given by a partition. St001609The number of coloured trees such that the multiplicities of colours are given by a partition. St001610The number of coloured endofunctions such that the multiplicities of colours are given by a partition. St001614The cyclic permutation representation number of a skew partition. St001627The number of coloured connected graphs such that the multiplicities of colours are given by a partition. St001628The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on simple connected graphs. St001733The number of weak left to right maxima of a Dyck path. St001763The Hurwitz number of an integer partition. St001767The largest minimal number of arrows pointing to a cell in the Ferrers diagram in any assignment. St001780The order of promotion on the set of standard tableaux of given shape. St001785The number of ways to obtain a partition as the multiset of antidiagonal lengths of the Ferrers diagram of a partition. 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. St001901The largest multiplicity of an irreducible representation contained in the higher Lie character for an integer partition. St001908The number of semistandard tableaux of distinct weight whose maximal entry is the length of the partition. St001913The number of preimages of an integer partition in Bulgarian solitaire. St001924The number of cells in an integer partition whose arm and leg length coincide. St001933The largest multiplicity of a part in an integer partition. St001934The number of monotone factorisations of genus zero of a permutation of given cycle type. St001936The number of transitive factorisations of a permutation of given cycle type into star transpositions. St001938The number of transitive monotone factorizations of genus zero of a permutation of given cycle type. St001939The number of parts that are equal to their multiplicity in the integer partition. St001940The number of distinct parts that are equal to their multiplicity in the integer partition. St001943The sum of the squares of the hook lengths of an integer partition. St001955The number of natural descents for set-valued two row standard Young tableaux. St000016The number of attacking pairs of a standard tableau. St000142The number of even parts of a partition. St000143The largest repeated part of a partition. St000145The Dyson rank of a partition. St000149The number of cells of the partition whose leg is zero and arm is odd. St000150The floored half-sum of the multiplicities of a partition. St000185The weighted size of a partition. St000205Number of non-integral Gelfand-Tsetlin polytopes with prescribed top row and partition weight. St000206Number of non-integral Gelfand-Tsetlin polytopes with prescribed top row and integer composition weight. St000256The number of parts from which one can substract 2 and still get an integer partition. St000257The number of distinct parts of a partition that occur at least twice. St000377The dinv defect of an integer partition. St000481The number of upper covers of a partition in dominance order. St000689The maximal n such that the minimal generator-cogenerator module in the LNakayama algebra of a Dyck path is n-rigid. St000749The smallest integer d such that the restriction of the representation corresponding to a partition of n to the symmetric group on n-d letters has a constituent of odd degree. St000877The depth of the binary word interpreted as a path. St000944The 3-degree of an integer partition. St000954Number of times the corresponding LNakayama algebra has $Ext^i(D(A),A)=0$ for $i>0$. St001067The number of simple modules of dominant dimension at least two in the corresponding Nakayama algebra. St001091The number of parts in an integer partition whose next smaller part has the same size. St001092The number of distinct even parts of a partition. St001125The number of simple modules that satisfy the 2-regular condition in the corresponding Nakayama algebra. St001175The size of a partition minus the hook length of the base cell. St001176The size of a partition minus its first part. St001177Twice the mean value of the major index among all standard Young tableaux of a partition. St001178Twelve times the variance of the major index among all standard Young tableaux of a partition. St001185The number of indecomposable injective modules of grade at least 2 in the corresponding Nakayama algebra. St001216The number of indecomposable injective modules in the corresponding Nakayama algebra that have non-vanishing second Ext-group with the regular module. St001217The projective dimension of the indecomposable injective module I[n-2] in the corresponding Nakayama algebra with simples enumerated from 0 to n-1. St001223Number of indecomposable projective non-injective modules P such that the modules X and Y in a an Auslander-Reiten sequence ending at P are torsionless. St001227The vector space dimension of the first extension group between the socle of the regular module and the Jacobson radical of the corresponding Nakayama algebra. St001230The number of simple modules with injective dimension equal to the dominant dimension equal to one and the dual property. St001233The number of indecomposable 2-dimensional modules with projective dimension one. St001248Sum of the even parts of a partition. St001252Half the sum of the even parts of a partition. St001274The number of indecomposable injective modules with projective dimension equal to two. St001279The sum of the 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. St001371The length of the longest Yamanouchi prefix of a binary word. St001440The number of standard Young tableaux whose major index is congruent one modulo the size of a given integer partition. St001586The number of odd parts smaller than the largest even part in an integer partition. St001594The number of indecomposable projective modules in the Nakayama algebra corresponding to the Dyck path such that the UC-condition is satisfied. St001604The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on polygons. St001714The number of subpartitions of an integer partition that do not dominate the conjugate subpartition. St001721The degree of a binary word. St001912The length of the preperiod in Bulgarian solitaire corresponding to an integer partition. St001932The number of pairs of singleton blocks in the noncrossing set partition corresponding to a Dyck path, that can be merged to create another noncrossing set partition. St001961The sum of the greatest common divisors of all pairs of parts. St000474Dyson's crank of a partition. 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 $K[x]/(x^n)$. St001569The maximal modular displacement of a permutation. St000102The charge of a semistandard tableau. St001556The number of inversions of the third entry of a permutation. St001948The number of augmented double ascents of a permutation. St000134The size of the orbit of an alternating sign matrix under gyration. St000822The Hadwiger number of the graph. St000898The number of maximal entries in the last diagonal of the monotone triangle. St001555The order of a signed permutation. St001879The number of indecomposable summands of the top of the first syzygy of the dual of the regular module in the incidence algebra of the lattice. St001880The number of 2-Gorenstein indecomposable injective modules in the incidence algebra of the lattice. St001893The flag descent of a signed permutation. St000096The number of spanning trees of a graph. St000181The number of connected components of the Hasse diagram for the poset. St000261The edge connectivity of a graph. St000262The vertex connectivity of a graph. St000287The number of connected components of a graph. St000309The number of vertices with even degree. St000310The minimal degree of a vertex of a graph. St000450The number of edges minus the number of vertices plus 2 of a graph. St000739The first entry in the last row of a semistandard tableau. St000958The number of Bruhat factorizations of a permutation. St001195The global dimension of the algebra $A/AfA$ of the corresponding Nakayama algebra $A$ with minimal left faithful projective-injective module $Af$. St001204Call 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. St001236The dominant dimension of the corresponding Comp-Nakayama algebra. St001260The permanent of an alternating sign matrix. St001404The number of distinct entries in a Gelfand Tsetlin pattern. St001410The minimal entry of a semistandard tableau. St001490The number of connected components of a skew partition. St001605The number of colourings of a cycle such that the multiplicities of colours are given by a partition. St001738The minimal order of a graph which is not an induced subgraph of the given graph. St001805The maximal overlap of a cylindrical tableau associated with a semistandard tableau. St001820The size of the image of the pop stack sorting operator. St001828The Euler characteristic of a graph. St001889The size of the connectivity set of a signed permutation. St001904The length of the initial strictly increasing segment of a parking function. St001937The size of the center of a parking function. St000045The number of linear extensions of a binary tree. St000095The number of triangles of a graph. St000101The cocharge of a semistandard tableau. St000188The area of the Dyck path corresponding to a parking function and the total displacement of a parking function. St000195The number of secondary dinversion pairs of the dyck path corresponding to a parking function. St000274The number of perfect matchings of a graph. St000303The determinant of the product of the incidence matrix and its transpose of a graph divided by $4$. St000315The number of isolated vertices of a graph. St000894The trace of an alternating sign matrix. St000943The number of spots the most unlucky car had to go further in a parking function. St001001The number of indecomposable modules with projective and injective dimension equal to the global dimension of the Nakayama algebra corresponding to the Dyck path. St001314The number of tilting modules of arbitrary projective dimension that have no simple modules as a direct summand in the corresponding Nakayama algebra. St001429The number of negative entries in a signed permutation. St001631The number of simple modules $S$ with $dim Ext^1(S,A)=1$ in the incidence algebra $A$ of the poset. St001633The number of simple modules with projective dimension two in the incidence algebra of the poset. 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. St001771The number of occurrences of the signed pattern 1-2 in a signed permutation. St001783The number of odd automorphisms of a graph. St001846The number of elements which do not have a complement in the lattice. St001856The number of edges in the reduced word graph of a permutation. St001862The number of crossings of a signed permutation. St001866The nesting alignments of a signed permutation. St001868The number of alignments of type NE of a signed permutation. St001870The number of positive entries followed by a negative entry in a signed permutation. St001871The number of triconnected components of a graph. St001882The number of occurrences of a type-B 231 pattern in a signed permutation. St001895The oddness of a signed permutation. St001903The number of fixed points of a parking function. St001926Sparre Andersen's position of the maximum of a signed permutation. St001964The interval resolution global dimension of a poset.