St000325The width of the tree associated to a permutation. St000397The Strahler number of a rooted tree. St000451The length of the longest pattern of the form k 1 2. St000470The number of runs in a permutation. St000686The finitistic dominant dimension of a Dyck path. St000862The number of parts of the shifted shape of a permutation. St000920The logarithmic height of a Dyck path. 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: St001239The largest vector space dimension of the double dual of a simple module in the corresponding Nakayama algebra. St001804The minimal height of the rectangular inner shape in a cylindrical tableau associated to a tableau. St000021The number of descents of a permutation. St000035The number of left outer peaks of a permutation. St000162The number of nontrivial cycles in the cycle decomposition of a permutation. St000183The side length of the Durfee square of an integer partition. St000306The bounce count of a Dyck path. St000329The number of evenly positioned ascents of the Dyck path, with the initial position equal to 1. St000337The lec statistic, the sum of the inversion numbers of the hook factors of a permutation. St000352The Elizalde-Pak rank of a permutation. St000353The number of inner valleys of a permutation. St000374The number of exclusive right-to-left minima of a permutation. St000662The staircase size of the code of a permutation. St000688The global dimension minus the dominant dimension of the LNakayama algebra associated to a Dyck path. St000703The number of deficiencies of a permutation. St000711The number of big exceedences of a permutation. St000834The number of right outer peaks of a permutation. St000884The number of isolated descents of a permutation. St000897The number of different multiplicities of parts of an integer partition. St000970Number of peaks minus the dominant dimension of the corresponding LNakayama algebra. St000994The number of cycle peaks and the number of cycle valleys of a permutation. St001028Number of simple modules with injective dimension equal to the dominant dimension in the Nakayama algebra corresponding to the Dyck path. St001035The convexity degree of the parallelogram polyomino associated with the Dyck path. St001192The maximal dimension of $Ext_A^2(S,A)$ for a simple module $S$ over the corresponding Nakayama algebra $A$. 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 $eA$. 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. 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. St001394The genus of a permutation. 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. 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. St001761The maximal multiplicity of a letter in a reduced word of a permutation. St001801Half the number of preimage-image pairs of different parity in a permutation. St001874Lusztig's a-function for the symmetric group. St001928The number of non-overlapping descents in a permutation. St001942The number of loops of the quiver corresponding to the reduced incidence algebra of a poset. St000007The number of saliances of the permutation. St000010The length of the partition. St000011The number of touch points (or returns) of a Dyck path. St000013The height of a Dyck path. St000015The number of peaks of a Dyck path. St000031The number of cycles in the cycle decomposition of a permutation. St000058The order of a permutation. St000062The length of the longest increasing subsequence of the permutation. St000071The number of maximal chains in a poset. 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. St000120The number of left tunnels of a Dyck path. St000147The largest part of an integer partition. St000155The number of exceedances (also excedences) of a permutation. St000172The Grundy number of a graph. St000201The number of leaf nodes in a binary tree. St000208Number of integral Gelfand-Tsetlin polytopes with prescribed top row and integer partition weight. St000213The number of weak exceedances (also weak excedences) of a permutation. St000239The number of small weak excedances. St000243The number of cyclic valleys and cyclic peaks of a permutation. St000291The number of descents of a binary word. St000307The number of rowmotion orbits of a poset. St000308The height of the tree associated to a permutation. St000314The number of left-to-right-maxima of a permutation. St000318The number of addable cells of the Ferrers diagram of an integer partition. St000321The number of integer partitions of n that are dominated by an integer partition. St000345The number of refinements of a partition. St000346The number of coarsenings of a partition. St000354The number of recoils of a permutation. St000390The number of runs of ones in a binary word. St000392The length of the longest run of ones in a binary word. St000396The register function (or Horton-Strahler number) of a binary tree. St000443The number of long tunnels of a Dyck path. St000444The length of the maximal rise of a Dyck path. St000527The width of the poset. St000528The height of a poset. St000542The number of left-to-right-minima of a permutation. St000568The hook number of a binary tree. St000574The number of occurrences of the pattern {{1},{2}} such that 1 is a minimal and 2 a maximal element. St000619The number of cyclic descents of a permutation. St000630The length of the shortest palindromic decomposition of a binary word. St000640The rank of the largest boolean interval in a poset. St000670The reversal length of a permutation. St000676The number of odd rises of a Dyck path. St000679The pruning number of an ordered tree. St000684The global dimension of the LNakayama algebra associated to a Dyck path. St000695The number of blocks in the first part of the atomic decomposition of a set partition. St000701The protection number of a binary tree. St000702The number of weak deficiencies of a permutation. St000755The number of real roots of the characteristic polynomial of a linear recurrence associated with an integer partition. St000758The length of the longest staircase fitting into an integer composition. 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. St000822The Hadwiger number of the graph. St000829The Ulam distance of a permutation to the identity permutation. St000845The maximal number of elements covered by an element in a poset. St000846The maximal number of elements covering an element of a poset. St000864The number of circled entries of the shifted recording tableau of a permutation. St000886The number of permutations with the same antidiagonal sums. St000930The k-Gorenstein degree of the corresponding Nakayama algebra with linear quiver. St000935The number of ordered refinements of an integer partition. St000955Number of times one has $Ext^i(D(A),A)>0$ for $i>0$ for the corresponding LNakayama algebra. St000982The length of the longest constant subword. 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. St001014Number of indecomposable injective modules with codominant dimension equal to the dominant dimension of the Nakayama algebra corresponding to the Dyck path. St001029The size of the core of a graph. St001031The height of the bicoloured Motzkin path associated with the Dyck path. St001039The maximal height of a column in the parallelogram polyomino associated with a Dyck path. St001052The length of the exterior of a permutation. St001068Number of torsionless simple modules in the corresponding Nakayama algebra. St001096The size of the overlap set of a permutation. St001116The game chromatic number of a graph. 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. St001235The global dimension of the corresponding Comp-Nakayama algebra. St001257The dominant dimension of the double dual of A/J when A is the corresponding Nakayama algebra with Jacobson radical J. St001261The Castelnuovo-Mumford regularity of a graph. St001273The projective dimension of the first term in an injective coresolution of the regular module. St001285The number of primes in the column sums of the two line notation of a permutation. St001299The product of all non-zero projective dimensions of simple modules of the corresponding Nakayama algebra. St001302The number of minimally dominating sets of vertices of a graph. St001304The number of maximally independent sets of vertices of a graph. St001330The hat guessing number of a graph. St001343The dimension of the reduced incidence algebra of a poset. St001359The number of permutations in the equivalence class of a permutation obtained by taking inverses of cycles. St001389The number of partitions of the same length below the given integer partition. St001390The number of bumps occurring when Schensted-inserting the letter 1 of a permutation. 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. St001486The number of corners of the ribbon associated with an integer composition. St001494The Alon-Tarsi number of a graph. St001498The normalised height of a Nakayama algebra with magnitude 1. St001500The global dimension of magnitude 1 Nakayama algebras. St001503The largest distance of a vertex to a vertex in a cycle in the resolution quiver of the corresponding Nakayama algebra. St001530The depth of a Dyck path. St001569The maximal modular displacement of a permutation. St001580The acyclic chromatic number of a graph. St001581The achromatic number of a graph. St001597The Frobenius rank of a skew partition. St001632The number of indecomposable injective modules $I$ with $dim Ext^1(I,A)=1$ for the incidence algebra A of a poset. St001642The Prague dimension of a graph. St001661Half the permanent of the Identity matrix plus the permutation matrix associated to the permutation. St001670The connected partition number of a graph. St001717The largest size of an interval in a poset. St001732The number of peaks visible from the left. St001733The number of weak left to right maxima of a Dyck path. St001735The number of permutations with the same set of runs. St001741The largest integer such that all patterns of this size are contained in the permutation. St001760The number of prefix or suffix reversals needed to sort a permutation. St001806The upper middle entry of a permutation. St001807The lower middle entry of a permutation. St001883The mutual visibility number of a graph. St001963The tree-depth of a graph. St000023The number of inner peaks 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. St000039The number of crossings of a permutation. St000053The number of valleys of the Dyck path. St000080The rank of the poset. St000141The maximum drop size of a permutation. St000142The number of even parts of a partition. St000154The sum of the descent bottoms of a permutation. St000157The number of descents of a standard tableau. St000159The number of distinct parts of the integer partition. St000185The weighted size of a partition. St000196The number of occurrences of the contiguous pattern [[.,.],[.,. St000238The number of indices that are not small weak excedances. St000245The number of ascents of a permutation. St000272The treewidth of a graph. 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. St000319The spin of an integer partition. St000320The dinv adjustment of an integer partition. St000331The number of upper interactions of a Dyck path. St000333The dez statistic, the number of descents of a permutation after replacing fixed points by zeros. St000336The leg major index of a standard tableau. St000340The number of non-final maximal constant sub-paths of length greater than one. St000358The number of occurrences of the pattern 31-2. St000362The size of a minimal vertex cover of a graph. St000386The number of factors DDU in a Dyck path. St000387The matching number of a graph. St000429The number of occurrences of the pattern 123 or of the pattern 321 in a permutation. St000442The maximal area to the right of an up step of a Dyck path. 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. St000481The number of upper covers of a partition in dominance order. St000486The number of cycles of length at least 3 of a permutation. St000506The number of standard desarrangement tableaux of shape equal to the given partition. St000533The minimum of the number of parts and the size of the first part of an integer partition. St000535The rank-width of a graph. St000536The pathwidth of a graph. St000537The cutwidth of a graph. St000538The number of even inversions of a permutation. St000539The number of odd inversions of a permutation. St000563The number of overlapping pairs of blocks of a set partition. St000585The number of occurrences of the pattern {{1,3},{2}} such that 2 is maximal, (1,3) 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. St000646The number of big ascents of a permutation. St000647The number of big descents 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. St000660The number of rises of length at least 3 of a Dyck path. St000665The number of rafts of a permutation. St000672The number of minimal elements in Bruhat order not less than the permutation. St000710The number of big deficiencies of a permutation. St000725The smallest label of a leaf of the increasing binary tree associated to a permutation. St000731The number of double exceedences of a permutation. St000732The number of double deficiencies of a permutation. St000742The number of big ascents of a permutation after prepending zero. St000754The Grundy value for the game of removing nestings in a perfect matching. St000779The tier of a permutation. St000783The side length of the largest staircase partition fitting into a partition. St000836The number of descents of distance 2 of a permutation. St000837The number of ascents of distance 2 of a permutation. St000875The semilength of the longest Dyck word in the Catalan factorisation of a binary word. St000891The number of distinct diagonal sums of a permutation matrix. St000919The number of maximal left branches of a binary tree. St000985The number of positive eigenvalues of the adjacency matrix of the graph. St000996The number of exclusive left-to-right maxima of a permutation. St001021Sum of the differences between projective and codominant dimension of the non-projective indecomposable injective modules in the Nakayama algebra corresponding to the Dyck path. St001022Number of simple modules with projective dimension 3 in 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. St001036The number of inner corners of the parallelogram polyomino associated with the Dyck path. St001037The number of inner corners of the upper path 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,. St001083The number of boxed occurrences of 132 in a permutation. St001085The number of occurrences of the vincular pattern |21-3 in a permutation. St001089Number of indecomposable projective non-injective modules minus the number of indecomposable projective non-injective modules with dominant dimension equal to the injective dimension in the corresponding Nakayama algebra. St001090The number of pop-stack-sorts needed to sort a permutation. St001092The number of distinct even parts of a partition. St001115The number of even descents of a permutation. St001125The number of simple modules that satisfy the 2-regular condition 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. St001169Number of simple modules with projective dimension at least two in the corresponding Nakayama algebra. St001174The Gorenstein dimension of the algebra $A/I$ when $I$ is the tilting module corresponding to the permutation in the Auslander algebra of $K[x]/(x^n)$. St001176The size of a partition minus its first part. St001180Number of indecomposable injective modules with projective dimension at most 1. St001181Number of indecomposable injective modules with grade at least 3 in the corresponding Nakayama algebra. St001183The maximum of $projdim(S)+injdim(S)$ over all simple modules in the Nakayama algebra corresponding to the Dyck path. St001194The injective dimension of $A/AfA$ in the corresponding Nakayama algebra $A$ when $Af$ is the minimal faithful projective-injective left $A$-module 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 $eA$. St001216The number of indecomposable injective modules in the corresponding Nakayama algebra that have non-vanishing second Ext-group with the regular module. St001221The number of simple modules in the corresponding LNakayama algebra that have 2 dimensional second Extension group with the regular module. St001225The vector space dimension of the first extension group between J and itself when J is 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. St001251The number of parts of a partition that are not congruent 1 modulo 3. St001252Half the sum of the even parts of a partition. St001258Gives the maximum of injective plus projective dimension of an indecomposable module over the corresponding Nakayama algebra. St001270The bandwidth of a graph. St001274The number of indecomposable injective modules with projective dimension equal to two. St001277The degeneracy of a graph. St001278The number of indecomposable modules that are fixed by $\tau \Omega^1$ composed with its inverse in the corresponding Nakayama algebra. St001280The number of parts of an integer partition that are at least two. St001290The first natural number n such that the tensor product of n copies of D(A) is zero for the corresponding Nakayama algebra A. St001294The maximal torsionfree index of a simple non-projective module in the corresponding Nakayama algebra. St001296The maximal torsionfree index of an indecomposable non-projective module in the corresponding Nakayama algebra. St001298The number of repeated entries in the Lehmer code of a permutation. St001333The cardinality of a minimal edge-isolating set of a graph. St001349The number of different graphs obtained from the given graph by removing an edge. St001354The number of series nodes in the modular decomposition of a graph. St001358The largest degree of a regular subgraph of a graph. St001375The pancake length of a permutation. St001393The induced matching number of a graph. St001420Half the length of a longest factor which is its own reverse-complement of a binary word. St001421Half the length of a longest factor which is its own reverse-complement and begins with a one of a binary word. St001424The number of distinct squares in a binary word. St001427The number of descents of a signed permutation. St001431Half of the Loewy length minus one of a modified stable Auslander algebra of the Nakayama algebra corresponding to the Dyck path. St001440The number of standard Young tableaux whose major index is congruent one modulo the size of a given integer partition. St001444The rank of the skew-symmetric form which is non-zero on crossing arcs of a perfect matching. St001466The number of transpositions swapping cyclically adjacent numbers in a permutation. St001469The holeyness of a permutation. St001470The cyclic holeyness of a permutation. St001502The global dimension minus the dominant dimension of magnitude 1 Nakayama algebras. 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. St001509The degree of the standard monomial associated to a Dyck path relative to the trivial lower boundary. St001579The number of cyclically simple transpositions decreasing the number of cyclic descents needed to sort a permutation. St001587Half of the largest even part of an integer partition. St001613The binary logarithm of the size of the center of a lattice. St001621The number of atoms of a lattice. St001644The dimension of a graph. St001657The number of twos in an integer partition. St001671Haglund's hag of a permutation. St001687The number of distinct positions of the pattern letter 2 in occurrences of 213 in a permutation. St001726The number of visible inversions of a permutation. St001728The number of invisible descents of a permutation. St001731The factorization defect of a permutation. St001743The discrepancy of a graph. St001744The number of occurrences of the arrow pattern 1-2 with an arrow from 1 to 2 in a permutation. St001792The arboricity of a graph. St001812The biclique partition number of a graph. St001823The Stasinski-Voll length of a signed permutation. St001839The number of excedances of a set partition. St001840The number of descents of a set partition. St001859The number of factors of the Stanley symmetric function associated with a permutation. St001896The number of right descents of a signed permutations. St001905The number of preferred parking spots in a parking function less than the index of the car. St001918The degree of the cyclic sieving polynomial corresponding to an integer partition. St001946The number of descents in a parking function. St001960The number of descents of a permutation minus one if its first entry is not one. St001961The sum of the greatest common divisors of all pairs of parts. St001962The proper pathwidth of a graph. St000025The number of initial rises of a Dyck path. St000032The number of elements smaller than the given Dyck path in the Tamari Order. St000038The product of the heights of the descending steps of a Dyck path. St000040The number of regions of the inversion arrangement of a permutation. St000054The first entry of the permutation. St000056The decomposition (or block) number of a permutation. St000060The greater neighbor of the maximum. St000061The number of nodes on the left branch of a binary tree. St000063The number of linear extensions of a certain poset defined for an integer partition. St000068The number of minimal elements in a poset. St000069The number of maximal elements of a poset. St000084The number of subtrees. St000086The number of subgraphs. St000087The number of induced subgraphs. St000093The cardinality of a maximal independent set of vertices of a graph. St000105The number of blocks in the set partition. St000108The number of partitions contained in the given partition. 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. St000124The cardinality of the preimage of the Simion-Schmidt map. St000153The number of adjacent cycles of a permutation. St000164The number of short pairs. St000166The depth minus 1 of an ordered tree. St000167The number of leaves of an ordered tree. St000175Degree of the polynomial counting the number of semistandard Young tableaux when stretching the shape. St000193The row of the unique '1' in the first column of the alternating sign matrix. St000211The rank of the set partition. St000216The absolute length of a permutation. St000237The number of small exceedances. St000240The number of indices that are not small excedances. St000244The cardinality of the automorphism group of a graph. St000251The number of nonsingleton blocks of a set partition. St000253The crossing number of a set partition. St000254The nesting number of a set partition. St000258The burning number of a graph. St000259The diameter of a connected graph. St000260The radius of a connected graph. St000269The number of acyclic orientations of a graph. St000270The number of forests contained in a graph. St000273The domination number of a graph. St000278The size of the preimage of the map 'to partition' from Integer compositions to Integer partitions. St000283The size of the preimage of the map 'to graph' from Binary trees to Graphs. St000286The number of connected components of the complement of a graph. St000288The number of ones in a binary word. St000297The number of leading ones in a binary word. St000299The number of nonisomorphic vertex-induced subtrees. St000326The position of the first one in a binary word after appending a 1 at the end. St000328The maximum number of child nodes in a tree. St000335The difference of lower and upper interactions. St000343The number of spanning subgraphs of a graph. St000363The number of minimal vertex covers of a graph. St000364The exponent of the automorphism group of a graph. St000378The diagonal inversion number of an integer partition. St000381The largest part of an integer composition. St000402Half the size of the symmetry class of a permutation. St000415The size of the automorphism group of the rooted tree underlying the ordered tree. St000418The number of Dyck paths that are weakly below a Dyck path. St000452The number of distinct eigenvalues of a graph. St000453The number of distinct Laplacian eigenvalues of a graph. St000468The Hosoya index of a graph. St000469The distinguishing number of a graph. St000476The sum of the semi-lengths of tunnels before a valley of a Dyck path. St000479The Ramsey number of a graph. St000482The (zero)-forcing number of a graph. St000483The number of times a permutation switches from increasing to decreasing or decreasing to increasing. St000485The length of the longest cycle of a permutation. St000495The number of inversions of distance at most 2 of a permutation. St000504The cardinality of the first block of a set partition. St000507The number of ascents of a standard tableau. St000511The number of invariant subsets when acting with a permutation of given cycle type. St000522The number of 1-protected nodes of a rooted tree. 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. St000532The total number of rook placements on a Ferrers board. St000541The number of indices greater than or equal to 2 of a permutation such that all smaller indices appear to its right. St000547The number of even non-empty partial sums of an integer partition. St000553The number of blocks of a graph. St000617The number of global maxima of a Dyck path. St000633The size of the automorphism group of a poset. St000636The hull number of a graph. St000638The number of up-down runs of a permutation. St000652The maximal difference between successive positions of a permutation. St000654The first descent of a permutation. St000668The least common multiple of the parts of the partition. St000669The number of permutations obtained by switching ascents or descents of size 2. St000675The number of centered multitunnels of a Dyck path. St000678The number of up steps after the last double rise of a Dyck path. St000694The number of affine bounded permutations that project to a given permutation. St000700The protection number of an ordered tree. 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. St000720The size of the largest partition in the oscillating tableau corresponding to the perfect matching. St000722The number of different neighbourhoods in a graph. St000730The maximal arc length of a set partition. St000733The row containing the largest entry of a standard tableau. St000734The last entry in the first row of a standard tableau. St000738The first entry in the last row of a standard tableau. St000743The number of entries in a standard Young tableau such that the next integer is a neighbour. St000744The length of the path to the largest entry in a standard Young tableau. St000745The index of the last row whose first entry is the row number in a standard Young tableau. St000746The number of pairs with odd minimum in a perfect matching. St000753The Grundy value for the game of Kayles on a binary word. St000757The length of the longest weakly inreasing subsequence of parts of an integer composition. St000759The smallest missing part in an integer partition. St000760The length of the longest strictly decreasing subsequence of parts of an integer composition. St000764The number of strong records in an integer composition. St000765The number of weak records in an integer composition. St000767The number of runs in an integer composition. St000774The maximal multiplicity of a Laplacian eigenvalue in a graph. St000777The number of distinct eigenvalues of the distance Laplacian of a connected graph. St000778The metric dimension of a graph. St000786The maximal number of occurrences of a colour in a proper colouring of a graph. St000793The length of the longest partition in the vacillating tableau corresponding to a set partition. St000805The number of peaks of the associated bargraph. St000808The number of up steps of the associated bargraph. St000809The reduced reflection length of the permutation. St000810The sum of the entries in the column specified by the partition of the change of basis matrix from powersum symmetric functions to monomial symmetric functions. St000831The number of indices that are either descents or recoils. St000843The decomposition number of a perfect matching. St000844The size of the largest block in the direct sum decomposition of a permutation. St000868The aid statistic in the sense of Shareshian-Wachs. St000876The number of factors in the Catalan decomposition of a binary word. St000883The number of longest increasing subsequences of a permutation. St000885The number of critical steps in the Catalan decomposition of a binary word. St000887The maximal number of nonzero entries on a diagonal of a permutation matrix. St000889The number of alternating sign matrices with the same antidiagonal sums. St000903The number of different parts of an integer composition. St000905The number of different multiplicities of parts of an integer composition. St000912The number of maximal antichains in a poset. St000916The packing number of a graph. St000917The open packing number of a graph. St000918The 2-limited packing number of a graph. St000925The number of topologically connected components of a set partition. St000926The clique-coclique number of a graph. St000933The number of multipartitions of sizes given by an integer partition. St000942The number of critical left to right maxima of the parking functions. St000971The smallest closer of a set partition. St000972The composition number of a graph. St000983The length of the longest alternating subword. St000988The orbit size of a permutation under Foata's bijection. St000999Number of indecomposable projective module with injective dimension equal to the global dimension in the Nakayama algebra corresponding to the Dyck path. St001000Number of indecomposable modules with projective dimension equal to the global dimension in the Nakayama algebra corresponding to the Dyck path. St001009Number of indecomposable injective modules with projective dimension g when g is the global dimension of the Nakayama algebra corresponding to the Dyck path. St001024Maximum of dominant dimensions of the simple modules in the Nakayama algebra corresponding to the Dyck path. St001038The minimal height of a column in the parallelogram polyomino associated with the Dyck path. St001044The number of pairs whose larger element is at most one more than half the size of the perfect matching. St001050The number of terminal closers of a set partition. St001051The depth of the label 1 in the decreasing labelled unordered tree associated with the set partition. St001057The Grundy value of the game of creating an independent set in a graph. St001058The breadth of the ordered tree. St001062The maximal size of a block of a set partition. St001076The minimal length of a factorization of a permutation into transpositions that are cyclic shifts of (12). St001081The number of minimal length factorizations of a permutation into star transpositions. St001088Number of indecomposable projective non-injective modules with dominant dimension equal to the injective dimension in the corresponding Nakayama algebra. 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. St001105The number of greedy linear extensions of a poset. St001106The number of supergreedy linear extensions of a poset. St001108The 2-dynamic chromatic number of a graph. St001109The number of proper colourings of a graph with as few colours as possible. St001110The 3-dynamic chromatic number of a graph. St001111The weak 2-dynamic chromatic number of a graph. St001128The exponens consonantiae of a partition. St001135The projective dimension of the first simple module in the Nakayama algebra corresponding to the Dyck path. St001136The largest label with larger sister in the leaf labelled binary unordered tree associated with the perfect matching. St001151The number of blocks with odd minimum. St001184Number of indecomposable injective modules with grade at least 1 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. St001220The width of a permutation. 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. St001241The number of non-zero radicals of the indecomposable projective modules that have injective dimension and projective dimension at most one. St001246The maximal difference between two consecutive entries of a permutation. St001267The length of the Lyndon factorization of the binary word. St001286The annihilation number of a graph. St001288The number of primes obtained by multiplying preimage and image of a permutation and adding one. St001315The dissociation number of a graph. St001316The domatic 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. St001322The size of a minimal independent dominating set in a graph. St001337The upper domination number of a graph. St001338The upper irredundance number of a graph. St001339The irredundance number of a graph. St001342The number of vertices in the center of a graph. St001355Number of non-empty prefixes of a binary word that contain equally many 0's and 1's. St001366The maximal multiplicity of a degree of a vertex of a graph. St001368The number of vertices of maximal degree in a graph. St001372The length of a longest cyclic run of ones of a binary word. St001385The number of conjugacy classes of subgroups with connected subgroups of sizes prescribed by an integer partition. St001399The distinguishing number of a poset. St001400The total number of Littlewood-Richardson tableaux of given shape. St001402The number of separators in a permutation. St001405The number of bonds in a permutation. St001415The length of the longest palindromic prefix of a binary word. St001418Half of the global dimension of the stable Auslander algebra of the Nakayama algebra corresponding to the Dyck path. St001419The length of the longest palindromic factor beginning with a one of a binary word. St001432The order dimension of the partition. St001437The flex of a binary word. St001462The number of factors of a standard tableaux under concatenation. St001465The number of adjacent transpositions in the cycle decomposition of a permutation. St001468The smallest fixpoint of a permutation. St001474The evaluation of the Tutte polynomial of the graph at (x,y) equal to (2,-1). St001481The minimal height of a peak of a Dyck path. St001484The number of singletons of an integer partition. St001487The number of inner corners of a skew partition. St001488The number of corners of a skew partition. St001497The position of the largest weak excedence of a permutation. St001499The number of indecomposable projective-injective modules of a magnitude 1 Nakayama algebra. St001512The minimum rank of a graph. St001514The dimension of the top of the Auslander-Reiten translate of the regular modules as a bimodule. St001531Number of partial orders contained in the poset determined by the Dyck path. St001555The order of a signed permutation. St001566The length of the longest arithmetic progression in a permutation. St001568The smallest positive integer that does not appear twice in the partition. St001571The Cartan determinant of the integer partition. St001589The nesting number of a perfect matching. St001624The breadth of a lattice. St001645The pebbling number of a connected graph. St001652The length of a longest interval of consecutive numbers. St001654The monophonic hull number of a graph. St001655The general position number of a graph. St001656The monophonic position number of a graph. St001662The length of the longest factor of consecutive numbers in a permutation. St001672The restrained domination number of a graph. St001674The number of vertices of the largest induced star graph in the graph. St001707The length of a longest path in a graph such that the remaining vertices can be partitioned into two sets of the same size without edges between them. St001716The 1-improper chromatic number of a graph. St001725The harmonious chromatic number of a graph. St001734The lettericity of a graph. St001746The coalition number of a graph. St001757The number of orbits of toric promotion on a graph. St001758The number of orbits of promotion on a graph. St001773The number of minimal elements in Bruhat order not less than the signed permutation. St001774The degree of the minimal polynomial of the smallest eigenvalue of a graph. St001775The degree of the minimal polynomial of the largest eigenvalue of a graph. St001778The largest greatest common divisor of an element and its image in a permutation. St001784The minimum of the smallest closer and the second element of the block containing 1 in a set partition. St001802The number of endomorphisms of a graph. St001809The index of the step at the first peak of maximal height in a Dyck path. St001814The number of partitions interlacing the given partition. St001829The common independence number of a graph. St001844The maximal degree of a generator of the invariant ring of the automorphism group of a graph. St001863The number of weak excedances of a signed permutation. St001864The number of excedances of a signed permutation. St001870The number of positive entries followed by a negative entry in a signed permutation. 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. St001907The number of Bastidas - Hohlweg - Saliola excedances of a signed permutation. St001913The number of preimages of an integer partition in Bulgarian solitaire. St001914The size of the orbit 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. St001941The evaluation at 1 of the modified Kazhdan--Lusztig R polynomial (as in [1, Section 5. St001955The number of natural descents for set-valued two row standard Young tableaux. St001959The product of the heights of the peaks of a Dyck path. St000004The major index of a permutation. St000009The charge of a standard tableau. St000012The area of a Dyck path. St000016The number of attacking pairs of a standard tableau. St000018The number of inversions of a permutation. St000019The cardinality of the support of a permutation. St000022The number of fixed points of a permutation. St000029The depth of a permutation. St000030The sum of the descent differences of a permutations. St000034The maximum defect over any reduced expression for a permutation and any subexpression. St000052The number of valleys of a Dyck path not on the x-axis. St000055The inversion sum of a permutation. St000059The inversion number of a standard tableau as defined by Haglund and Stevens. St000081The number of edges of a graph. St000083The number of left oriented leafs of a binary tree except the first one. St000091The descent variation of a composition. St000094The depth of an ordered tree. St000118The number of occurrences of the contiguous pattern [.,[.,[.,.]]] in a binary tree. St000122The number of occurrences of the contiguous pattern [.,[.,[[.,.],.]]] in a binary tree. St000123The difference in Coxeter length of a permutation and its image under the Simion-Schmidt map. St000143The largest repeated part of a partition. St000144The pyramid weight of the Dyck path. St000148The number of odd parts 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. St000156The Denert index of a permutation. St000160The multiplicity of the smallest part of a partition. St000168The number of internal nodes of an ordered tree. St000169The cocharge of a standard tableau. St000171The degree of the graph. St000203The number of external nodes of a binary tree. St000209Maximum difference of elements in cycles. St000214The number of adjacencies of a permutation. St000215The number of adjacencies of a permutation, zero appended. St000217The number of occurrences of the pattern 312 in a permutation. St000222The number of alignments in the permutation. St000223The number of nestings in the permutation. St000224The sorting index of a permutation. St000225Difference between largest and smallest parts in a partition. St000228The size of a partition. St000234The number of global ascents of a permutation. St000236The number of cyclical small weak excedances. St000241The number of cyclical small excedances. St000242The number of indices that are not cyclical small weak excedances. St000247The number of singleton blocks of a set partition. St000249The number of singletons (St000247) plus the number of antisingletons (St000248) of a set partition. 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. St000261The edge connectivity of a graph. St000262The vertex connectivity of a graph. St000263The Szeged index of a graph. St000265The Wiener index of a graph. St000274The number of perfect matchings of a graph. St000295The length of the border of a binary word. St000300The number of independent sets of vertices of a graph. St000301The number of facets of the stable set polytope of a graph. St000305The inverse major index of a permutation. St000310The minimal degree of a vertex of a graph. St000330The (standard) major index of a standard tableau. St000332The positive inversions of an alternating sign matrix. St000334The maz index, the major index of a permutation after replacing fixed points by zeros. St000355The number of occurrences of the pattern 21-3. St000356The number of occurrences of the pattern 13-2. St000357The number of occurrences of the pattern 12-3. St000359The number of occurrences of the pattern 23-1. St000360The number of occurrences of the pattern 32-1. St000361The second Zagreb index of a graph. St000365The number of double ascents of a permutation. St000366The number of double descents of a permutation. St000367The number of simsun double descents of a permutation. 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 $3$. St000375The number of non weak exceedences of a permutation that are mid-points of a decreasing subsequence of length $3$. St000377The dinv defect of an integer partition. St000384The maximal part of the shifted composition of an integer partition. St000389The number of runs of ones of odd length in a binary word. St000394The sum of the heights of the peaks of a Dyck path minus the number of peaks. St000421The number of Dyck paths that are weakly below a Dyck path, except for the path itself. St000423The number of occurrences of the pattern 123 or of the pattern 132 in a permutation. St000427The number of occurrences of the pattern 123 or of the pattern 231 in a permutation. St000437The number of occurrences of the pattern 312 or of the pattern 321 in a permutation. St000439The position of the first down step of a Dyck path. St000445The number of rises of length 1 of a Dyck path. St000454The largest eigenvalue of a graph if it is integral. St000459The hook length of the base cell of a partition. St000461The rix statistic of a permutation. St000462The major index minus the number of excedences of a permutation. St000466The Gutman (or modified Schultz) index of a connected graph. St000472The sum of the ascent bottoms of a permutation. St000475The number of parts equal to 1 in a partition. St000490The intertwining number of a set partition. St000494The number of inversions of distance at most 3 of a permutation. St000516The number of stretching pairs of a permutation. St000519The largest length of a factor maximising the subword complexity. St000521The number of distinct subtrees of an ordered tree. St000523The number of 2-protected nodes of a rooted tree. St000534The number of 2-rises of a permutation. St000546The number of global descents of a permutation. St000548The number of different non-empty partial sums of an integer partition. St000549The number of odd partial sums of an integer partition. St000561The number of occurrences of the pattern {{1,2,3}} in a set partition. St000565The major index of a set partition. St000566The number of ways to select a row of a Ferrers shape and two cells in this row. St000576The number of occurrences of the pattern {{1},{2}} such that 1 is a maximal and 2 a minimal element. St000590The number of occurrences of the pattern {{1},{2,3}} such that 2 is minimal, 1 is maximal, (2,3) are consecutive in a block. St000601The number of occurrences of the pattern {{1},{2,3}} such that 1,2 are minimal, (2,3) are consecutive in a block. St000603The number of occurrences of the pattern {{1},{2},{3}} such that 2,3 are minimal. St000606The number of occurrences of the pattern {{1},{2,3}} such that 1,3 are maximal, (2,3) 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. St000621The number of standard tableaux of shape equal to the given partition such that the minimal cyclic descent is even. St000648The number of 2-excedences of a permutation. St000649The number of 3-excedences of a permutation. St000650The number of 3-rises of a permutation. St000658The number of rises of length 2 of a Dyck path. St000661The number of rises of length 3 of a Dyck path. St000663The number of right floats of a permutation. St000664The number of right ropes of a permutation. St000671The maximin edge-connectivity for choosing a subgraph. St000673The number of non-fixed points of a permutation. 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. St000691The number of changes of a binary word. St000692Babson and Steingrímsson's statistic of a permutation. St000724The label of the leaf of the path following the smaller label in the increasing binary tree associated to a permutation. St000740The last entry of a permutation. St000741The Colin de Verdière graph invariant. St000752The Grundy value for the game 'Couples are forever' on an integer partition. St000761The number of ascents in an integer composition. St000768The number of peaks in an integer composition. St000769The major index of a composition regarded as a word. St000784The maximum of the length and the largest part of the integer partition. St000787The number of flips required to make a perfect matching noncrossing. St000795The mad of 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. St000807The sum of the heights of the valleys of the associated bargraph. St000811The sum of the entries in the column specified by the partition of the change of basis matrix from powersum symmetric functions to Schur symmetric functions. St000835The minimal difference in size when partitioning the integer partition into two subpartitions. St000848The balance constant multiplied with the number of linear extensions of a poset. St000866The number of admissible inversions of a permutation in the sense of Shareshian-Wachs. St000867The sum of the hook lengths in the first row of an integer partition. St000869The sum of the hook lengths of an integer partition. St000871The number of very big ascents of a permutation. St000872The number of very big descents of a permutation. St000873The aix statistic of a permutation. St000874The position of the last double rise in a Dyck path. St000877The depth of the binary word interpreted as a path. St000893The number of distinct diagonal sums of an alternating sign matrix. St000931The number of occurrences of the pattern UUU in a Dyck path. St000932The number of occurrences of the pattern UDU in a Dyck path. St000938The number of zeros of the symmetric group character corresponding to the partition. St000940The number of characters of the symmetric group whose value on the partition is zero. St000946The sum of the skew hook positions in a Dyck path. St000954Number of times the corresponding LNakayama algebra has $Ext^i(D(A),A)=0$ for $i>0$. St000956The maximal displacement of a permutation. St000957The number of Bruhat lower covers of a permutation. St000976The sum of the positions of double up-steps of a Dyck path. St000981The length of the longest zigzag subpath. St000984The number of boxes below precisely one peak. St000987The number of positive eigenvalues of the Laplacian matrix of the graph. St000989The number of final rises of a permutation. St000992The alternating sum of the parts of an integer partition. St001004The number of indices that are either left-to-right maxima or right-to-left minima. St001005The number of indices for a permutation that are either left-to-right maxima or right-to-left minima but not both. 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. St001017Number of indecomposable injective modules with projective dimension equal to the codominant dimension in the Nakayama algebra corresponding to the Dyck path. St001046The maximal number of arcs nesting a given arc of a perfect matching. St001055The Grundy value for the game of removing cells of a row in an integer partition. St001056The Grundy value for the game of deleting vertices of a graph until it has no edges. St001061The number of indices that are both descents and recoils of a permutation. St001067The number of simple modules of dominant dimension at least two in the corresponding Nakayama algebra. St001071The beta invariant of the graph. St001077The prefix exchange distance of a permutation. St001079The minimal length of a factorization of a permutation using the permutations (12)(34). St001082The number of boxed occurrences of 123 in a permutation. St001084The number of occurrences of the vincular pattern |1-23 in a permutation. St001086The number of occurrences of the consecutive pattern 132 in a permutation. St001087The number of occurrences of the vincular pattern |12-3 in a permutation. St001091The number of parts in an integer partition whose next smaller part has the same size. 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. St001112The 3-weak dynamic number of a graph. St001113Number of indecomposable projective non-injective modules with reflexive Auslander-Reiten sequences in the corresponding Nakayama algebra. St001114The number of odd descents of a permutation. St001117The game chromatic index of a graph. St001119The length of a shortest maximal path in a graph. St001120The length of a longest path in a graph. St001121The multiplicity of the irreducible representation indexed by the partition in the Kronecker square corresponding to the partition. St001124The multiplicity of the standard representation in the Kronecker square corresponding to a partition. St001126Number of simple module that are 1-regular in the corresponding Nakayama algebra. St001127The sum of the squares of the parts of a partition. St001137Number of simple modules that are 3-regular in the corresponding Nakayama algebra. St001139The number of occurrences of hills of size 2 in a Dyck path. St001153The number of blocks with even minimum in a set partition. 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. 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. St001167The number of simple modules that appear as the top of an indecomposable non-projective modules that is reflexive in the corresponding Nakayama algebra. St001171The vector space dimension of $Ext_A^1(I_o,A)$ when $I_o$ is the tilting module corresponding to the permutation $o$ in the Auslander algebra $A$ of $K[x]/(x^n)$. St001186Number of simple modules with grade at least 3 in the corresponding Nakayama algebra. St001189The number of simple modules with dominant and codominant dimension equal to zero in the Nakayama algebra corresponding to the Dyck path. St001195The global dimension of the algebra $A/AfA$ of the corresponding Nakayama algebra $A$ with minimal left faithful projective-injective module $Af$. 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 $K[x]/(x^n)$. St001214The aft of an integer partition. 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. 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. St001229The vector space dimension of the first extension group between the Jacobson radical J and J^2. St001233The number of indecomposable 2-dimensional modules with projective dimension one. St001247The number of parts of a partition that are not congruent 2 modulo 3. St001253The number of non-projective indecomposable reflexive modules in the corresponding Nakayama algebra. St001263The index of the maximal parabolic seaweed algebra associated with the composition. St001264The smallest index i such that the i-th simple module has projective dimension equal to the global dimension of the corresponding Nakayama algebra. St001265The maximal i such that the i-th simple module has projective dimension equal to the global dimension in the corresponding Nakayama algebra. St001266The largest vector space dimension of an indecomposable non-projective module that is reflexive in the corresponding Nakayama algebra. St001271The competition number of a graph. St001279The sum of the parts of an integer partition that are at least two. St001291The number of indecomposable summands of the tensor product of two copies of the dual of the Nakayama algebra associated to a Dyck path. St001295Gives the vector space dimension of the homomorphism space between J^2 and J^2. 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. St001331The size of the minimal feedback vertex set. St001335The cardinality of a minimal cycle-isolating set of a graph. St001336The minimal number of vertices in a graph whose complement is triangle-free. St001340The cardinality of a minimal non-edge isolating set of a graph. St001341The number of edges in the center of a graph. St001345The Hamming dimension of a graph. St001353The number of prime nodes in the modular decomposition of a graph. St001357The maximal degree of a regular spanning subgraph of a graph. St001362The normalized Knill dimension of a graph. St001388The number of non-attacking neighbors of a permutation. St001391The disjunction number of a graph. St001395The number of strictly unfriendly partitions of a graph. St001411The number of patterns 321 or 3412 in a permutation. St001412Number of minimal entries in the Bruhat order matrix of a permutation. St001413Half the length of the longest even length palindromic prefix of a binary word. St001414Half the length of the longest odd length palindromic prefix of a binary word. St001423The number of distinct cubes in a binary word. St001439The number of even weak deficiencies and of odd weak exceedences. St001442The number of standard Young tableaux whose major index is divisible by the size of a given integer partition. St001479The number of bridges of a graph. St001480The number of simple summands of the module J^2/J^3. 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. St001511The minimal number of transpositions needed to sort a permutation in either direction. St001513The number of nested exceedences of a permutation. St001524The degree of symmetry of a binary word. St001526The Loewy length of the Auslander-Reiten translate of the regular module as a bimodule of the Nakayama algebra corresponding to the Dyck path. St001549The number of restricted non-inversions between exceedances. St001557The number of inversions of the second entry of a permutation. St001558The number of transpositions that are smaller or equal to a permutation in Bruhat order. St001559The number of transpositions that are smaller or equal to a permutation in Bruhat order while not being inversions. 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. 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. St001582The grades of the simple modules corresponding to the points in the poset of the symmetric group under the Bruhat order. St001584The area statistic between a Dyck path and its bounce path. St001588The number of distinct odd parts smaller than the largest even part in an integer partition. St001592The maximal number of simple paths between any two different vertices of a graph. St001594The number of indecomposable projective modules in the Nakayama algebra corresponding to the Dyck path such that the UC-condition is satisfied. St001638The book thickness of a graph. St001640The number of ascent tops in the permutation such that all smaller elements appear before. St001649The length of a longest trail in a graph. 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. St001684The reduced word complexity of 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. St001697The shifted natural comajor index of a standard Young tableau. St001702The absolute value of the determinant of the adjacency matrix of a graph. St001712The number of natural descents of a standard Young tableau. St001727The number of invisible inversions of a permutation. St001730The number of times the path corresponding to a binary word crosses the base line. St001738The minimal order of a graph which is not an induced subgraph of the given graph. St001767The largest minimal number of arrows pointing to a cell in the Ferrers diagram in any assignment. St001769The reflection length of a signed permutation. St001777The number of weak descents in an integer composition. St001783The number of odd automorphisms of a graph. St001794Half the number of sets of vertices in a graph which are dominating and non-blocking. St001803The maximal overlap of the cylindrical tableau associated with a tableau. St001810The number of fixed points of a permutation smaller than its largest moved point. St001811The Castelnuovo-Mumford regularity of a permutation. St001826The maximal number of leaves on a vertex of a graph. St001827The number of two-component spanning forests of a graph. St001842The major index of a set partition. St001862The number of crossings of a signed permutation. St001867The number of alignments of type EN of a signed permutation. St001869The maximum cut size of a graph. St001871The number of triconnected components of a graph. St001906Half of the difference between the total displacement and the number of inversions and the reflection length of a permutation. St001931The weak major index of an integer composition regarded as a word. St001935The number of ascents in a parking function. 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. St001948The number of augmented double ascents of a permutation. St001949The rigidity index of a graph. St000967The value p(1) for the Coxeterpolynomial p of the corresponding LNakayama algebra. 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 $c_{n-1}$. St000998Number of indecomposable projective modules with injective dimension smaller than or equal to the dominant dimension in the Nakayama algebra corresponding to the Dyck path. St001012Number of simple modules with projective dimension at most 2 in the Nakayama algebra corresponding to the Dyck path. St001179Number of indecomposable injective modules with projective dimension at most 2 in the corresponding Nakayama algebra. St001473The absolute value of the sum of all entries of the Coxeter matrix of the corresponding LNakayama algebra. 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. St001625The Möbius invariant of a lattice. St001634The trace of the Coxeter matrix of the incidence algebra of a poset. St000489The number of cycles of a permutation of length at most 3. St000677The standardized bi-alternating inversion number of a permutation. St001080The minimal length of a factorization of a permutation using the transposition (12) and the cycle (1,. 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. St000823The number of unsplittable factors of the set partition. 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. St000990The first ascent of a permutation. St001346The number of parking functions that give the same permutation. St001820The size of the image of the pop stack sorting operator. St001878The projective dimension of the simple modules corresponding to the minimum of L in the incidence algebra of the lattice L. St000289The decimal representation of a binary word. St000391The sum of the positions of the ones in a binary word. St000493The los statistic of a set partition. St000558The number of occurrences of the pattern {{1,2}} in a set partition. St000577The number of occurrences of the pattern {{1},{2}} such that 1 is a maximal element. St000653The last descent of a permutation. St000693The modular (standard) major index of a standard tableau. St000792The Grundy value for the game of ruler on a binary word. St000794The mak of a permutation. St000796The stat' of a permutation. St000797The stat`` of a permutation. St000798The makl of a permutation. St000929The constant term of the character polynomial of an integer partition. St000934The 2-degree of an integer partition. 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. St001604The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on polygons. St001629The coefficient of the integer composition in the quasisymmetric expansion of the relabelling action of the symmetric group on cycles. St001668The number of points of the poset minus the width of the poset. St001860The number of factors of the Stanley symmetric function associated with a signed permutation. St000455The second largest eigenvalue of a graph if it is integral. St001630The global dimension of the incidence algebra of the lattice over the rational numbers. St000882The number of connected components of short braid edges in the graph of braid moves of a permutation. St001232The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2. St000285The size of the preimage of the map 'to inverse des composition' from Parking functions to Integer compositions. St001118The acyclic chromatic index of a graph. St001199The dominant dimension of $eAe$ for the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. St001250The number of parts of a partition that are not congruent 0 modulo 3. St001515The vector space dimension of the socle of the first syzygy module of the regular module (as a bimodule). St001885The number of binary words with the same proper border set. St001570The minimal number of edges to add to make a graph Hamiltonian. St001880The number of 2-Gorenstein indecomposable injective modules in the incidence algebra of the lattice. St000050The depth or height of a binary tree. St000064The number of one-box pattern of a permutation. St000134The size of the orbit of an alternating sign matrix under gyration. St000280The size of the preimage of the map 'to labelling permutation' from Parking functions to Permutations. St000290The major index of a binary word. St000382The first part of an integer composition. St000385The number of vertices with out-degree 1 in a binary tree. St000393The number of strictly increasing runs in a binary word. St000414The binary logarithm of the number of binary trees with the same underlying unordered tree. St000420The number of Dyck paths that are weakly above 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. St000487The length of the shortest cycle of a permutation. St000488The number of cycles of a permutation of length at most 2. St000510The number of invariant oriented cycles when acting with a permutation of given cycle type. St000514The number of invariant simple graphs when acting with a permutation of given cycle type. St000515The number of invariant set partitions when acting with a permutation of given cycle type. St000530The number of permutations with the same descent word as the given permutation. St000681The Grundy value of Chomp on Ferrers diagrams. St000696The number of cycles in the breakpoint graph of a permutation. St000727The largest label of a leaf in the binary search tree associated with the permutation. St000771The largest multiplicity of a distance Laplacian eigenvalue in a connected graph. St000772The multiplicity of the largest distance Laplacian eigenvalue in 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. St000824The sum of the number of descents and the number of recoils of a permutation. St000842The breadth of a permutation. St000863The length of the first row of the shifted shape of a permutation. St000870The product of the hook lengths of the diagonal cells in an integer partition. St000922The minimal number such that all substrings of this length are unique. St000923The minimal number with no two order isomorphic substrings of this length in a permutation. St000952Gives the number of irreducible factors of the Coxeter polynomial of the Dyck path over the rational numbers. St000953The largest degree of an irreducible factor of the Coxeter polynomial of the Dyck path over the rational numbers. St000993The multiplicity of the largest part of an integer partition. St001032The number of horizontal steps in the bicoloured Motzkin path associated with the Dyck path. St001042The size of the automorphism group of the leaf labelled binary unordered tree associated with the perfect matching. St001133The smallest label in the subtree rooted at the sister of 1 in the decreasing labelled binary unordered tree associated with the perfect matching. St001245The cyclic maximal difference between two consecutive entries of a permutation. St001275The projective dimension of the second term in a minimal injective coresolution of the regular module. 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. St001384The number of boxes in the diagram of a partition that do not lie in the largest triangle it contains. St001416The length of a longest palindromic factor of a binary word. St001417The length of a longest palindromic subword of a binary word. St001436The index of a given binary word in the lex-order among all its cyclic shifts. St001485The modular major index of a binary word. St001491The number of indecomposable projective-injective modules in the algebra corresponding to a subset. St001501The dominant dimension of magnitude 1 Nakayama algebras. St001516The number of cyclic bonds of a permutation. St001523The degree of symmetry of a Dyck path. St001545The second Elser number of a connected graph. St001554The number of distinct nonempty subtrees of a binary tree. St001605The number of colourings of a cycle such that the multiplicities of colours are given by a partition. St001607The number of coloured graphs such that the multiplicities of colours are given by a partition. St001608The number of coloured rooted trees 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. St001641The number of ascent tops in the flattened set partition such that all smaller elements appear before. St001660The number of ways to place as many non-attacking rooks as possible on a skew Ferrers board. St001704The size of the largest multi-subset-intersection of the deck of a graph with the deck of another graph. St001710The number of permutations such that conjugation with a permutation of given cycle type yields the inverse permutation. St001808The box weight or horizontal decoration of a Dyck path. St001925The minimal number of zeros in a row of an alternating sign matrix. St001929The number of meanders with top half given by the noncrossing matching corresponding to the Dyck path. St001958The degree of the polynomial interpolating the values of a permutation. St000219The number of occurrences of the pattern 231 in a permutation. St000782The indicator function of whether a given perfect matching is an L & P matching. St000833The comajor index of a permutation. St001060The distinguishing index of a graph. St001583The projective dimension of the simple module corresponding to the point in the poset of the symmetric group under bruhat order. 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. St000456The monochromatic index of a connected graph. St000880The number of connected components of long braid edges in the graph of braid moves of a permutation. St001600The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on simple graphs. 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. St001846The number of elements which do not have a complement in the lattice. St000736The last entry in the first row of a semistandard tableau. 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 $K[x]/(x^n)$. St001722The number of minimal chains with small intervals between a binary word and the top element. St001816Eigenvalues of the top-to-random operator acting on a simple module. St000075The orbit size of a standard tableau under promotion. St000112The sum of the entries reduced by the index of their row in a semistandard tableau. St000177The number of free tiles in the pattern. St000178Number of free entries. St001520The number of strict 3-descents. St000036The evaluation at 1 of the Kazhdan-Lusztig polynomial with parameters given by the identity and the permutation. St000079The number of alternating sign matrices for a given Dyck path. St000082The number of elements smaller than a binary tree in Tamari order. St000100The number of linear extensions of a poset. St000174The flush statistic of a semistandard tableau. St000315The number of isolated vertices of a graph. St000412The number of binary trees with the same underlying unordered tree. St000502The number of successions of a set partitions. St000570The Edelman-Greene number of a permutation. St000589The number of occurrences of the pattern {{1},{2,3}} such that 1 is maximal, (2,3) are consecutive in a block. St000680The Grundy value for Hackendot on posets. St000717The number of ordinal summands of a poset. St000729The minimal arc length of a set partition. St000770The major index of an integer partition when read from bottom to top. St000815The number of semistandard Young tableaux of partition weight of given shape. 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. St000906The length of the shortest maximal chain in a poset. St000909The number of maximal chains of maximal size in a poset. St000958The number of Bruhat factorizations of a permutation. St000964Gives the dimension of Ext^g(D(A),A) of the corresponding LNakayama algebra, when g denotes the global dimension of that algebra. St000965The sum of the dimension of Ext^i(D(A),A) for i=1,. St001006Number of simple modules with projective dimension equal to the global dimension of the Nakayama algebra corresponding to the Dyck path. St001008Number of indecomposable injective modules with projective dimension 1 in the Nakayama algebra corresponding to the Dyck path. St001013Number of indecomposable injective modules with codominant dimension equal to the global dimension in the Nakayama algebra corresponding to the Dyck path. St001097The coefficient of the monomial symmetric function indexed by the partition in the formal group law for linear orders. St001162The minimum jump of a permutation. St001191Number of simple modules $S$ with $Ext_A^i(S,A)=0$ for all $i=0,1,...,g-1$ in the corresponding Nakayama algebra $A$ with global dimension $g$. St001236The dominant dimension of the corresponding Comp-Nakayama algebra. St001238The number of simple modules S such that the Auslander-Reiten translate of S is isomorphic to the Nakayama functor applied to the second syzygy of S. St001313The number of Dyck paths above the lattice path given by a binary word. St001344The neighbouring number of a permutation. St001365The number of lattice paths of the same length weakly above the path given by a binary word. St001493The number of simple modules with maximal even projective dimension in the corresponding Nakayama algebra. St001556The number of inversions of the third entry of a permutation. 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. St000089The absolute variation of a composition. St000090The variation of a composition. St000232The number of crossings of a set partition. St000248The number of anti-singletons of a set partition. St000287The number of connected components of a graph. St000338The number of pixed points of a permutation. St000348The non-inversion sum of a binary word. St000407The number of occurrences of the pattern 2143 in a permutation. St000408The number of occurrences of the pattern 4231 in a permutation. St000422The energy of a graph, if it is integral. St000440The number of occurrences of the pattern 4132 or of the pattern 4231 in a permutation. St000450The number of edges minus the number of vertices plus 2 of a graph. St000491The number of inversions of a set partition. St000492The rob statistic of a set partition. St000497The lcb statistic of a set partition. St000498The lcs statistic of a set partition. St000560The number of occurrences of the pattern {{1,2},{3,4}} in a set partition. St000562The number of internal points of a set partition. St000588The number of occurrences of the pattern {{1},{2},{3}} such that 1,3 are 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. St000600The number of occurrences of the pattern {{1,3},{2}} such that 1 is minimal, (1,3) are consecutive in a block. St000604The number of occurrences of the pattern {{1},{2},{3}} such that 3 is minimal, 2 is maximal. St000611The number of occurrences of the pattern {{1},{2,3}} such that 1 is maximal. St000613The number of occurrences of the pattern {{1,3},{2}} such that 2 is minimal, 3 is maximal, (1,3) are consecutive in a block. St000622The number of occurrences of the patterns 2143 or 4231 in a permutation. St000682The Grundy value of Welter's game on a binary word. St000689The maximal n such that the minimal generator-cogenerator module in the LNakayama algebra of a Dyck path is n-rigid. St000739The first entry in the last row of a semistandard tableau. St000751The number of occurrences of either of the pattern 2143 or 2143 in a permutation. St001001The number of indecomposable modules with projective and injective dimension equal to the global dimension of the Nakayama algebra corresponding to the Dyck path. St001130The number of two successive successions in a permutation. St001140Number of indecomposable modules with projective and injective dimension at least two in the corresponding Nakayama algebra. St001163The number of simple modules with dominant dimension at least three in the corresponding Nakayama algebra. St001193The dimension of $Ext_A^1(A/AeA,A)$ in the corresponding Nakayama algebra $A$ such that $eA$ is a minimal faithful projective-injective module. St001219Number of simple modules S in the corresponding Nakayama algebra such that the Auslander-Reiten sequence ending at S has the property that all modules in the exact sequence are reflexive. St001377The major index minus the number of inversions of a permutation. St001435The number of missing boxes in the first row. St001438The number of missing boxes of a skew partition. St001535The number of cyclic alignments of a permutation. St001551The number of restricted non-inversions between exceedances where the rightmost exceedance is linked. St001623The number of doubly irreducible elements of a lattice. St001633The number of simple modules with projective dimension two in the incidence algebra of the poset. St001637The number of (upper) dissectors of a poset. St001667The maximal size of a pair of weak twins for a permutation. St001705The number of occurrences of the pattern 2413 in a permutation. St001745The number of occurrences of the arrow pattern 13 with an arrow from 1 to 2 in a permutation. St001822The number of alignments of a signed permutation. St001841The number of inversions of a set partition. St001856The number of edges in the reduced word graph of a permutation. St001857The number of edges in the reduced word graph of a signed permutation. St001866The nesting alignments of a signed permutation. St001868The number of alignments of type NE of a signed permutation. St001882The number of occurrences of a type-B 231 pattern in a signed permutation. St001911A descent variant minus the number of inversions. St001926Sparre Andersen's position of the maximum of a signed permutation. St001964The interval resolution global dimension of a poset. St000383The last part of an integer composition. St000839The largest opener of a set partition. St000973The length of the boundary of an ordered tree. St000975The length of the boundary minus the length of the trunk of an ordered tree. St000230Sum of the minimal elements of the blocks of a set partition. St001287The number of primes obtained by multiplying preimage and image of a permutation and subtracting one.