St000552The number of cut vertices of a graph. St000662The staircase size of the code of a permutation. St000672The number of minimal elements in Bruhat order not less than the permutation. St000829The Ulam distance of a permutation to the identity permutation. St001298The number of repeated entries in the Lehmer code of a permutation. St001692The number of vertices with higher degree than the average degree in a graph. St000062The length of the longest increasing subsequence of the permutation. St000144The pyramid weight of the Dyck path. St000203The number of external nodes of a binary tree. St000213The number of weak exceedances (also weak excedences) of a permutation. St000259The diameter of a connected graph. St000308The height of the tree associated to a permutation. St000381The largest part of an integer composition. St000443The number of long tunnels of a Dyck path. St000528The height of a poset. St000619The number of cyclic descents of a permutation. St000702The number of weak deficiencies of a permutation. St000725The smallest label of a leaf of the increasing binary tree associated to a permutation. 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. St001090The number of pop-stack-sorts needed to sort a permutation. St001120The length of a longest path in a graph. St001187The number of simple modules with grade at least one in the corresponding Nakayama algebra. St001224Let X be the direct sum of all simple modules of the corresponding Nakayama algebra. St001488The number of corners of a skew partition. St001512The minimum rank of a graph. St001526The Loewy length of the Auslander-Reiten translate of the regular module as a bimodule of the Nakayama algebra corresponding to the Dyck path. St001649The length of a longest trail in a graph. St000998Number of indecomposable projective modules with injective dimension smaller than or equal to the dominant dimension in the Nakayama algebra corresponding to the Dyck path. St001004The number of indices that are either left-to-right maxima or right-to-left minima. St001093The detour number of a graph. St001180Number of indecomposable injective modules with projective dimension at most 1. St000007The number of saliances of the permutation. St000010The length of the partition. St000013The height of a Dyck path. St000021The number of descents of a permutation. St000028The number of stack-sorts needed to sort a permutation. St000031The number of cycles in the cycle decomposition of a permutation. St000035The number of left outer peaks of a permutation. St000039The number of crossings of a permutation. St000053The number of valleys of the Dyck path. St000083The number of left oriented leafs of a binary tree except the first one. St000097The order of the largest clique of the graph. St000098The chromatic number of a graph. St000120The number of left tunnels of a Dyck path. St000141The maximum drop size of a permutation. St000147The largest part of an integer partition. St000153The number of adjacent cycles of a permutation. St000155The number of exceedances (also excedences) of a permutation. St000168The number of internal nodes of an ordered tree. St000175Degree of the polynomial counting the number of semistandard Young tableaux when stretching the shape. St000211The rank of the set partition. St000238The number of indices that are not small weak excedances. St000242The number of indices that are not cyclical small weak excedances. St000306The bounce count of a Dyck path. St000316The number of non-left-to-right-maxima 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. St000332The positive inversions of an alternating sign matrix. St000337The lec statistic, the sum of the inversion numbers of the hook factors of a permutation. St000354The number of recoils of a permutation. St000362The size of a minimal vertex cover of a graph. St000374The number of exclusive right-to-left minima of a permutation. St000392The length of the longest run of ones in a binary word. St000394The sum of the heights of the peaks of a Dyck path minus the number of peaks. St000442The maximal area to the right of an up step of a Dyck path. St000475The number of parts equal to 1 in a partition. St000628The balance of a binary word. St000648The number of 2-excedences of a permutation. St000651The maximal size of a rise in a permutation. St000670The reversal length of a permutation. St000676The number of odd rises of a Dyck path. St000691The number of changes of a binary word. St000703The number of deficiencies of a permutation. St000742The number of big ascents of a permutation after prepending zero. St000836The number of descents of distance 2 of a permutation. St000864The number of circled entries of the shifted recording tableau of a permutation. St000877The depth of the binary word interpreted as a path. St000994The number of cycle peaks and the number of cycle valleys of a permutation. St000996The number of exclusive left-to-right maxima of a permutation. St001087The number of occurrences of the vincular pattern |12-3 in a permutation. St001096The size of the overlap set of a permutation. St001142The projective dimension of the socle of the regular module as a bimodule in the Nakayama algebra corresponding to the Dyck path. St001169Number of simple modules with projective dimension at least two in the corresponding Nakayama algebra. St001176The size of a partition minus its first part. St001189The number of simple modules with dominant and codominant dimension equal to zero in the Nakayama algebra corresponding to the Dyck path. St001197The global dimension of $eAe$ for the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. 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. St001372The length of a longest cyclic run of ones of a binary word. St001405The number of bonds in a permutation. St001420Half the length of a longest factor which is its own reverse-complement of a binary word. St001480The number of simple summands of the module J^2/J^3. St001489The maximum of the number of descents and the number of inverse descents. St001506Half the projective dimension of the unique simple module with even projective dimension in a magnitude 1 Nakayama algebra. St001508The degree of the standard monomial associated to a Dyck path relative to the diagonal boundary. St001509The degree of the standard monomial associated to a Dyck path relative to the trivial lower boundary. St001682The number of distinct positions of the pattern letter 1 in occurrences of 123 in a permutation. St001712The number of natural descents of a standard Young tableau. St001760The number of prefix or suffix reversals needed to sort a permutation. St001761The maximal multiplicity of a letter in a reduced word of a permutation. St001773The number of minimal elements in Bruhat order not less than the signed permutation. St001863The number of weak excedances of a signed permutation. St001918The degree of the cyclic sieving polynomial corresponding to an integer partition. St001935The number of ascents in a parking function. St001955The number of natural descents for set-valued two row standard Young tableaux. St001960The number of descents of a permutation minus one if its first entry is not one. St000015The number of peaks of a Dyck path. St000060The greater neighbor of the maximum. St000093The cardinality of a maximal independent set of vertices of a graph. St000105The number of blocks in the set partition. St000201The number of leaf nodes in a binary tree. St000236The number of cyclical small weak excedances. St000239The number of small weak excedances. St000278The size of the preimage of the map 'to partition' from Integer compositions to Integer partitions. St000288The number of ones in a binary word. St000314The number of left-to-right-maxima of a permutation. St000325The width of the tree associated to a permutation. St000326The position of the first one in a binary word after appending a 1 at the end. St000335The difference of lower and upper interactions. St000389The number of runs of ones of odd length in a binary word. St000444The length of the maximal rise of a Dyck path. St000470The number of runs in a permutation. St000482The (zero)-forcing number of a graph. St000495The number of inversions of distance at most 2 of a permutation. St000507The number of ascents of a standard tableau. St000542The number of left-to-right-minima of a permutation. St000553The number of blocks of a graph. St000636The hull number of a graph. St000638The number of up-down runs of a permutation. St000652The maximal difference between successive positions of a permutation. St000695The number of blocks in the first part of the atomic decomposition of a set partition. St000720The size of the largest partition in the oscillating tableau corresponding to the perfect matching. St000784The maximum of the length and the largest part of the integer partition. St000786The maximal number of occurrences of a colour in a proper colouring of a graph. St000808The number of up steps of the associated bargraph. St000831The number of indices that are either descents or recoils. St000904The maximal number of repetitions of an integer composition. St000912The number of maximal antichains in a poset. St000937The number of positive values of the symmetric group character corresponding to the partition. St000956The maximal displacement of a permutation. St000982The length of the longest constant subword. St000983The length of the longest alternating subword. St001027Number of simple modules with projective dimension equal to injective 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. St001068Number of torsionless simple modules in the corresponding Nakayama algebra. St001088Number of indecomposable projective non-injective modules with dominant dimension equal to the injective dimension in the corresponding Nakayama algebra. St001119The length of a shortest maximal path in a graph. St001203We associate to a CNakayama algebra (a Nakayama algebra with a cyclic quiver) with Kupisch series $L=[c_0,c_1,...,c_{n-1}]$ such that $n=c_0 < c_i$ for all $i > 0$ a Dyck path as follows: St001245The cyclic maximal difference between two consecutive entries of a permutation. St001246The maximal difference between two consecutive entries of a permutation. St001286The annihilation number of a graph. St001315The dissociation number of a graph. St001337The upper domination number of a graph. St001338The upper irredundance number of a graph. St001343The dimension of the reduced incidence algebra of a poset. 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. St001424The number of distinct squares in a binary word. St001439The number of even weak deficiencies and of odd weak exceedences. St001461The number of topologically connected components of the chord diagram of a permutation. St001462The number of factors of a standard tableaux under concatenation. St001497The position of the largest weak excedence of a permutation. St001514The dimension of the top of the Auslander-Reiten translate of the regular modules as a bimodule. St001566The length of the longest arithmetic progression in a permutation. St001581The achromatic number of a graph. St001654The monophonic hull number of a graph. St001655The general position number of a graph. St001656The monophonic position number of a graph. St001668The number of points of the poset minus the width of the poset. St000250The number of blocks (St000105) plus the number of antisingletons (St000248) of a set partition. St000488The number of cycles of a permutation of length at most 2. St000489The number of cycles of a permutation of length at most 3. St000863The length of the first row of the shifted shape of a permutation. St000876The number of factors in the Catalan decomposition of a binary word. St001005The number of indices for a permutation that are either left-to-right maxima or right-to-left minima but not both. St001012Number of simple modules with projective dimension at most 2 in the Nakayama algebra corresponding to the Dyck path. St001028Number of simple modules with injective dimension equal to the dominant dimension in the Nakayama algebra corresponding to the Dyck path. St001179Number of indecomposable injective modules with projective dimension at most 2 in the corresponding Nakayama algebra. 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. St001240The number of indecomposable modules e_i J^2 that have injective dimension at most one in 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. St001505The number of elements generated by the Dyck path as a map in the full transformation monoid. 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. St001784The minimum of the smallest closer and the second element of the block containing 1 in a set partition. St000637The length of the longest cycle in a graph. St001040The depth of the decreasing labelled binary unordered tree associated with the perfect matching. St001237The number of simple modules with injective dimension at most one or dominant dimension at least one. St001078The minimal number of occurrences of (12) in a factorization of a permutation into transpositions (12) and cycles (1,. St000058The order of a permutation. St001464The number of bases of the positroid corresponding to the permutation, with all fixed points counterclockwise. St001499The number of indecomposable projective-injective modules of a magnitude 1 Nakayama algebra. St000290The major index of a binary word. St000538The number of even inversions of a permutation. St000646The number of big ascents of a permutation. St000710The number of big deficiencies of a permutation. St000837The number of ascents of distance 2 of a permutation. St001388The number of non-attacking neighbors of a permutation. St001485The modular major index of a binary word. St001579The number of cyclically simple transpositions decreasing the number of cyclic descents needed to sort a permutation. St000054The first entry of the permutation. St000056The decomposition (or block) number of a permutation. St000068The number of minimal elements in a poset. St000172The Grundy number of a graph. St000208Number of integral Gelfand-Tsetlin polytopes with prescribed top row and integer partition weight. St000299The number of nonisomorphic vertex-induced subtrees. St000453The number of distinct Laplacian eigenvalues of a graph. St000525The number of posets with the same zeta polynomial. 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. St000626The minimal period of a binary word. St000654The first descent of a permutation. St000822The Hadwiger number of the graph. St000845The maximal number of elements covered by an element in a poset. St000846The maximal number of elements covering an element of a poset. St000886The number of permutations with the same antidiagonal sums. St000988The orbit size of a permutation under Foata's bijection. 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. St001052The length of the exterior of a permutation. St001105The number of greedy linear extensions of a poset. St001106The number of supergreedy linear extensions of a poset. St001116The game chromatic number of a graph. St001199The dominant dimension of $eAe$ for the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. St001235The global dimension of the corresponding Comp-Nakayama algebra. St001267The length of the Lyndon factorization of the binary word. St001285The number of primes in the column sums of the two line notation of a permutation. 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. St001437The flex of a binary word. St001494The Alon-Tarsi number of a graph. St001555The order of a signed permutation. St001580The acyclic chromatic number of a graph. St001670The connected partition number of a graph. St001674The number of vertices of the largest induced star graph in the graph. St001883The mutual visibility number of a graph. St001884The number of borders of a binary word. St001963The tree-depth of a graph. St000154The sum of the descent bottoms of a permutation. St000234The number of global ascents of a permutation. St000249The number of singletons (St000247) plus the number of antisingletons (St000248) of a set partition. St000272The treewidth of a graph. St000293The number of inversions of a binary word. St000295The length of the border of a binary word. St000305The inverse major index 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. St000437The number of occurrences of the pattern 312 or of the pattern 321 in a permutation. St000462The major index minus the number of excedences of a permutation. St000536The pathwidth of a graph. St000537The cutwidth of a graph. St000632The jump number of the poset. St000668The least common multiple of the parts of the partition. St000708The product of the parts of an integer partition. St000711The number of big exceedences of a permutation. St000724The label of the leaf of the path following the smaller label in the increasing binary tree associated to a permutation. St000848The balance constant multiplied with the number of linear extensions of a poset. St000893The number of distinct diagonal sums of an alternating sign matrix. 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. St001035The convexity degree of the parallelogram polyomino associated with the Dyck path. St001082The number of boxed occurrences of 123 in a permutation. St001270The bandwidth of a graph. St001277The degeneracy of a graph. St001358The largest degree of a regular subgraph of a graph. St001427The number of descents of a signed permutation. St001436The index of a given binary word in the lex-order among all its cyclic shifts. St001502The global dimension minus the dominant dimension of magnitude 1 Nakayama algebras. St001553The number of indecomposable summands of the square of the Jacobson radical as a bimodule in the Nakayama algebra corresponding to the Dyck path. St001557The number of inversions of the second entry of a permutation. St001726The number of visible inversions of a permutation. St001743The discrepancy of a graph. St001769The reflection length of a signed permutation. St001792The arboricity of a graph. St001811The Castelnuovo-Mumford regularity of a permutation. St001812The biclique partition number of a graph. St001823The Stasinski-Voll length of a signed permutation. St001864The number of excedances of a signed permutation. St001896The number of right descents of a signed permutations. St001907The number of Bastidas - Hohlweg - Saliola excedances of a signed permutation. St001948The number of augmented double ascents of a permutation. St001962The proper pathwidth of a graph. St000806The semiperimeter of the associated bargraph. St000386The number of factors DDU in a Dyck path. St001720The minimal length of a chain of small intervals in a lattice. St000485The length of the longest cycle of a permutation. St000216The absolute length of a permutation. St000539The number of odd inversions of a permutation. St000809The reduced reflection length of the permutation. St001076The minimal length of a factorization of a permutation into transpositions that are cyclic shifts of (12). St001080The minimal length of a factorization of a permutation using the transposition (12) and the cycle (1,. St000061The number of nodes on the left branch of a binary tree. St000933The number of multipartitions of sizes given by an integer partition. St001062The maximal size of a block of a set partition. St000297The number of leading ones in a binary word. St000730The maximal arc length of a set partition. St000753The Grundy value for the game of Kayles on a binary word. St000796The stat' of a permutation. St000797The stat`` of a permutation. St000798The makl of a permutation. St001061The number of indices that are both descents and recoils of a permutation. 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. 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. St001431Half of the Loewy length minus one of a modified stable Auslander algebra of the Nakayama algebra corresponding to the Dyck path. St001592The maximal number of simple paths between any two different vertices of a graph. St001860The number of factors of the Stanley symmetric function associated with a signed permutation. St000686The finitistic dominant dimension of a 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. St001037The number of inner corners of the upper path of the parallelogram polyomino associated with the Dyck path. St001165Number of simple modules with even projective dimension in the corresponding Nakayama algebra. St001184Number of indecomposable injective modules with grade at least 1 in the corresponding Nakayama algebra. St001471The magnitude of a Dyck path. St001530The depth of a Dyck path. St000454The largest eigenvalue of a graph if it is integral. St001632The number of indecomposable injective modules $I$ with $dim Ext^1(I,A)=1$ for the incidence algebra A of a poset. St000640The rank of the largest boolean interval in a poset. St000741The Colin de Verdière graph invariant. St000939The number of characters of the symmetric group whose value on the partition is positive. St001394The genus of a permutation. St000777The number of distinct eigenvalues of the distance Laplacian of a connected graph. St000675The number of centered multitunnels of a Dyck path. St000678The number of up steps after the last double rise of a Dyck path. St000888The maximal sum of entries on a diagonal of an alternating sign matrix. St000892The maximal number of nonzero entries on a diagonal of an alternating sign matrix. St000925The number of topologically connected components of a set partition. St001060The distinguishing index of a graph. St000568The hook number of a binary tree. St000993The multiplicity of the largest part of an integer partition. 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 $eA$. St001637The number of (upper) dissectors of a poset. St001626The number of maximal proper sublattices of a lattice. St000973The length of the boundary of an ordered tree. St000975The length of the boundary minus the length of the trunk of an ordered tree. St000352The Elizalde-Pak rank of a permutation. St000659The number of rises of length at least 2 of a Dyck path. St000771The largest multiplicity of a distance Laplacian eigenvalue in a connected graph. St000834The number of right outer peaks of a permutation. St000919The number of maximal left branches of a binary tree. 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 $eA$. St001498The normalised height of a Nakayama algebra with magnitude 1. St000455The second largest eigenvalue of a graph if it is integral. St000522The number of 1-protected nodes of a rooted tree. St001733The number of weak left to right maxima of a Dyck path. St001877Number of indecomposable injective modules with projective dimension 2. St000521The number of distinct subtrees of an ordered tree. St000260The radius of a connected graph. St000439The position of the first down step of a Dyck path. 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. St000684The global dimension of the LNakayama algebra associated to a Dyck path. St000930The k-Gorenstein degree of the corresponding Nakayama algebra with linear quiver. 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 $c_{n-1}$. St001024Maximum of dominant dimensions of the simple modules in the Nakayama algebra corresponding to the Dyck path. St001118The acyclic chromatic index of a graph. 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. St001207The Lowey length of the algebra $A/T$ when $T$ is the 1-tilting module corresponding to the permutation in the Auslander algebra of $K[x]/(x^n)$. St001290The first natural number n such that the tensor product of n copies of D(A) is zero for the corresponding Nakayama algebra A. St001291The number of indecomposable summands of the tensor product of two copies of the dual of the Nakayama algebra associated to a Dyck path. St001570The minimal number of edges to add to make a graph Hamiltonian. St001814The number of partitions interlacing the given partition. St000492The rob statistic of a set partition. St000519The largest length of a factor maximising the subword complexity. St000839The largest opener of a set partition. St000922The minimal number such that all substrings of this length are unique. St000022The number of fixed points of a permutation. St000647The number of big descents of a permutation. St000884The number of isolated descents of a permutation. St001232The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2. St000251The number of nonsingleton blocks of a set partition. St000253The crossing number of a set partition. St000356The number of occurrences of the pattern 13-2. St000373The number of weak exceedences of a permutation that are also mid-points of a decreasing subsequence of length $3$. St001115The number of even descents of a permutation. St001568The smallest positive integer that does not appear twice in the partition. St001893The flag descent of a signed permutation. St000718The largest Laplacian eigenvalue of a graph if it is integral. St000456The monochromatic index of a connected graph. St000609The number of occurrences of the pattern {{1},{2,3}} such that 1,2 are minimal. St001083The number of boxed occurrences of 132 in a permutation. St001086The number of occurrences of the consecutive pattern 132 in a permutation. St001693The excess length of a longest path consisting of elements and blocks of a set partition. St000493The los statistic of a set partition. St000891The number of distinct diagonal sums of a permutation matrix. St001050The number of terminal closers of a set partition. St001075The minimal size of a block of a set partition. St001623The number of doubly irreducible elements of a lattice. St000451The length of the longest pattern of the form k 1 2. St001636The number of indecomposable injective modules with projective dimension at most one in the incidence algebra of the poset. St001645The pebbling number of a connected graph. St000075The orbit size of a standard tableau under promotion. St000023The number of inner peaks of a permutation. St000779The tier of a permutation. St001469The holeyness of a permutation. St001520The number of strict 3-descents. St000099The number of valleys of a permutation, including the boundary. St001517The length of a longest pair of twins in a permutation. St000735The last entry on the main diagonal of a standard tableau. St000162The number of nontrivial cycles in the cycle decomposition of a permutation. St000196The number of occurrences of the contiguous pattern [[.,.],[.,. St000221The number of strong fixed points of a permutation. St000254The nesting number of a set partition. St000353The number of inner valleys of a permutation. St000360The number of occurrences of the pattern 32-1. St000387The matching number of a graph. St000624The normalized sum of the minimal distances to a greater element. St000985The number of positive eigenvalues of the adjacency matrix of the graph. St001114The number of odd descents of a permutation. 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. 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. St001354The number of series nodes in the modular decomposition of a graph. St001470The cyclic holeyness of a permutation. St001556The number of inversions of the third entry of a permutation. St001582The grades of the simple modules corresponding to the points in the poset of the symmetric group under the Bruhat order. St001583The projective dimension of the simple module corresponding to the point in the poset of the symmetric group under bruhat order. St001665The number of pure excedances of a permutation. St001685The number of distinct positions of the pattern letter 1 in occurrences of 132 in a permutation. St001689The number of celebrities in a graph. St001728The number of invisible descents of a permutation. St001729The number of visible descents of a permutation. St001737The number of descents of type 2 in a permutation. St001781The interlacing number of a set partition. St001801Half the number of preimage-image pairs of different parity in a permutation. St001810The number of fixed points of a permutation smaller than its largest moved point. St001822The number of alignments of a signed permutation. St001839The number of excedances of a set partition. St001840The number of descents of a set partition. St001862The number of crossings of a signed permutation. St001928The number of non-overlapping descents in a permutation. St001946The number of descents in a parking function. St000092The number of outer peaks of a permutation. St000163The size of the orbit of the set partition under rotation. St000166The depth minus 1 of an ordered tree. St000209Maximum difference of elements in cycles. St001273The projective dimension of the first term in an injective coresolution of the regular module. St001296The maximal torsionfree index of an indecomposable non-projective module in the corresponding Nakayama algebra. St001421Half the length of a longest factor which is its own reverse-complement and begins with a one of a binary word. St001466The number of transpositions swapping cyclically adjacent numbers in a permutation. St001642The Prague dimension of a graph. St001667The maximal size of a pair of weak twins for a permutation. St001686The order of promotion on a Gelfand-Tsetlin pattern. St001716The 1-improper chromatic number of a graph. St001741The largest integer such that all patterns of this size are contained in the permutation. St001778The largest greatest common divisor of an element and its image in a permutation. St000094The depth of an ordered tree. St000844The size of the largest block in the direct sum decomposition of a permutation. St000923The minimal number with no two order isomorphic substrings of this length in a permutation. 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. St001515The vector space dimension of the socle of the first syzygy module of the regular module (as a bimodule). St001704The size of the largest multi-subset-intersection of the deck of a graph with the deck of another graph. St000230Sum of the minimal elements of the blocks of a set partition. St000515The number of invariant set partitions when acting with a permutation of given cycle type. St001621The number of atoms of a lattice. St000550The number of modular elements of a lattice. St000551The number of left modular elements of a lattice. St000014The number of parking functions supported by a Dyck path. St000243The number of cyclic valleys and cyclic peaks of a permutation. St000393The number of strictly increasing runs in a binary word. St000395The sum of the heights of the peaks of a Dyck path. St000418The number of Dyck paths that are weakly below a Dyck path. St000420The number of Dyck paths that are weakly above a Dyck path. St000514The number of invariant simple graphs when acting with a permutation of given cycle type. St000529The number of permutations whose descent word is the given binary word. St000543The size of the conjugacy class of a binary word. St000630The length of the shortest palindromic decomposition of a binary word. St000674The number of hills of a Dyck path. St000685The dominant dimension of the LNakayama algebra associated to a Dyck path. St000707The product of the factorials of the parts. St000714The number of semistandard Young tableau of given shape, with entries at most 2. 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. St000887The maximal number of nonzero entries on a diagonal of a permutation matrix. 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. St000968We make a CNakayama algebra out of the LNakayama algebra (corresponding to the Dyck path) $[c_0,c_1,...,c_{n−1}]$ by adding $c_0$ to $c_{n−1}$. St001018Sum of projective dimension of the indecomposable injective modules of the Nakayama algebra corresponding to the Dyck path. St001020Sum of the codominant dimensions of the non-projective indecomposable injective modules of the Nakayama algebra corresponding to the Dyck path. St001023Number of simple modules with projective dimension at most 3 in the Nakayama algebra corresponding to the Dyck path. St001032The number of horizontal steps in the bicoloured Motzkin path associated with the Dyck path. St001038The minimal height of a column in the parallelogram polyomino associated with the Dyck path. St001065Number of indecomposable reflexive modules in the corresponding Nakayama algebra. St001135The projective dimension of the first simple module in the Nakayama algebra corresponding to the Dyck path. 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. 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. St001190Number of simple modules with projective dimension at most 4 in the corresponding Nakayama algebra. St001201The grade of the simple module $S_0$ in the special CNakayama algebra corresponding to the Dyck path. St001211The number of simple modules in the corresponding Nakayama algebra that have vanishing second Ext-group with the regular module. St001239The largest vector space dimension of the double dual of a simple module in the corresponding Nakayama algebra. St001257The dominant dimension of the double dual of A/J when A is the corresponding Nakayama algebra with Jacobson radical J. St001275The projective dimension of the second term in a minimal injective coresolution of the regular module. St001299The product of all non-zero projective dimensions of simple modules of the corresponding Nakayama 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. St001500The global dimension of magnitude 1 Nakayama algebras. St001501The dominant dimension of magnitude 1 Nakayama algebras. St001504The sum of all indegrees of vertices with indegree at least two in the resolution quiver of a Nakayama algebra corresponding to the Dyck path. St001523The degree of symmetry of a Dyck path. St001531Number of partial orders contained in the poset determined by the Dyck path. St001545The second Elser number of a connected graph. St001605The number of colourings of a cycle such that the multiplicities of colours are given by a partition. St001650The order of Ringel's homological bijection associated to the linear Nakayama algebra corresponding to the Dyck path. St001658The total number of rook placements on a Ferrers board. 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. St001959The product of the heights of the peaks of a Dyck path. St000486The number of cycles of length at least 3 of a permutation. St000649The number of 3-excedences of a permutation. St000824The sum of the number of descents and the number of recoils of a permutation. St001174The Gorenstein dimension of the algebra $A/I$ when $I$ is the tilting module corresponding to the permutation in the Auslander algebra of $K[x]/(x^n)$. St001516The number of cyclic bonds of a permutation. St001681The number of inclusion-wise minimal subsets of a lattice, whose meet is the bottom element. St001875The number of simple modules with projective dimension at most 1. St000849The number of 1/3-balanced pairs in a poset. St001633The number of simple modules with projective dimension two in the incidence algebra of the poset. St000910The number of maximal chains of minimal length in a poset. St001510The number of self-evacuating linear extensions of a finite poset. St000906The length of the shortest maximal chain in a poset. St000643The size of the largest orbit of antichains under Panyushev complementation. St001782The order of rowmotion on the set of order ideals of a poset. St000460The hook length of the last cell along the main diagonal of an integer partition. St000870The product of the hook lengths of the diagonal cells in an integer partition. 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. St001491The number of indecomposable projective-injective modules in the algebra corresponding to a subset. 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. St001638The book thickness of a graph. St001914The size of the orbit of an integer partition in Bulgarian solitaire. St000307The number of rowmotion orbits of a poset. St001644The dimension of a graph. St000782The indicator function of whether a given perfect matching is an L & P matching. St001630The global dimension of the incidence algebra of the lattice over the rational numbers. St001876The number of 2-regular simple modules in the incidence algebra of the lattice. St000264The girth of a graph, which is not a tree. St000477The weight of a partition according to Alladi. St000510The number of invariant oriented cycles when acting with a permutation of given cycle type. St000681The Grundy value of Chomp on Ferrers diagrams. St000706The product of the factorials of the multiplicities of an integer partition. St000997The even-odd crank of an integer partition. St001880The number of 2-Gorenstein indecomposable injective modules in the incidence algebra of the lattice. St000422The energy of a graph, if it is integral. St000101The cocharge of a semistandard tableau. St001856The number of edges in the reduced word graph of a permutation. St001878The projective dimension of the simple modules corresponding to the minimum of L in the incidence algebra of the lattice L. St000739The first entry in the last row of a semistandard tableau. St001401The number of distinct entries in a semistandard tableau. St001569The maximal modular displacement of a permutation. St001926Sparre Andersen's position of the maximum of a signed permutation. St000002The number of occurrences of the pattern 123 in a permutation. St000095The number of triangles of a graph. St000102The charge of a semistandard tableau. St000357The number of occurrences of the pattern 12-3. St000372The number of mid points of increasing subsequences of length 3 in a permutation. St000603The number of occurrences of the pattern {{1},{2},{3}} such that 2,3 are minimal. St000804The number of occurrences of the vincular pattern |123 in a permutation. St000813The number of zero-one matrices with weakly decreasing column sums and row sums given by the partition. St000879The number of long braid edges in the graph of braid moves of a permutation. St000881The number of short braid edges in the graph of braid moves of a permutation. St001084The number of occurrences of the vincular pattern |1-23 in a permutation. 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 $K[x]/(x^n)$. St001314The number of tilting modules of arbitrary projective dimension that have no simple modules as a direct summand in the corresponding Nakayama algebra. St001435The number of missing boxes in the first row. St001438The number of missing boxes of a skew partition. St001572The minimal number of edges to remove to make a graph bipartite. St001573The minimal number of edges to remove to make a graph triangle-free. St001575The minimal number of edges to add or remove to make a graph edge transitive. St001577The minimal number of edges to add or remove to make a graph a cograph. St001578The minimal number of edges to add or remove to make a graph a line graph. St001603The number of colourings of a polygon such that the multiplicities of a colour are given by a partition. St001684The reduced word complexity of a permutation. St001745The number of occurrences of the arrow pattern 13 with an arrow from 1 to 2 in a permutation. St001857The number of edges in the reduced word graph of a signed permutation. St001882The number of occurrences of a type-B 231 pattern in a signed permutation. St001964The interval resolution global dimension of a poset. St000116The major index of a semistandard tableau obtained by standardizing. St000133The "bounce" of a permutation. St000173The segment statistic of a semistandard tableau. St000174The flush statistic of a semistandard tableau. St000199The column of the unique '1' in the last row of the alternating sign matrix. St000338The number of pixed points of a permutation. St000358The number of occurrences of the pattern 31-2. St000371The number of mid points of decreasing subsequences of length 3 in a permutation. St000375The number of non weak exceedences of a permutation that are mid-points of a decreasing subsequence of length $3$. St000612The number of occurrences of the pattern {{1},{2,3}} such that 1 is minimal, (2,3) are consecutive in a block. St000736The last entry in the first row of a semistandard tableau. St000880The number of connected components of long braid edges in the graph of braid moves of a permutation. St000942The number of critical left to right maxima of the parking functions. St000958The number of Bruhat factorizations of a permutation. St000989The number of final rises of a permutation. St001225The vector space dimension of the first extension group between J and itself when J is the Jacobson radical of the corresponding Nakayama algebra. St001278The number of indecomposable modules that are fixed by $\tau \Omega^1$ composed with its inverse in the corresponding Nakayama algebra. St001487The number of inner corners of a skew partition. St001591The number of graphs with the given composition of multiplicities of Laplacian eigenvalues. St001596The number of two-by-two squares inside a skew partition. St001640The number of ascent tops in the permutation such that all smaller elements appear before. St001742The difference of the maximal and the minimal degree in a graph. St001744The number of occurrences of the arrow pattern 1-2 with an arrow from 1 to 2 in a permutation. St001768The number of reduced words of a signed permutation. St001904The length of the initial strictly increasing segment of a parking function. St001905The number of preferred parking spots in a parking function less than the index of the car. St000004The major index of a permutation. St000210Minimum over maximum difference of elements in cycles. St000334The maz index, the major index of a permutation after replacing fixed points by zeros. St000339The maf index of a permutation. St000461The rix statistic of a permutation. St000499The rcb statistic of a set partition. St000504The cardinality of the first block of a set partition. St000558The number of occurrences of the pattern {{1,2}} in a set partition. St000605The number of occurrences of the pattern {{1},{2,3}} such that 3 is maximal, (2,3) are consecutive in a block. St000653The last descent of a permutation. St000794The mak of a permutation. St000823The number of unsplittable factors of the set partition. St000833The comajor index of a permutation. St000873The aix statistic of a permutation. St000961The shifted major index of a permutation. St000963The 2-shifted major index of a permutation. St001117The game chromatic index of a graph. St001220The width of a permutation. St001722The number of minimal chains with small intervals between a binary word and the top element. St001738The minimal order of a graph which is not an induced subgraph of the given graph. St001861The number of Bruhat lower covers of a permutation. St001874Lusztig's a-function for the symmetric group. St000135The number of lucky cars of the parking function. St000744The length of the path to the largest entry in a standard Young tableau. St001002Number of indecomposable modules with projective and injective dimension at most 1 in the Nakayama algebra corresponding to the Dyck path. St001417The length of a longest palindromic subword of a binary word. St001927Sparre Andersen's number of positives of a signed permutation. St000044The number of vertices of the unicellular map given by a perfect matching.