St001273The projective dimension of the first term in an injective coresolution of the regular module. St001355Number of non-empty prefixes of a binary word that contain equally many 0's and 1's. St001491The number of indecomposable projective-injective modules in the algebra corresponding to a subset. St000678The number of up steps after the last double rise of a Dyck path. St001024Maximum of dominant dimensions of the simple modules in the Nakayama algebra corresponding to the Dyck path. St001135The projective dimension of the first simple module in the Nakayama algebra corresponding to the Dyck path. St001201The grade of the simple module $S_0$ in the special CNakayama algebra corresponding to the Dyck path. St001733The number of weak left to right maxima of a Dyck path. 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 $c_{n-1}$. St000124The cardinality of the preimage of the Simion-Schmidt map. St000153The number of adjacent cycles of a permutation. St000288The number of ones in a binary word. St000295The length of the border of a binary word. St000296The length of the symmetric border of a binary word. St000389The number of runs of ones of odd length in a binary word. St000390The number of runs of ones in a binary word. St000445The number of rises of length 1 of a Dyck path. St000546The number of global descents of a permutation. St000644The number of graphs with given frequency partition. St000658The number of rises of length 2 of a Dyck path. St000683The number of points below the Dyck path such that the diagonal to the north-east hits the path between two down steps, and the diagonal to the north-west hits the path between two up steps. St000689The maximal n such that the minimal generator-cogenerator module in the LNakayama algebra of a Dyck path is n-rigid. 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. St000877The depth of the binary word interpreted as a path. St000884The number of isolated descents of a permutation. St000954Number of times the corresponding LNakayama algebra has $Ext^i(D(A),A)=0$ for $i>0$. St000989The number of final rises of a permutation. St001010Number of indecomposable injective modules with projective dimension g-1 when g is the global dimension of the Nakayama algebra corresponding to the Dyck path. St001027Number of simple modules with projective dimension equal to injective dimension in the Nakayama algebra corresponding to the Dyck path. St001172The number of 1-rises at odd height of a Dyck path. St001185The number of indecomposable injective modules of grade at least 2 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. St001233The number of indecomposable 2-dimensional modules with projective dimension one. St001265The maximal i such that the i-th simple module has projective dimension equal to the global dimension in the corresponding Nakayama algebra. St001285The number of primes in the column sums of the two line notation of a permutation. St001371The length of the longest Yamanouchi prefix of a binary word. St001372The length of a longest cyclic run of ones of a binary word. St001413Half the length of the longest even length palindromic prefix of a binary word. St001510The number of self-evacuating linear extensions of a finite poset. St001524The degree of symmetry of a binary word. St001594The number of indecomposable projective modules in the Nakayama algebra corresponding to the Dyck path such that the UC-condition is satisfied. St001640The number of ascent tops in the permutation such that all smaller elements appear before. St001744The number of occurrences of the arrow pattern 1-2 with an arrow from 1 to 2 in a permutation. St001777The number of weak descents in an integer composition. St001948The number of augmented double ascents of a permutation. St001955The number of natural descents for set-valued two row standard Young tableaux. St001956The comajor index for set-valued two-row standard Young tableaux. St000011The number of touch points (or returns) of a Dyck path. St000025The number of initial rises of a Dyck path. St000026The position of the first return of a Dyck path. St000090The variation of a composition. St000146The Andrews-Garvan crank of a partition. St000326The position of the first one in a binary word after appending a 1 at the end. St000335The difference of lower and upper interactions. St000338The number of pixed points of a permutation. St000461The rix statistic of a permutation. St000501The size of the first part in the decomposition of a permutation. St000617The number of global maxima of a Dyck path. St000654The first descent of a permutation. St000655The length of the minimal rise of a Dyck path. St000669The number of permutations obtained by switching ascents or descents of size 2. St000675The number of centered multitunnels of a Dyck path. 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. St000765The number of weak records in an integer composition. St000873The aix statistic of a permutation. St000930The k-Gorenstein degree of the corresponding Nakayama algebra with linear quiver. St000952Gives the number of irreducible factors of the Coxeter polynomial of the Dyck path over the rational numbers. St000990The first ascent of a permutation. St000999Number of indecomposable projective module with injective 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. St001014Number of indecomposable injective modules with codominant dimension equal to the dominant dimension of the Nakayama algebra corresponding to the Dyck path. St001015Number of indecomposable injective modules with codominant dimension equal to one in the Nakayama algebra corresponding to the Dyck path. St001016Number of indecomposable injective modules with codominant dimension at most 1 in the Nakayama algebra corresponding to the Dyck path. St001017Number of indecomposable injective modules with projective dimension equal to the codominant dimension in the Nakayama algebra corresponding to the Dyck path. St001050The number of terminal closers of a set partition. St001088Number of indecomposable projective non-injective modules with dominant dimension equal to the injective dimension in the corresponding Nakayama algebra. St001126Number of simple module that are 1-regular in the corresponding Nakayama algebra. St001184Number of indecomposable injective modules with grade at least 1 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. 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. 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. St001419The length of the longest palindromic factor beginning with a one of a binary word. St001481The minimal height of a peak of a Dyck path. St001516The number of cyclic bonds of a permutation. St001806The upper middle entry of a permutation. St001807The lower middle entry of a permutation. St001910The height of the middle non-run of a Dyck path. St000054The first entry of the permutation. St000439The position of the first down step of a Dyck path. St001226The number of integers i such that the radical of the i-th indecomposable projective module has vanishing first extension group with the Jacobson radical J in the corresponding Nakayama algebra. St001290The first natural number n such that the tensor product of n copies of D(A) is zero for the corresponding Nakayama algebra A. St000006The dinv of a Dyck path. St000022The number of fixed points of a permutation. St000023The number of inner peaks of a permutation. St000028The number of stack-sorts needed to sort a permutation. St000035The number of left outer peaks of a permutation. St000051The size of the left subtree of a binary tree. St000053The number of valleys of the Dyck path. St000088The row sums of the character table of the symmetric group. St000091The descent variation of a composition. St000120The number of left tunnels of a Dyck path. St000133The "bounce" of a permutation. St000142The number of even parts of a partition. St000143The largest repeated part of a partition. St000150The floored half-sum of the multiplicities of a partition. St000155The number of exceedances (also excedences) of a permutation. St000162The number of nontrivial cycles in the cycle decomposition of a permutation. St000210Minimum over maximum difference of elements in cycles. St000212The number of standard Young tableaux for an integer partition such that no two consecutive entries appear in the same row. St000214The number of adjacencies of a permutation. St000215The number of adjacencies of a permutation, zero appended. St000219The number of occurrences of the pattern 231 in a permutation. St000221The number of strong fixed points of a permutation. St000234The number of global ascents of a permutation. St000237The number of small exceedances. St000239The number of small weak excedances. St000241The number of cyclical small excedances. St000245The number of ascents of a permutation. St000247The number of singleton blocks of a set partition. St000261The edge connectivity of a graph. St000262The vertex connectivity of a graph. St000268The number of strongly connected orientations of a graph. St000271The chromatic index of a graph. St000274The number of perfect matchings of a graph. St000276The size of the preimage of the map 'to graph' from Ordered trees to Graphs. St000282The size of the preimage of the map 'to poset' from Ordered trees to Posets. St000283The size of the preimage of the map 'to graph' from Binary trees to Graphs. St000290The major index of a binary word. St000291The number of descents of a binary word. St000297The number of leading ones in a binary word. St000306The bounce count of a Dyck path. St000310The minimal degree of a vertex of a graph. St000317The cycle descent number of a permutation. 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. St000340The number of non-final maximal constant sub-paths of length greater than one. St000352The Elizalde-Pak rank of a permutation. St000355The number of occurrences of the pattern 21-3. St000359The number of occurrences of the pattern 23-1. St000374The number of exclusive right-to-left minima of a permutation. St000376The bounce deficit of a Dyck path. St000377The dinv defect of an integer partition. St000392The length of the longest run of ones in a binary word. St000414The binary logarithm of the number of binary trees with the same underlying unordered tree. St000419The number of Dyck paths that are weakly above the Dyck path, except for the path itself. St000441The number of successions of a permutation. St000450The number of edges minus the number of vertices plus 2 of a graph. St000462The major index minus the number of excedences of a permutation. St000473The number of parts of a partition that are strictly bigger than the number of ones. St000475The number of parts equal to 1 in a partition. St000483The number of times a permutation switches from increasing to decreasing or decreasing to increasing. St000489The number of cycles of a permutation of length at most 3. St000502The number of successions of a set partitions. St000534The number of 2-rises of a permutation. St000541The number of indices greater than or equal to 2 of a permutation such that all smaller indices appear to its right. St000549The number of odd partial sums of an integer partition. St000594The number of occurrences of the pattern {{1,3},{2}} such that 1,2 are minimal, (1,3) 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. 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. St000624The normalized sum of the minimal distances to a greater element. St000645The sum of the areas of the rectangles formed by two consecutive peaks and the valley in between. St000648The number of 2-excedences 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. St000661The number of rises of length 3 of a Dyck path. St000663The number of right floats of a permutation. St000665The number of rafts of a permutation. St000670The reversal length of a permutation. St000672The number of minimal elements in Bruhat order not less than the permutation. St000674The number of hills of a Dyck path. St000677The standardized bi-alternating inversion number of a permutation. St000682The Grundy value of Welter's game on a binary word. St000691The number of changes of a binary word. St000698The number of 2-rim hooks removed from an integer partition to obtain its associated 2-core. St000703The number of deficiencies of a permutation. St000714The number of semistandard Young tableau of given shape, with entries at most 2. 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. St000766The number of inversions of an integer composition. St000769The major index of a composition regarded as a word. St000779The tier of a permutation. St000791The number of pairs of left tunnels, one strictly containing the other, of a Dyck path. St000800The number of occurrences of the vincular pattern |231 in a permutation. St000801The number of occurrences of the vincular pattern |312 in a permutation. St000803The number of occurrences of the vincular pattern |132 in a permutation. St000834The number of right outer peaks of a permutation. St000864The number of circled entries of the shifted recording tableau of a permutation. St000875The semilength of the longest Dyck word in the Catalan factorisation of a binary word. St000931The number of occurrences of the pattern UUU in a Dyck path. St000948The chromatic discriminant of a graph. 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. St001008Number of indecomposable injective modules with projective dimension 1 in the Nakayama algebra corresponding to the Dyck path. St001011Number of simple modules of projective dimension 2 in the Nakayama algebra corresponding to the Dyck path. St001013Number of indecomposable injective modules with codominant dimension equal to the global dimension in the Nakayama algebra corresponding to the Dyck path. St001031The height of the bicoloured Motzkin path associated with the Dyck path. St001056The Grundy value for the game of deleting vertices of a graph until it has no edges. St001057The Grundy value of the game of creating an independent set in a graph. St001061The number of indices that are both descents and recoils of a permutation. St001070The absolute value of the derivative of the chromatic polynomial of the graph at 1. St001071The beta invariant of the graph. St001073The number of nowhere zero 3-flows of a graph. St001078The minimal number of occurrences of (12) in a factorization of a permutation into transpositions (12) and cycles (1,. St001104The number of descents of the invariant in a tensor power of the adjoint representation of the rank two general linear group. St001114The number of odd descents of a permutation. St001115The number of even descents of a permutation. St001125The number of simple modules that satisfy the 2-regular condition in the corresponding Nakayama algebra. St001139The number of occurrences of hills of size 2 in a Dyck path. St001142The projective dimension of the socle of the regular module as a bimodule in the Nakayama algebra corresponding to the Dyck path. St001160The number of proper blocks (or intervals) of a permutations. St001163The number of simple modules with dominant dimension at least three in the corresponding Nakayama algebra. 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. St001167The number of simple modules that appear as the top of an indecomposable non-projective modules that is reflexive in the corresponding Nakayama algebra. St001169Number of simple modules with projective dimension at least two in the corresponding Nakayama algebra. 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. 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 $g$. St001192The maximal dimension of $Ext_A^2(S,A)$ for a simple module $S$ over the corresponding Nakayama algebra $A$. St001194The injective dimension of $A/AfA$ in the corresponding Nakayama algebra $A$ when $Af$ is the minimal faithful projective-injective left $A$-module St001196The global dimension of $A$ minus the global dimension of $eAe$ for the corresponding Nakayama algebra with minimal faithful projective-injective module $eA$. 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 $eA$. St001212The number of simple modules in the corresponding Nakayama algebra that have non-zero second Ext-group with the regular module. St001215Let X be the direct sum of all simple modules of the corresponding Nakayama algebra. St001216The number of indecomposable injective modules in the corresponding Nakayama algebra that have non-vanishing second Ext-group with the regular 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. St001222Number of simple modules in the corresponding LNakayama algebra that have a unique 2-extension 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. St001227The vector space dimension of the first extension group between the socle of the regular module and the Jacobson radical of the corresponding Nakayama algebra. St001230The number of simple modules with injective dimension equal to the dominant dimension equal to one and the dual property. St001231The number of simple modules that are non-projective and non-injective with the property that they have projective dimension equal to one and that also the Auslander-Reiten translates of the module and the inverse Auslander-Reiten translate of the module have the same projective dimension. St001234The number of indecomposable three dimensional modules with projective dimension one. St001244The number of simple modules of projective dimension one that are not 1-regular for the Nakayama algebra associated to a Dyck path. St001250The number of parts of a partition that are not congruent 0 modulo 3. St001251The number of parts of a partition that are not congruent 1 modulo 3. St001252Half the sum of the even parts of a partition. 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. St001269The sum of the minimum of the number of exceedances and deficiencies in each cycle of a permutation. St001274The number of indecomposable injective modules with projective dimension equal to two. St001276The number of 2-regular indecomposable modules in 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. St001283The number of finite solvable groups that are realised by the given partition over the complex numbers. St001284The number of finite groups that are realised by the given partition over the complex numbers. 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. St001332The number of steps on the non-negative side of the walk associated with the permutation. St001357The maximal degree of a regular spanning subgraph of a graph. St001367The smallest number which does not occur as degree of a vertex in a graph. St001375The pancake length of a permutation. St001392The largest nonnegative integer which is not a part and is smaller than the largest part of the partition. St001402The number of separators in a permutation. St001403The number of vertical separators in a permutation. St001405The number of bonds in a permutation. St001421Half the length of a longest factor which is its own reverse-complement and begins with a one of a binary word. St001423The number of distinct cubes in a binary word. St001424The number of distinct squares in a binary word. St001465The number of adjacent transpositions in the cycle decomposition of a permutation. St001466The number of transpositions swapping cyclically adjacent numbers in a permutation. St001479The number of bridges of a graph. St001485The modular major index of a binary word. St001498The normalised height of a Nakayama algebra with magnitude 1. St001506Half the projective dimension of the unique simple module with even projective dimension in a magnitude 1 Nakayama algebra. St001507The sum of projective dimension of simple modules with even projective dimension divided by 2 in the LNakayama algebra corresponding to Dyck paths. St001509The degree of the standard monomial associated to a Dyck path relative to the trivial lower boundary. St001511The minimal number of transpositions needed to sort a permutation in either direction. St001534The alternating sum of the coefficients of the Poincare polynomial of the poset cone. 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. St001561The value of the elementary symmetric function evaluated at 1. St001569The maximal modular displacement of a permutation. St001582The grades of the simple modules corresponding to the points in the poset of the symmetric group under the Bruhat order. St001601The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on trees. St001631The number of simple modules $S$ with $dim Ext^1(S,A)=1$ in the incidence algebra $A$ of the poset. St001637The number of (upper) dissectors of a poset. St001641The number of ascent tops in the flattened set partition such that all smaller elements appear before. St001657The number of twos in an integer partition. St001665The number of pure excedances of a permutation. St001675The number of parts equal to the part in the reversed composition. 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. St001721The degree of a binary word. St001729The number of visible descents of a permutation. St001730The number of times the path corresponding to a binary word crosses the base line. St001760The number of prefix or suffix reversals needed to sort a permutation. St001767The largest minimal number of arrows pointing to a cell in the Ferrers diagram in any assignment. St001781The interlacing number of a set partition. St001783The number of odd automorphisms of a graph. St001801Half the number of preimage-image pairs of different parity in a permutation. 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. St001816Eigenvalues of the top-to-random operator acting on a simple module. St001826The maximal number of leaves on a vertex of a graph. St001828The Euler characteristic of a graph. St001928The number of non-overlapping descents in a permutation. St001931The weak major index of an integer composition regarded as a word. St001940The number of distinct parts that are equal to their multiplicity in the integer partition. St000007The number of saliances of the permutation. St000015The number of peaks of a Dyck path. St000031The number of cycles in the cycle decomposition of a permutation. St000056The decomposition (or block) number of a permutation. St000061The number of nodes on the left branch of a binary tree. St000062The length of the longest increasing subsequence of the permutation. St000066The column of the unique '1' in the first row of the alternating sign matrix. St000068The number of minimal elements in a poset. St000069The number of maximal elements of a poset. St000084The number of subtrees. St000099The number of valleys of a permutation, including the boundary. St000117The number of centered tunnels of a Dyck path. St000154The sum of the descent bottoms of a permutation. St000181The number of connected components of the Hasse diagram for the poset. St000193The row of the unique '1' in the first column of the alternating sign matrix. St000236The number of cyclical small weak excedances. St000248The number of anti-singletons of a set partition. St000286The number of connected components of the complement of a graph. St000308The height of the tree associated to a permutation. St000314The number of left-to-right-maxima of a permutation. St000334The maz index, the major index of a permutation after replacing fixed points by zeros. St000363The number of minimal vertex covers of a graph. St000382The first part of an integer composition. St000383The last part of an integer composition. St000420The number of Dyck paths that are weakly above a Dyck path. St000444The length of the maximal rise of a Dyck path. St000451The length of the longest pattern of the form k 1 2. St000460The hook length of the last cell along the main diagonal of an integer partition. St000478Another weight of a partition according to Alladi. St000487The length of the shortest cycle of a permutation. St000488The number of cycles of a permutation of length at most 2. St000504The cardinality of the first block of a set partition. St000505The biggest entry in the block containing the 1. St000542The number of left-to-right-minima of a permutation. St000619The number of cyclic descents of a permutation. St000638The number of up-down runs of a permutation. St000657The smallest part of an integer composition. St000676The number of odd rises of a Dyck path. St000684The global dimension of the LNakayama algebra associated to a Dyck path. St000685The dominant dimension of the LNakayama algebra associated to a Dyck path. St000686The finitistic dominant dimension of a Dyck path. St000693The modular (standard) major index of a standard tableau. St000700The protection number of an ordered tree. St000717The number of ordinal summands of a poset. St000729The minimal arc length of a set partition. St000733The row containing the largest entry of a standard tableau. St000740The last entry of a permutation. St000745The index of the last row whose first entry is the row number in a standard Young tableau. St000823The number of unsplittable factors of the set partition. St000831The number of indices that are either descents or recoils. St000838The number of terminal right-hand endpoints when the vertices are written in order. St000843The decomposition number of a perfect matching. St000876The number of factors in the Catalan decomposition of a binary word. St000883The number of longest increasing subsequences of a permutation. St000887The maximal number of nonzero entries on a diagonal of a permutation matrix. St000888The maximal sum of entries on a diagonal of an alternating sign matrix. St000895The number of ones on the main diagonal of an alternating sign matrix. St000898The number of maximal entries in the last diagonal of the monotone triangle. St000899The maximal number of repetitions of an integer composition. St000900The minimal number of repetitions of a part in an integer composition. St000902 The minimal number of repetitions of an integer composition. St000904The maximal number of repetitions of an integer composition. St000906The length of the shortest maximal chain in a poset. St000907The number of maximal antichains of minimal length in a poset. St000908The length of the shortest maximal antichain in a poset. St000909The number of maximal chains of maximal size in a poset. St000910The number of maximal chains of minimal length in a poset. St000911The number of maximal antichains of maximal size in a poset. St000914The sum of the values of the Möbius function of a poset. St000925The number of topologically connected components of a set partition. St000928The sum of the coefficients of the character polynomial of an integer partition. St000971The smallest closer of a set partition. St000982The length of the longest constant subword. St000988The orbit size of a permutation under Foata's bijection. St000991The number of right-to-left minima of a permutation. St001000Number of indecomposable modules with projective dimension equal to the global dimension in the Nakayama algebra corresponding to the Dyck path. St001006Number of simple modules with projective dimension equal to the global dimension of the Nakayama algebra corresponding to the Dyck path. St001038The minimal height of a column in the parallelogram polyomino associated with the Dyck path. St001039The maximal height of a column in the parallelogram polyomino associated with a Dyck path. St001045The number of leaves in the subtree not containing one in the decreasing labelled binary unordered tree associated with the perfect matching. St001048The number of leaves in the subtree containing 1 in the decreasing labelled binary unordered tree associated with the perfect matching. St001051The depth of the label 1 in the decreasing labelled unordered tree associated with the set partition. St001066The number of simple reflexive modules in the corresponding Nakayama algebra. St001068Number of torsionless simple modules in the corresponding Nakayama algebra. St001075The minimal size of a block of a set partition. St001107The number of times one can erase the first up and the last down step in a Dyck path and still remain a Dyck path. St001165Number of simple modules with even projective dimension in the corresponding Nakayama algebra. 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: St001235The global 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. St001239The largest vector space dimension of the double dual of a simple module in the corresponding Nakayama algebra. St001246The maximal difference between two consecutive entries of a permutation. St001267The length of the Lyndon factorization of the binary word. St001288The number of primes obtained by multiplying preimage and image of a permutation and adding one. St001316The domatic number of a graph. St001365The number of lattice paths of the same length weakly above the path given by a binary word. St001368The number of vertices of maximal degree in a graph. St001377The major index minus the number of inversions of a permutation. St001390The number of bumps occurring when Schensted-inserting the letter 1 of a permutation. St001399The distinguishing number of a poset. St001415The length of the longest palindromic prefix 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. St001437The flex of a binary word. St001439The number of even weak deficiencies and of odd weak exceedences. St001459The number of zero columns in the nullspace of a graph. St001461The number of topologically connected components of the chord diagram of a permutation. St001462The number of factors of a standard tableaux under concatenation. St001471The magnitude of a Dyck path. St001483The number of simple module modules that appear in the socle of the regular module but have no nontrivial selfextensions with the regular module. St001500The global dimension of magnitude 1 Nakayama algebras. St001501The dominant dimension of magnitude 1 Nakayama algebras. St001523The degree of symmetry of a Dyck path. St001530The depth of a Dyck path. St001652The length of a longest interval of consecutive numbers. St001662The length of the longest factor of consecutive numbers in a permutation. St001672The restrained domination number 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. St001800The number of 3-Catalan paths having this Dyck path as first and last coordinate projections. St001884The number of borders of a binary word. St001904The length of the initial strictly increasing segment of a parking function. St001937The size of the center of a parking function. St000058The order of a permutation. St000485The length of the longest cycle of a permutation. St000724The label of the leaf of the path following the smaller label in the increasing binary tree associated to a permutation. St000725The smallest label of a leaf of the increasing binary tree associated to a permutation. St000738The first entry in the last row of a standard tableau. St000951The dimension of $Ext^{1}(D(A),A)$ of the corresponding LNakayama algebra. St000983The length of the longest alternating subword. St001028Number of simple modules with injective dimension equal to the dominant dimension in the Nakayama algebra corresponding to the Dyck path. St001180Number of indecomposable injective modules with projective dimension at most 1. St001468The smallest fixpoint of a permutation. 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. St001505The number of elements generated by the Dyck path as a map in the full transformation monoid. St000756The sum of the positions of the left to right maxima of a permutation. St000981The length of the longest zigzag subpath. St001240The number of indecomposable modules e_i J^2 that have injective dimension at most one in the corresponding Nakayama algebra St001634The trace of the Coxeter matrix of the incidence algebra of a poset. St001650The order of Ringel's homological bijection associated to the linear Nakayama algebra corresponding to the Dyck path. St001809The index of the step at the first peak of maximal height in a Dyck path. 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. St000668The least common multiple of the parts of the partition. St000708The product of the parts of an integer partition. St000933The number of multipartitions of sizes given by an integer 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. St000946The sum of the skew hook positions in a Dyck path. St000984The number of boxes below precisely one peak. St001418Half of the global dimension of the stable Auslander algebra of the Nakayama algebra corresponding to the Dyck path. St001480The number of simple summands of the module J^2/J^3. St000083The number of left oriented leafs of a binary tree except the first one. St000216The absolute length of a permutation. St000354The number of recoils of a permutation. St000442The maximal area to the right of an up step of a Dyck path. St000472The sum of the ascent bottoms of a permutation. St000476The sum of the semi-lengths of tunnels before a valley of a Dyck path. St000494The number of inversions of distance at most 3 of a permutation. St000495The number of inversions of distance at most 2 of a permutation. St000503The maximal difference between two elements in a common block. St000539The number of odd inversions of a permutation. St000653The last descent of a permutation. St000728The dimension of a set partition. St000730The maximal arc length of a set partition. St000795The mad of a permutation. St000796The stat' of a permutation. St000797The stat`` of a permutation. St000798The makl of a permutation. St000809The reduced reflection length of the permutation. St000829The Ulam distance of a permutation to the identity permutation. St000849The number of 1/3-balanced pairs in a poset. St000866The number of admissible inversions of a permutation in the sense of Shareshian-Wachs. St000874The position of the last double rise in a Dyck path. St000947The major index east count of a Dyck path. St000956The maximal displacement of a permutation. St000957The number of Bruhat lower covers of a permutation. St000961The shifted major index of a permutation. St001076The minimal length of a factorization of a permutation into transpositions that are cyclic shifts of (12). St001077The prefix exchange distance of a permutation. St001080The minimal length of a factorization of a permutation using the transposition (12) and the cycle (1,. St001207The Lowey length of the algebra $A/T$ when $T$ is the 1-tilting module corresponding to the permutation in the Auslander algebra of $K[x]/(x^n)$. St001583The projective dimension of the simple module corresponding to the point in the poset of the symmetric group under bruhat order. St001600The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on simple graphs. St000045The number of linear extensions of a binary tree. St000082The number of elements smaller than a binary tree in Tamari order. St000100The number of linear extensions of a poset. St000280The size of the preimage of the map 'to labelling permutation' from Parking functions to Permutations. St000490The intertwining number of a set partition. St000493The los statistic of a set partition. St000574The number of occurrences of the pattern {{1},{2}} such that 1 is a minimal and 2 a maximal element. St000577The number of occurrences of the pattern {{1},{2}} such that 1 is a maximal element. St000578The number of occurrences of the pattern {{1},{2}} such that 1 is a singleton. St000579The number of occurrences of the pattern {{1},{2}} such that 2 is a maximal element. St000690The size of the conjugacy class of a permutation. St000702The number of weak deficiencies of a permutation. St000727The largest label of a leaf in the binary search tree associated with the permutation. St000794The mak of a permutation. St000833The comajor index of a permutation. St000844The size of the largest block in the direct sum decomposition of a permutation. St000870The product of the hook lengths of the diagonal cells in an integer partition. St000892The maximal number of nonzero entries on a diagonal of an alternating sign matrix. St001030Half the number of non-boundary horizontal edges in the fully packed loop corresponding to the alternating sign matrix. St001062The maximal size of a block of a set partition. St001232The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2. St001346The number of parking functions that give the same permutation. St001380The number of monomer-dimer tilings of a Ferrers diagram. St001383The BG-rank of an integer partition. St001808The box weight or horizontal decoration of a Dyck path. St001915The size of the component corresponding to a necklace in Bulgarian solitaire. St001959The product of the heights of the peaks of a Dyck path. St000474Dyson's crank of a partition. St000438The position of the last up step in a Dyck path. St000656The number of cuts of a poset. St000639The number of relations in a poset. St000634The number of endomorphisms of a poset. St000145The Dyson rank of a partition. St000175Degree of the polynomial counting the number of semistandard Young tableaux when stretching the shape. St000259The diameter of a connected graph. St000289The decimal representation of a binary word. St000319The spin of an integer partition. St000320The dinv adjustment of an integer partition. St000327The number of cover relations in a poset. St000391The sum of the positions of the ones in a binary word. St000454The largest eigenvalue of a graph if it is integral. St000492The rob statistic of a set partition. St000498The lcs statistic of a set partition. St000499The rcb statistic of a set partition. St000747A variant of the major index of a set partition. St000771The largest multiplicity of a distance Laplacian eigenvalue in a connected graph. St000772The multiplicity of the largest distance Laplacian eigenvalue in a connected graph. St000777The number of distinct eigenvalues of the distance Laplacian of a connected graph. St000878The number of ones minus the number of zeros of a binary word. St000921The number of internal inversions of a binary word. St000934The 2-degree of an integer partition. St001199The dominant dimension of $eAe$ for the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. St001247The number of parts of a partition that are not congruent 2 modulo 3. St001249Sum of the odd parts of a partition. St001281The normalized isoperimetric number of a graph. St001382The number of boxes in the diagram of a partition that do not lie in its Durfee square. St001384The number of boxes in the diagram of a partition that do not lie in the largest triangle it contains. St001408The number of maximal entries in a semistandard tableau. St001487The number of inner corners of a skew partition. St001541The Gini index of an integer partition. St001570The minimal number of edges to add to make a graph Hamiltonian. St001592The maximal number of simple paths between any two different vertices of a graph. St001593This is the number of standard Young tableaux of the given shifted shape. St001604The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on polygons. St001606The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on set partitions. St001629The coefficient of the integer composition in the quasisymmetric expansion of the relabelling action of the symmetric group on cycles. St001632The number of indecomposable injective modules $I$ with $dim Ext^1(I,A)=1$ for the incidence algebra A of a poset. St001645The pebbling number of a connected graph. St001668The number of points of the poset minus the width of the poset. St001697The shifted natural comajor index of a standard Young tableau. St001860The number of factors of the Stanley symmetric function associated with a signed permutation. St001918The degree of the cyclic sieving polynomial corresponding to an integer partition. St000144The pyramid weight of the Dyck path. St000184The size of the centralizer of any permutation of given cycle type. St000207Number of integral Gelfand-Tsetlin polytopes with prescribed top row and integer composition weight. St000208Number of integral Gelfand-Tsetlin polytopes with prescribed top row and integer partition weight. St000228The size of a partition. St000260The radius of a connected graph. St000293The number of inversions of a binary word. St000302The determinant of the distance matrix of a connected graph. St000384The maximal part of the shifted composition of an integer partition. St000395The sum of the heights of the peaks of a Dyck path. St000459The hook length of the base cell of a partition. St000466The Gutman (or modified Schultz) index of a connected graph. St000519The largest length of a factor maximising the subword complexity. St000527The width of the poset. St000531The leading coefficient of the rook polynomial of an integer partition. St000631The number of distinct palindromic decompositions of a binary word. St000667The greatest common divisor of the parts of the partition. St000679The pruning number of an ordered tree. St000680The Grundy value for Hackendot on posets. St000699The toughness times the least common multiple of 1,. St000770The major index of an integer partition when read from bottom to top. St000784The maximum of the length and the largest part of the integer partition. St000894The trace of an alternating sign matrix. St000922The minimal number such that all substrings of this length are unique. St000993The multiplicity of the largest part of an integer partition. 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. St001032The number of horizontal steps in the bicoloured Motzkin path associated with the Dyck path. St001118The acyclic chromatic index of a graph. St001183The maximum of $projdim(S)+injdim(S)$ over all simple modules in the Nakayama algebra corresponding to the Dyck path. 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 $eA$. St001258Gives the maximum of injective plus projective dimension of an indecomposable module over the corresponding Nakayama algebra. St001360The number of covering relations in Young's lattice below a partition. St001389The number of partitions of the same length below the given integer partition. St001407The number of minimal entries in a semistandard tableau. St001416The length of a longest palindromic factor of a binary word. St001417The length of a longest palindromic subword of a binary word. St001435The number of missing boxes in the first row. St001438The number of missing boxes of a skew partition. St001488The number of corners of a skew partition. St001527The cyclic permutation representation number of an integer partition. St001571The Cartan determinant of the integer partition. St001605The number of colourings of a cycle 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. St001612The number of coloured multisets of cycles such that the multiplicities of colours are given by a partition. St001659The number of ways to place as many non-attacking rooks as possible on a Ferrers board. St001908The number of semistandard tableaux of distinct weight whose maximal entry is the length of the partition. St001914The size of the orbit of an integer partition in Bulgarian solitaire. St001964The interval resolution global dimension of a poset. St000063The number of linear extensions of a certain poset defined for an integer partition. St000108The number of partitions contained in the given partition. St000294The number of distinct factors of a binary word. St000380Half of the maximal perimeter of a rectangle fitting into the diagram of an integer partition. St000518The number of distinct subsequences in a binary word. St000532The total number of rook placements on a Ferrers board. St000625The sum of the minimal distances to a greater element. St000643The size of the largest orbit of antichains under Panyushev complementation. St000973The length of the boundary of an ordered tree. St000975The length of the boundary minus the length of the trunk of an ordered tree. 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. St001023Number of simple modules with projective dimension at most 3 in the Nakayama algebra corresponding to the Dyck path. St001065Number of indecomposable reflexive modules in the corresponding Nakayama algebra. St001179Number of indecomposable injective modules with projective dimension at most 2 in the corresponding Nakayama algebra. St001190Number of simple modules with projective dimension at most 4 in the corresponding Nakayama algebra. St001228The vector space dimension of the space of module homomorphisms between J and itself when J denotes the Jacobson radical of the corresponding Nakayama algebra. St001237The number of simple modules with injective dimension at most one or dominant dimension at least one. St001254The vector space dimension of the first extension-group between A/soc(A) and J when A is the corresponding Nakayama algebra with Jacobson radical J. St001348The bounce of the parallelogram polyomino associated with the Dyck path. St001400The total number of Littlewood-Richardson tableaux of given shape. St000520The number of patterns in a permutation. St000641The number of non-empty boolean intervals in a poset. St000967The value p(1) for the Coxeterpolynomial p of the corresponding LNakayama algebra. St001218Smallest index k greater than or equal to one such that the Coxeter matrix C of the corresponding Nakayama algebra has C^k=1. St001643The Frobenius dimension of the Nakayama algebra corresponding to the Dyck path. 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. St000227The osculating paths major index of an alternating sign matrix. St000827The decimal representation of a binary word with a leading 1. St001003The number of indecomposable modules with projective dimension at most 1 in the Nakayama algebra corresponding to the Dyck path. St001213The number of indecomposable modules in the corresponding Nakayama algebra that have vanishing first Ext-group with the regular module. St001259The vector space dimension of the double dual of D(A) in the corresponding Nakayama algebra.