St000566The number of ways to select a row of a Ferrers shape and two cells in this row. St001011Number of simple modules of projective dimension 2 in 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. St001251The number of parts of a partition that are not congruent 1 modulo 3. St001252Half the sum of the even parts of a partition. St001280The number of parts of an integer partition that are at least two. St001657The number of twos in an integer partition. St000321The number of integer partitions of n that are dominated by an integer partition. St000345The number of refinements of a partition. St000935The number of ordered refinements of an integer partition. St001389The number of partitions of the same length below the given integer partition. St000024The number of double up and double down steps of a Dyck path. St000053The number of valleys of the Dyck path. St000149The number of cells of the partition whose leg is zero and arm is odd. St000150The floored half-sum of the multiplicities of a partition. St000185The weighted size of a partition. St000211The rank of the set partition. St000253The crossing number of a set partition. St000272The treewidth of a graph. St000292The number of ascents of a binary word. St000340The number of non-final maximal constant sub-paths of length greater than one. St000362The size of a minimal vertex cover of a graph. St000377The dinv defect of an integer partition. St000387The matching number of a graph. St000442The maximal area to the right of an up step of a Dyck path. St000536The pathwidth of a graph. St000558The number of occurrences of the pattern {{1,2}} in a set partition. St000658The number of rises of length 2 of a Dyck path. St000877The depth of the binary word interpreted as a path. St000985The number of positive eigenvalues of the adjacency matrix of the graph. St001125The number of simple modules that satisfy the 2-regular condition in the corresponding Nakayama algebra. St001176The size of a partition minus its first part. St001197The global dimension of $eAe$ for the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. St001276The number of 2-regular indecomposable modules in the corresponding Nakayama algebra. St001277The degeneracy of a graph. St001354The number of series nodes in the modular decomposition of a graph. St001358The largest degree of a regular subgraph of a graph. St001506Half the projective dimension of the unique simple module with even projective dimension in a magnitude 1 Nakayama algebra. St001512The minimum rank of a graph. St001693The excess length of a longest path consisting of elements and blocks of a set partition. St000010The length of the partition. St000011The number of touch points (or returns) of a Dyck path. St000013The height of a Dyck path. St000097The order of the largest clique of the graph. St000098The chromatic number of a graph. St000172The Grundy number of a graph. St000326The position of the first one in a binary word after appending a 1 at the end. St000444The length of the maximal rise of a Dyck path. St000507The number of ascents of a standard tableau. St000814The sum of the entries in the column specified by the partition of the change of basis matrix from elementary symmetric functions to Schur symmetric functions. St001007Number of simple modules with projective dimension 1 in the Nakayama algebra corresponding to the Dyck path. St001029The size of the core of a graph. St001068Number of torsionless simple modules in the corresponding Nakayama algebra. St001116The game chromatic number of 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: St001302The number of minimally dominating sets of vertices of a graph. St001304The number of maximally independent sets of vertices of a graph. St001471The magnitude of a Dyck path. St001494The Alon-Tarsi number of a graph. St001580The acyclic chromatic number of a graph. St001581The achromatic number of a graph. St001670The connected partition number of a graph. St001674The number of vertices of the largest induced star graph in the graph. St001963The tree-depth of a graph. St001028Number of simple modules with injective dimension equal to the dominant dimension in the Nakayama algebra corresponding to the Dyck path. St001505The number of elements generated by the Dyck path as a map in the full transformation monoid. St000336The leg major index of a standard tableau. St001333The cardinality of a minimal edge-isolating set of a graph. St001393The induced matching number of a graph. St001261The Castelnuovo-Mumford regularity of a graph. St000201The number of leaf nodes in a binary tree. St001199The dominant dimension of $eAe$ for the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. St001214The aft of an integer partition. St000568The hook number of a binary tree. St000299The number of nonisomorphic vertex-induced subtrees. St000884The number of isolated descents of a permutation. 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. St001712The number of natural descents of a standard Young tableau. St000374The number of exclusive right-to-left minima of a permutation. St000703The number of deficiencies of a permutation. St000443The number of long tunnels of a Dyck path. 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. St000742The number of big ascents of a permutation after prepending zero. St000354The number of recoils of a permutation. St000829The Ulam distance of a permutation to the identity permutation. St001269The sum of the minimum of the number of exceedances and deficiencies in each cycle of a permutation. St001489The maximum of the number of descents and the number of inverse descents. St001665The number of pure excedances of a permutation. St001729The number of visible descents of a permutation. St001737The number of descents of type 2 in a permutation. St001928The number of non-overlapping descents in a permutation. St000470The number of runs in a permutation. St000670The reversal length of a permutation. St000834The number of right outer peaks of a permutation. St000306The bounce count of a Dyck path. St000668The least common multiple of the parts of the partition. St001726The number of visible inversions of a permutation. St000809The reduced reflection length of the permutation. St000167The number of leaves of an ordered tree. St000159The number of distinct parts of the integer partition. St000259The diameter of a connected graph. St000260The radius of a connected graph. St000386The number of factors DDU in a Dyck path. St000318The number of addable cells of the Ferrers diagram of an integer partition. St000632The jump number of the poset. St000035The number of left outer peaks of a permutation. St000662The staircase size of the code of a permutation. St000665The number of rafts of a permutation. St001630The global dimension of the incidence algebra of the lattice over the rational numbers. St000396The register function (or Horton-Strahler number) of a binary tree. St000245The number of ascents of a permutation. St001086The number of occurrences of the consecutive pattern 132 in a permutation. St000243The number of cyclic valleys and cyclic peaks of a permutation. St000021The number of descents of a permutation. St000955Number of times one has $Ext^i(D(A),A)>0$ for $i>0$ for the corresponding LNakayama algebra. St001165Number of simple modules with even projective dimension in the corresponding Nakayama algebra. St001597The Frobenius rank of a skew partition. St001212The number of simple modules in the corresponding Nakayama algebra that have non-zero second Ext-group with the regular module. 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. St001244The number of simple modules of projective dimension one that are not 1-regular for the Nakayama algebra associated to a Dyck path. St001568The smallest positive integer that does not appear twice in the partition. St001465The number of adjacent transpositions in the cycle decomposition of a permutation. St000031The number of cycles in the cycle decomposition of a permutation. St000141The maximum drop size of a permutation. St000546The number of global descents of a permutation. St000647The number of big descents of a permutation. St000007The number of saliances of the permutation. St000672The number of minimal elements in Bruhat order not less than the permutation. St001060The distinguishing index of a graph. St000702The number of weak deficiencies of a permutation. St000257The number of distinct parts of a partition that occur at least twice. St000153The number of adjacent cycles of a permutation. St001732The number of peaks visible from the left. St000755The number of real roots of the characteristic polynomial of a linear recurrence associated with an integer partition. St001767The largest minimal number of arrows pointing to a cell in the Ferrers diagram in any assignment. St001083The number of boxed occurrences of 132 in a permutation. St001432The order dimension of the partition. St000018The number of inversions of a permutation. St000019The cardinality of the support of a permutation. St000214The number of adjacencies of a permutation. St000215The number of adjacencies of a permutation, zero appended. St000237The number of small exceedances. St000337The lec statistic, the sum of the inversion numbers of the hook factors of a permutation. St001104The number of descents of the invariant in a tensor power of the adjoint representation of the rank two general linear group. St001427The number of descents of a signed permutation. St001878The projective dimension of the simple modules corresponding to the minimum of L in the incidence algebra of the lattice L. St000145The Dyson rank of a partition. St000319The spin of an integer partition. St000320The dinv adjustment of an integer partition. St000510The number of invariant oriented cycles when acting with a permutation of given cycle type. St000681The Grundy value of Chomp on Ferrers diagrams. St000939The number of characters of the symmetric group whose value on the partition is positive. St001384The number of boxes in the diagram of a partition that do not lie in the largest triangle it contains. St001392The largest nonnegative integer which is not a part and is smaller than the largest part of the partition. St001918The degree of the cyclic sieving polynomial corresponding to an integer partition. St001006Number of simple modules with projective dimension equal to the global dimension of the Nakayama algebra corresponding to the Dyck path. St001493The number of simple modules with maximal even projective dimension in the corresponding Nakayama algebra. St000454The largest eigenvalue of a graph if it is integral. St000068The number of minimal elements in a poset. St000071The number of maximal chains in a poset. St000456The monochromatic index of a connected graph. St001907The number of Bastidas - Hohlweg - Saliola excedances of a signed permutation. St000527The width of the poset. St000162The number of nontrivial cycles in the cycle decomposition of a permutation. St000325The width of the tree associated to a permutation. St000155The number of exceedances (also excedences) of a permutation. St000196The number of occurrences of the contiguous pattern [[.,.],[.,. St001215Let X be the direct sum of all simple modules of the corresponding Nakayama algebra. St001222Number of simple modules in the corresponding LNakayama algebra that have a unique 2-extension with the regular module. St001298The number of repeated entries in the Lehmer code of a permutation. St001840The number of descents of a set partition. St001859The number of factors of the Stanley symmetric function associated with a permutation. St001874Lusztig's a-function for the symmetric group. St000083The number of left oriented leafs of a binary tree except the first one. St000120The number of left tunnels of a Dyck path. St000168The number of internal nodes of an ordered tree. St000216The absolute length of a permutation. St000238The number of indices that are not small weak excedances. St000316The number of non-left-to-right-maxima of a permutation. St000329The number of evenly positioned ascents of the Dyck path, with the initial position equal to 1. 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. 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 $eA$. St001216The number of indecomposable injective modules in the corresponding Nakayama algebra that have non-vanishing second Ext-group with the regular module. St001225The vector space dimension of the first extension group between J and itself when J is the Jacobson radical of the corresponding Nakayama algebra. St001230The number of simple modules with injective dimension equal to the dominant dimension equal to one and the dual property. St001274The number of indecomposable injective modules with projective dimension equal to two. St001278The number of indecomposable modules that are fixed by $\tau \Omega^1$ composed with its inverse in the corresponding 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. St001812The biclique partition number of a graph. St000015The number of peaks of a Dyck path. St000062The length of the longest increasing subsequence of the permutation. St000213The number of weak exceedances (also weak excedences) of a permutation. St000308The height of the tree associated to a permutation. St000314The number of left-to-right-maxima of a permutation. St000822The Hadwiger number of the 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. St001290The first natural number n such that the tensor product of n copies of D(A) is zero for the corresponding Nakayama algebra A. St000862The number of parts of the shifted shape of a permutation. St001331The size of the minimal feedback vertex set. 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 $eA$. St000781The number of proper colouring schemes of a Ferrers diagram. St001901The largest multiplicity of an irreducible representation contained in the higher Lie character for an integer partition. St001908The number of semistandard tableaux of distinct weight whose maximal entry is the length of the partition. St001924The number of cells in an integer partition whose arm and leg length coincide. St000092The number of outer peaks of a permutation. St001503The largest distance of a vertex to a vertex in a cycle in the resolution quiver of the corresponding Nakayama algebra. St000619The number of cyclic descents of a permutation. St000451The length of the longest pattern of the form k 1 2. St000481The number of upper covers of a partition in dominance order. St000353The number of inner valleys of a permutation. St000494The number of inversions of distance at most 3 of a permutation. St000495The number of inversions of distance at most 2 of a permutation. St000539The number of odd inversions of a permutation. St000795The mad of a permutation. St000831The number of indices that are either descents or recoils. St000866The number of admissible inversions of a permutation in the sense of Shareshian-Wachs. St000957The number of Bruhat lower covers of a permutation. St001061The number of indices that are both descents and recoils of a permutation. St001076The minimal length of a factorization of a permutation into transpositions that are cyclic shifts of (12). St001078The minimal number of occurrences of (12) in a factorization of a permutation into transpositions (12) and cycles (1,. St001412Number of minimal entries in the Bruhat order matrix of a permutation. St001466The number of transpositions swapping cyclically adjacent numbers in a permutation. St001558The number of transpositions that are smaller or equal to a permutation in Bruhat order. St001579The number of cyclically simple transpositions decreasing the number of cyclic descents needed to sort a permutation. St001687The number of distinct positions of the pattern letter 2 in occurrences of 213 in a permutation. St001801Half the number of preimage-image pairs of different parity in a permutation. St001330The hat guessing number of a graph. St001683The number of distinct positions of the pattern letter 3 in occurrences of 132 in a permutation. St000528The height of a poset. St001603The number of colourings of a polygon such that the multiplicities of a colour are given by a partition. St001604The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on polygons. St001605The number of colourings of a cycle such that the multiplicities of colours are given by a partition. St001469The holeyness of a permutation. St000646The number of big ascents of a permutation. St000771The largest multiplicity of a distance Laplacian eigenvalue in a connected graph. St000772The multiplicity of the largest distance Laplacian eigenvalue in a connected graph. St000054The first entry of the permutation. St001390The number of bumps occurring when Schensted-inserting the letter 1 of a permutation. St001085The number of occurrences of the vincular pattern |21-3 in a permutation. St001035The convexity degree of the parallelogram polyomino associated with the Dyck path. St001761The maximal multiplicity of a letter in a reduced word of a permutation. St001394The genus of a permutation. St000779The tier of a permutation. St000710The number of big deficiencies of a permutation. St000704The number of semistandard tableaux on a given integer partition with minimal maximal entry. St000663The number of right floats of a permutation. St001461The number of topologically connected components of the chord diagram of a permutation. St000164The number of short pairs. St000843The decomposition number of a perfect matching. St001162The minimum jump of a permutation. St001344The neighbouring number of a permutation. St001744The number of occurrences of the arrow pattern 1-2 with an arrow from 1 to 2 in a permutation. St000711The number of big exceedences of a permutation. St001728The number of invisible descents of a permutation. St001644The dimension of a graph. St000052The number of valleys of a Dyck path not on the x-axis. St001877Number of indecomposable injective modules with projective dimension 2. St000845The maximal number of elements covered by an element in a poset. St000846The maximal number of elements covering an element of a poset. St001942The number of loops of the quiver corresponding to the reduced incidence algebra of a poset. St000633The size of the automorphism group of a poset. St000640The rank of the largest boolean interval in a poset. St000914The sum of the values of the Möbius function of a poset. St000541The number of indices greater than or equal to 2 of a permutation such that all smaller indices appear to its right. St001232The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2. St000542The number of left-to-right-minima of a permutation. St000023The number of inner peaks of a permutation. St000080The rank of the poset. St000317The cycle descent number of a permutation. St001553The number of indecomposable summands of the square of the Jacobson radical as a bimodule in the Nakayama algebra corresponding to the Dyck path. St000099The number of valleys of a permutation, including the boundary. St001258Gives the maximum of injective plus projective dimension of an indecomposable module over the corresponding Nakayama algebra. St000029The depth of a permutation. St000030The sum of the descent differences of a permutations. St000055The inversion sum of a permutation. St000224The sorting index of a permutation. St000241The number of cyclical small excedances. St000242The number of indices that are not cyclical small weak excedances. 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. St000360The number of occurrences of the pattern 32-1. St000523The number of 2-protected nodes of a rooted tree. St000970Number of peaks minus the dominant dimension of the corresponding LNakayama algebra. St001046The maximal number of arcs nesting a given arc of a perfect matching. St001164Number of indecomposable injective modules whose socle has projective dimension at most g-1 (g the global dimension) minus the number of indecomposable projective-injective modules. 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. St001233The number of indecomposable 2-dimensional modules with projective dimension one. St001295Gives the vector space dimension of the homomorphism space between J^2 and J^2. St001296The maximal torsionfree index of an indecomposable non-projective module in the corresponding Nakayama algebra. St001388The number of non-attacking neighbors of a permutation. St001480The number of simple summands of the module J^2/J^3. 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. St001511The minimal number of transpositions needed to sort a permutation in either direction. St001689The number of celebrities in a graph. St001873For a Nakayama algebra corresponding to a Dyck path, we define the matrix C with entries the Hom-spaces between $e_i J$ and $e_j J$ (the radical of the indecomposable projective modules). St001890The maximum magnitude of the Möbius function of a poset. St000056The decomposition (or block) number of a permutation. St000061The number of nodes on the left branch of a binary tree. St000084The number of subtrees. St000166The depth minus 1 of an ordered tree. St000239The number of small weak excedances. St000328The maximum number of child nodes in a tree. St000720The size of the largest partition in the oscillating tableau corresponding to the perfect matching. St000991The number of right-to-left minima of a permutation. St001184Number of indecomposable injective modules with grade at least 1 in the corresponding Nakayama algebra. St001192The maximal dimension of $Ext_A^2(S,A)$ for a simple module $S$ over the corresponding Nakayama algebra $A$. 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. St001235The global dimension of the corresponding Comp-Nakayama algebra. St001241The number of non-zero radicals of the indecomposable projective modules that have injective dimension and projective dimension at most one. St001499The number of indecomposable projective-injective modules of a magnitude 1 Nakayama algebra. St001530The depth of a Dyck path. St000094The depth of an ordered tree. St001180Number of indecomposable injective modules with projective dimension at most 1. 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. St000455The second largest eigenvalue of a graph if it is integral. St001118The acyclic chromatic index of a graph. St000256The number of parts from which one can substract 2 and still get an integer partition. St001195The global dimension of the algebra $A/AfA$ of the corresponding Nakayama algebra $A$ with minimal left faithful projective-injective module $Af$. St001632The number of indecomposable injective modules $I$ with $dim Ext^1(I,A)=1$ for the incidence algebra A of a poset. St001864The number of excedances of a signed permutation. St001896The number of right descents of a signed permutations. St000982The length of the longest constant subword. St000871The number of very big ascents of a permutation. St000630The length of the shortest palindromic decomposition of a binary word. St001491The number of indecomposable projective-injective modules in the algebra corresponding to a subset. St001722The number of minimal chains with small intervals between a binary word and the top element. St000648The number of 2-excedences of a permutation. St000741The Colin de Verdière graph invariant. St000872The number of very big descents of a permutation. St000764The number of strong records in an integer composition. St001044The number of pairs whose larger element is at most one more than half the size of the perfect matching. St000534The number of 2-rises of a permutation. St000486The number of cycles of length at least 3 of a permutation. St001431Half of the Loewy length minus one of a modified stable Auslander algebra of the Nakayama algebra corresponding to the Dyck path. St001624The breadth of a lattice. St001905The number of preferred parking spots in a parking function less than the index of the car. St001946The number of descents in a parking function. St001960The number of descents of a permutation minus one if its first entry is not one. St000392The length of the longest run of ones in a binary word. St000758The length of the longest staircase fitting into an integer composition. St000217The number of occurrences of the pattern 312 in a permutation. St000358The number of occurrences of the pattern 31-2. St000375The number of non weak exceedences of a permutation that are mid-points of a decreasing subsequence of length $3$. St000437The number of occurrences of the pattern 312 or of the pattern 321 in a permutation. St000660The number of rises of length at least 3 of a Dyck path. St000732The number of double deficiencies of a permutation. St000761The number of ascents in an integer composition. St000807The sum of the heights of the valleys of the associated bargraph. St001089Number of indecomposable projective non-injective modules minus the number of indecomposable projective non-injective modules with dominant dimension equal to the injective dimension in the corresponding Nakayama algebra. St001229The vector space dimension of the first extension group between the Jacobson radical J and J^2. St001470The cyclic holeyness of a permutation. St001582The grades of the simple modules corresponding to the points in the poset of the symmetric group under the Bruhat order. St001673The degree of asymmetry of an integer composition. St001727The number of invisible inversions of a permutation. St001860The number of factors of the Stanley symmetric function associated with a signed permutation. St001935The number of ascents in a parking function. St000298The order dimension or Dushnik-Miller dimension of a poset. St000381The largest part of an integer composition. St000760The length of the longest strictly decreasing subsequence of parts of an integer composition. St000805The number of peaks of the associated bargraph. St000903The number of different parts of an integer composition. St000983The length of the longest alternating subword. St001194The injective dimension of $A/AfA$ in the corresponding Nakayama algebra $A$ when $Af$ is the minimal faithful projective-injective left $A$-module St001273The projective dimension of the first term in an injective coresolution of the regular module. St001372The length of a longest cyclic run of ones of a binary word. St001487The number of inner corners of a skew partition. St001589The nesting number of a perfect matching. 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 $eA$. St001526The Loewy length of the Auslander-Reiten translate of the regular module as a bimodule of the Nakayama algebra corresponding to the Dyck path. St001738The minimal order of a graph which is not an induced subgraph of the given graph.