St000996The number of exclusive left-to-right maxima of a permutation. St001067The number of simple modules of dominant dimension at least two in the corresponding Nakayama algebra. St001163The number of simple modules with dominant dimension at least three in the corresponding Nakayama algebra. St001189The number of simple modules with dominant and codominant dimension equal to zero in the Nakayama algebra corresponding to the Dyck path. 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 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 $eA$. St001223Number of indecomposable projective non-injective modules P such that the modules X and Y in a an Auslander-Reiten sequence ending at P are torsionless. St001233The number of indecomposable 2-dimensional modules with projective dimension one. St001266The largest vector space dimension of an indecomposable non-projective module that is reflexive in the corresponding Nakayama algebra. St001296The maximal torsionfree index of an indecomposable non-projective module in the corresponding Nakayama algebra. St001372The length of a longest cyclic run of ones of a binary word. St000308The height of the tree associated to a permutation. St000444The length of the maximal rise of a Dyck path. St000542The number of left-to-right-minima of a permutation. St000686The finitistic dominant dimension of a Dyck path. St000808The number of up steps of the associated bargraph. St000971The smallest closer of a set partition. St000991The number of right-to-left minima of a permutation. St001051The depth of the label 1 in the decreasing labelled unordered tree associated with the set partition. St001062The maximal size of a block of a set partition. St001201The grade of the simple module $S_0$ in the special CNakayama algebra corresponding to the Dyck path. St001203We associate to a CNakayama algebra (a Nakayama algebra with a cyclic quiver) with Kupisch series $L=[c_0,c_1,...,c_{n-1}]$ such that $n=c_0 < c_i$ for all $i > 0$ a Dyck path as follows: St001235The global dimension of the corresponding Comp-Nakayama algebra. St001239The largest vector space dimension of the double dual of a simple module in the corresponding Nakayama algebra. St001273The projective dimension of the first term in an injective coresolution of the regular module. St001390The number of bumps occurring when Schensted-inserting the letter 1 of a permutation. St001530The depth of a Dyck path. St000702The number of weak deficiencies of a permutation. St001052The length of the exterior of a permutation. St000982The length of the longest constant subword. St000335The difference of lower and upper interactions. St000999Number of indecomposable projective module with injective dimension equal to the global dimension in the Nakayama algebra corresponding to the Dyck path. St000771The largest multiplicity of a distance Laplacian eigenvalue in a connected graph. St001638The book thickness of a graph. St001088Number of indecomposable projective non-injective modules with dominant dimension equal to the injective dimension in the corresponding Nakayama algebra. St001933The largest multiplicity of a part in an integer partition. St000053The number of valleys of the Dyck path. St000120The number of left tunnels of a Dyck path. St000291The number of descents of a binary word. St000390The number of runs of ones in a binary word. St000667The greatest common divisor of the parts of the partition. 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. St001184Number of indecomposable injective modules with grade at least 1 in the corresponding Nakayama algebra. St001199The dominant dimension of $eAe$ for the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. 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. St001499The number of indecomposable projective-injective modules of a magnitude 1 Nakayama algebra. St001571The Cartan determinant of the integer partition. St000772The multiplicity of the largest distance Laplacian eigenvalue in a connected graph. St000454The largest eigenvalue of a graph if it is integral. St001330The hat guessing number of a graph. St001644The dimension of a graph. St000208Number of integral Gelfand-Tsetlin polytopes with prescribed top row and integer partition weight. St000668The least common multiple of the parts of the partition. St000707The product of the factorials of the parts. St000708The product of the parts of an integer partition. St000755The number of real roots of the characteristic polynomial of a linear recurrence associated with an integer partition. St000875The semilength of the longest Dyck word in the Catalan factorisation of a binary word. 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. St001250The number of parts of a partition that are not congruent 0 modulo 3. St001389The number of partitions of the same length below the given integer partition. St001527The cyclic permutation representation number of an integer partition. St000983The length of the longest alternating subword. St000259The diameter of a connected graph. St001075The minimal size of a block of a set partition. St001568The smallest positive integer that does not appear twice in the partition. St000846The maximal number of elements covering an element of a poset. St000207Number of integral Gelfand-Tsetlin polytopes with prescribed top row and integer composition weight. St000260The radius of a connected graph. St000704The number of semistandard tableaux on a given integer partition with minimal maximal entry. St001128The exponens consonantiae of a partition. St001432The order dimension of the partition. St001913The number of preimages of an integer partition in Bulgarian solitaire. St000993The multiplicity of the largest part of an integer partition. St000307The number of rowmotion orbits of a poset. St001630The global dimension of the incidence algebra of the lattice over the rational numbers. St000460The hook length of the last cell along the main diagonal of an integer partition. St000681The Grundy value of Chomp on Ferrers diagrams. St000870The product of the hook lengths of the diagonal cells in an integer partition. St001247The number of parts of a partition that are not congruent 2 modulo 3. St001249Sum of the odd parts of a 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. St001785The number of ways to obtain a partition as the multiset of antidiagonal lengths of the Ferrers diagram of a partition. St001914The size of the orbit of an integer partition in Bulgarian solitaire. St000633The size of the automorphism group of a poset. St000640The rank of the largest boolean interval in a poset. St000654The first descent of a permutation. St001596The number of two-by-two squares inside a skew partition. St001633The number of simple modules with projective dimension two in the incidence algebra of the poset. St001864The number of excedances of a signed permutation. St000005The bounce statistic of a Dyck path. St000006The dinv of a Dyck path. St000015The number of peaks of a Dyck path. St000026The position of the first return of a Dyck path. St000063The number of linear extensions of a certain poset defined for an integer partition. St000108The number of partitions contained in the given partition. St000144The pyramid weight of the Dyck path. St000288The number of ones in a binary word. St000293The number of inversions of a binary word. St000297The number of leading ones in a binary word. St000318The number of addable cells of the Ferrers diagram of an integer partition. St000395The sum of the heights of the peaks of a Dyck path. St000443The number of long tunnels of a Dyck path. St000476The sum of the semi-lengths of tunnels before a valley of a Dyck path. St000511The number of invariant subsets when acting with a permutation of given cycle type. St000519The largest length of a factor maximising the subword complexity. St000532The total number of rook placements on a Ferrers board. St000655The length of the minimal rise of a Dyck path. St000674The number of hills 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. St000733The row containing the largest entry of a standard tableau. St000734The last entry in the first row of a standard tableau. St000738The first entry in the last row of a standard tableau. St000759The smallest missing part in an integer partition. St000922The minimal number such that all substrings of this length are unique. St000930The k-Gorenstein degree of the corresponding Nakayama algebra with linear quiver. St000947The major index east count of a Dyck path. St000952Gives the number of irreducible factors of the Coxeter polynomial of the Dyck path over the rational numbers. St000955Number of times one has $Ext^i(D(A),A)>0$ for $i>0$ for the corresponding LNakayama algebra. 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. St001007Number of simple modules with projective dimension 1 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. St001013Number of indecomposable injective modules with codominant dimension equal to the global dimension in the Nakayama algebra corresponding to the Dyck path. St001014Number of indecomposable injective modules with codominant dimension equal to the dominant dimension of the Nakayama algebra corresponding to the Dyck path. 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. St001018Sum of projective dimension of the indecomposable injective modules of the Nakayama algebra corresponding to the Dyck path. St001024Maximum of dominant dimensions of the simple modules in the Nakayama algebra corresponding to the Dyck path. 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. St001068Number of torsionless simple modules in the corresponding Nakayama algebra. St001118The acyclic chromatic index of a graph. St001135The projective dimension of the first simple module in the Nakayama algebra corresponding to the Dyck path. St001161The major index north count of a Dyck path. St001165Number of simple modules with even projective dimension 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. St001183The maximum of $projdim(S)+injdim(S)$ over all simple modules in the Nakayama algebra corresponding to the Dyck path. St001187The number of simple modules with grade at least one in the corresponding Nakayama algebra. 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 $g$. St001202Call a CNakayama algebra (a Nakayama algebra with a cyclic quiver) with Kupisch series $L=[c_0,c_1,...,c_{n−1}]$ such that $n=c_0 < c_i$ for all $i > 0$ a special CNakayama algebra. St001224Let X be the direct sum of all simple modules of the corresponding Nakayama algebra. St001227The vector space dimension of the first extension group between the socle of the regular module and the Jacobson radical of the corresponding Nakayama algebra. St001241The number of non-zero radicals of the indecomposable projective modules that have injective dimension and projective dimension at most one. St001257The dominant dimension of the double dual of A/J when A is the corresponding Nakayama algebra with Jacobson radical J. St001258Gives the maximum of injective plus projective dimension of an indecomposable module over the corresponding Nakayama algebra. St001291The number of indecomposable summands of the tensor product of two copies of the dual of the Nakayama algebra associated to a 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. St001400The total number of Littlewood-Richardson tableaux of given shape. St001415The length of the longest palindromic prefix of a binary word. St001416The length of a longest palindromic factor of a binary word. St001417The length of a longest palindromic subword of a binary word. St001419The length of the longest palindromic factor beginning with a one of a binary word. St001436The index of a given binary word in the lex-order among all its cyclic shifts. St001462The number of factors of a standard tableaux under concatenation. St001471The magnitude of a Dyck path. St001481The minimal height of a peak of a Dyck path. St001488The number of corners of a skew partition. St001498The normalised height of a Nakayama algebra with magnitude 1. St001514The dimension of the top of the Auslander-Reiten translate of the regular modules as a bimodule. St001515The vector space dimension of the socle of the first syzygy module of the regular module (as a bimodule). St001523The degree of symmetry of a Dyck path. St001526The Loewy length of the Auslander-Reiten translate of the regular module as a bimodule of the Nakayama algebra corresponding to the Dyck path. St001614The cyclic permutation representation number of a skew partition. St001660The number of ways to place as many non-attacking rooks as possible on a skew Ferrers board. St001732The number of peaks visible from the left. St001733The number of weak left to right maxima of a Dyck path. St001814The number of partitions interlacing the given partition. St001955The number of natural descents for set-valued two row standard Young tableaux. St001959The product of the heights of the peaks of a Dyck path. St000245The number of ascents of a permutation. St000373The number of weak exceedences of a permutation that are also mid-points of a decreasing subsequence of length $3$. St000672The number of minimal elements in Bruhat order not less than the permutation. St000698The number of 2-rim hooks removed from an integer partition to obtain its associated 2-core. St000834The number of right outer peaks of a permutation. St000871The number of very big ascents of a permutation. St001086The number of occurrences of the consecutive pattern 132 in a permutation. St001232The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2. St000035The number of left outer peaks of a permutation. St000153The number of adjacent cycles of a permutation. St000742The number of big ascents of a permutation after prepending zero. St000080The rank of the poset. St000456The monochromatic index of a connected graph. St000741The Colin de Verdière graph invariant. St000845The maximal number of elements covered by an element in a poset. St001942The number of loops of the quiver corresponding to the reduced incidence algebra of a poset. St000455The second largest eigenvalue of a graph if it is integral. St000528The height of a poset. St000907The number of maximal antichains of minimal length in a poset. 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. St001782The order of rowmotion on the set of order ideals of a poset. St000028The number of stack-sorts needed to sort a permutation. St000451The length of the longest pattern of the form k 1 2. St000910The number of maximal chains of minimal length in a poset. St000914The sum of the values of the Möbius function of a poset. St001105The number of greedy linear extensions of a poset. St001106The number of supergreedy linear extensions of a poset. St001632The number of indecomposable injective modules $I$ with $dim Ext^1(I,A)=1$ for the incidence algebra A of a poset. St000618The number of self-evacuating tableaux of given shape. St000781The number of proper colouring schemes of a Ferrers diagram. St001780The order of promotion on the set of standard tableaux of given shape. St001899The total number of irreducible representations contained in the higher Lie character for an integer partition. St001900The number of distinct irreducible representations contained in the higher Lie character for an integer partition. St001901The largest multiplicity of an irreducible representation contained in the higher Lie character for an integer partition. St001908The number of semistandard tableaux of distinct weight whose maximal entry is the length of the partition. St001924The number of cells in an integer partition whose arm and leg length coincide. St001934The number of monotone factorisations of genus zero of a permutation of given cycle type. St000815The number of semistandard Young tableaux of partition weight of given shape. St001637The number of (upper) dissectors of a poset. St001668The number of points of the poset minus the width of the poset. St001890The maximum magnitude of the Möbius function of a poset. St000381The largest part of an integer composition. St001603The number of colourings of a polygon such that the multiplicities of a colour are given by a partition. St001207The Lowey length of the algebra $A/T$ when $T$ is the 1-tilting module corresponding to the permutation in the Auslander algebra of $K[x]/(x^n)$. St001730The number of times the path corresponding to a binary word crosses the base line. St001292The injective dimension of the tensor product of two copies of the dual of the Nakayama algebra associated to a Dyck path. St001294The maximal torsionfree index of a simple non-projective module in the corresponding Nakayama algebra. St001413Half the length of the longest even length palindromic prefix of a binary word. St001414Half the length of the longest odd length palindromic prefix of a binary word. St001421Half the length of a longest factor which is its own reverse-complement and begins with a one of a binary word. 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. St001578The minimal number of edges to add or remove to make a graph a line graph. St001960The number of descents of a permutation minus one if its first entry is not one. St000225Difference between largest and smallest parts in a partition. St000328The maximum number of child nodes in a tree. St000670The reversal length of a permutation. St000757The length of the longest weakly inreasing subsequence of parts of an integer composition. St000765The number of weak records in an integer composition. St001570The minimal number of edges to add to make a graph Hamiltonian. St001589The nesting number of a perfect matching. St001742The difference of the maximal and the minimal degree in a graph. St001566The length of the longest arithmetic progression in a permutation. St000863The length of the first row of the shifted shape of a permutation. St000848The balance constant multiplied with the number of linear extensions of a poset. St000849The number of 1/3-balanced pairs in a poset. St001878The projective dimension of the simple modules corresponding to the minimum of L in the incidence algebra of the lattice L. St000386The number of factors DDU in a Dyck path. St000706The product of the factorials of the multiplicities of an integer partition. St000884The number of isolated descents of a permutation. St000939The number of characters of the symmetric group whose value on the partition is positive. St000994The number of cycle peaks and the number of cycle valleys of a permutation. St001123The multiplicity of the dual of the standard representation in the Kronecker square corresponding to a partition. St001435The number of missing boxes in the first row. St001605The number of colourings of a cycle such that the multiplicities of colours are given by a partition. St000891The number of distinct diagonal sums of a permutation matrix. St001877Number of indecomposable injective modules with projective dimension 2. St001624The breadth of a lattice. St000510The number of invariant oriented cycles when acting with a permutation of given cycle type. St000292The number of ascents of a binary word. St000022The number of fixed points of a permutation. St000100The number of linear extensions of a poset. St000282The size of the preimage of the map 'to poset' from Ordered trees to Posets. St000327The number of cover relations in a poset. St000442The maximal area to the right of an up step of a Dyck path. St000524The number of posets with the same order polynomial. St000525The number of posets with the same zeta polynomial. St000526The number of posets with combinatorially isomorphic order polytopes. St000567The sum of the products of all pairs of parts. St000620The number of standard tableaux of shape equal to the given partition such that the minimal cyclic descent is odd. St000635The number of strictly order preserving maps of a poset into itself. St000656The number of cuts of a poset. St000675The number of centered multitunnels of a Dyck path. St000678The number of up steps after the last double rise of a Dyck path. St000680The Grundy value for Hackendot on posets. St000714The number of semistandard Young tableau of given shape, with entries at most 2. St000717The number of ordinal summands of a poset. St000731The number of double exceedences of a permutation. St000735The last entry on the main diagonal of a standard tableau. St000744The length of the path to the largest entry in a standard Young tableau. St000906The length of the shortest maximal chain in a poset. St001039The maximal height of a column in the parallelogram polyomino associated with a Dyck path. St001099The 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 leaf labelled binary trees. St001100The 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 leaf labelled trees. 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. St001115The number of even descents of a permutation. St001500The global dimension of magnitude 1 Nakayama algebras. St001501The dominant dimension of magnitude 1 Nakayama algebras. St000703The number of deficiencies of a permutation. St000214The number of adjacencies of a permutation. St000215The number of adjacencies of a permutation, zero appended. St001060The distinguishing index of a graph. St000011The number of touch points (or returns) of a Dyck path. St000352The Elizalde-Pak rank of a permutation. St000483The number of times a permutation switches from increasing to decreasing or decreasing to increasing. St000007The number of saliances of the permutation. St000366The number of double descents of a permutation. St000665The number of rafts of a permutation. St000031The number of cycles in the cycle decomposition of a permutation. St000237The number of small exceedances. St000919The number of maximal left branches of a binary tree. St001083The number of boxed occurrences of 132 in a permutation. St001394The genus of a permutation. St001629The coefficient of the integer composition in the quasisymmetric expansion of the relabelling action of the symmetric group on cycles. St000337The lec statistic, the sum of the inversion numbers of the hook factors of a permutation. St000371The number of mid points of decreasing subsequences of length 3 in a permutation. St000441The number of successions of a permutation. St000931The number of occurrences of the pattern UUU in a Dyck path. St001037The number of inner corners of the upper path of the parallelogram polyomino associated with the Dyck path. St000389The number of runs of ones of odd length in a binary word. St000568The hook number of a binary tree. St000659The number of rises of length at least 2 of a Dyck path. St001621The number of atoms of a lattice. St001769The reflection length of a signed permutation. St000098The chromatic number of a graph. St001626The number of maximal proper sublattices of a lattice. St001096The size of the overlap set of a permutation. St001581The achromatic number of a graph. St000046The largest eigenvalue of the random to random operator acting on the simple module corresponding to the given partition. St000359The number of occurrences of the pattern 23-1. St000534The number of 2-rises of a permutation. St001085The number of occurrences of the vincular pattern |21-3 in a permutation. 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 $eA$. 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 $eA$. 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 $eA$. St001262The dimension of the maximal parabolic seaweed algebra corresponding to the partition. St001283The number of finite solvable groups that are realised by the given partition over the complex numbers. St001284The number of finite groups that are realised by the given partition over the complex numbers. St001360The number of covering relations in Young's lattice below a partition. St001364The number of permutations whose cube equals a fixed permutation of given cycle type. St001378The product of the cohook lengths of the integer partition. St001442The number of standard Young tableaux whose major index is divisible by the size of a given integer partition. St001561The value of the elementary symmetric function evaluated at 1. St001562The value of the complete homogeneous symmetric function evaluated at 1. St001563The value of the power-sum symmetric function evaluated at 1. St001564The value of the forgotten symmetric functions when all variables set to 1. St001593This is the number of standard Young tableaux of the given shifted shape. St001599The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on rooted trees. St001600The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on simple graphs. St001601The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on trees. St001602The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on endofunctions. St001606The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on set partitions. St001607The number of coloured graphs such that the multiplicities of colours are given by a partition. St001608The number of coloured rooted trees such that the multiplicities of colours are given by a partition. St001609The number of coloured trees such that the multiplicities of colours are given by a partition. St001610The number of coloured endofunctions such that the multiplicities of colours are given by a partition. St001611The number of multiset partitions such that the multiplicities of elements are given by a partition. St001627The number of coloured connected graphs such that the multiplicities of colours are given by a partition. St001628The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on simple connected graphs. St001763The Hurwitz number of an integer partition. St001936The number of transitive factorisations of a permutation of given cycle type into star transpositions. St001938The number of transitive monotone factorizations of genus zero of a permutation of given cycle type. St000647The number of big descents of a permutation. St001090The number of pop-stack-sorts needed to sort a permutation. St001863The number of weak excedances of a signed permutation. St000137The Grundy value of an integer partition. St000145The Dyson rank of a partition. St000284The Plancherel distribution on integer partitions. St000319The spin of an integer partition. St000320The dinv adjustment of an integer partition. St000356The number of occurrences of the pattern 13-2. St000474Dyson's crank of a partition. St000477The weight of a partition according to Alladi. St000478Another weight of a partition according to Alladi. St000509The diagonal index (content) of a partition. St000514The number of invariant simple graphs when acting with a permutation of given cycle type. St000515The number of invariant set partitions when acting with a permutation of given cycle type. St000566The number of ways to select a row of a Ferrers shape and two cells in this row. St000770The major index of an integer partition when read from bottom to top. St000782The indicator function of whether a given perfect matching is an L & P matching. St000813The number of zero-one matrices with weakly decreasing column sums and row sums given by the partition. St000850The number of 1/2-balanced pairs in a poset. St000901The cube of the number of standard Young tableaux with shape given by the partition. St000934The 2-degree of an integer partition. St000940The number of characters of the symmetric group whose value on the partition is zero. St001175The size of a partition minus the hook length of the base cell. St001176The size of a partition minus its first part. St001279The sum of the parts of an integer partition that are at least two. St001280The number of parts of an integer partition that are at least two. 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. St001541The Gini index of an integer partition. St001714The number of subpartitions of an integer partition that do not dominate the conjugate subpartition. St001767The largest minimal number of arrows pointing to a cell in the Ferrers diagram in any assignment. St001918The degree of the cyclic sieving polynomial corresponding to an integer partition. St001961The sum of the greatest common divisors of all pairs of parts. St000201The number of leaf nodes in a binary tree. St000445The number of rises of length 1 of a Dyck path. St001693The excess length of a longest path consisting of elements and blocks of a set partition. St001893The flag descent of a signed permutation. St000013The height of a Dyck path. St000071The number of maximal chains in a poset. St001153The number of blocks with even minimum in a set partition. St001867The number of alignments of type EN of a signed permutation. St001896The number of right descents of a signed permutations. St000243The number of cyclic valleys and cyclic peaks of a permutation. St000786The maximal number of occurrences of a colour in a proper colouring of a graph. St000527The width of the poset. St000023The number of inner peaks of a permutation. St000174The flush statistic of a semistandard tableau. St000317The cycle descent number of a permutation. St000353The number of inner valleys of a permutation. St000486The number of cycles of length at least 3 of a permutation. St000646The number of big ascents of a permutation. St000663The number of right floats of a permutation. St000710The number of big deficiencies of a permutation. St000711The number of big exceedences of a permutation. St001469The holeyness of a permutation. St001470The cyclic holeyness of a permutation. St001712The number of natural descents of a standard Young tableau. St001728The number of invisible descents of a 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. St000062The length of the longest increasing subsequence of the permutation. St000092The number of outer peaks of a permutation. St000099The number of valleys of a permutation, including the boundary. St000162The number of nontrivial cycles in the cycle decomposition of a permutation. St000239The number of small weak excedances. St000254The nesting number of a set partition. St000354The number of recoils of a permutation. St000502The number of successions of a set partitions. St000864The number of circled entries of the shifted recording tableau of a permutation. St000887The maximal number of nonzero entries on a diagonal of a permutation matrix. St001061The number of indices that are both descents and recoils of a permutation. St001114The number of odd descents of a permutation. St001151The number of blocks with odd minimum. St001489The maximum of the number of descents and the number of inverse descents. St001652The length of a longest interval of consecutive numbers. St001662The length of the longest factor of consecutive numbers in a permutation. St001737The number of descents of type 2 in a permutation. St001905The number of preferred parking spots in a parking function less than the index of the car. St000824The sum of the number of descents and the number of recoils of a permutation. St001287The number of primes obtained by multiplying preimage and image of a permutation and subtracting one. St000004The major index of a permutation. St000021The number of descents of a permutation. St000034The maximum defect over any reduced expression for a permutation and any subexpression. St000039The number of crossings of a permutation. St000072The number of circled entries. St000083The number of left oriented leafs of a binary tree except the first one. St000091The descent variation of a composition. St000155The number of exceedances (also excedences) of a permutation. St000173The segment statistic of a semistandard tableau. St000196The number of occurrences of the contiguous pattern [[.,.],[.,. St000221The number of strong fixed points of a permutation. St000234The number of global ascents of a permutation. St000241The number of cyclical small excedances. St000247The number of singleton blocks of a set partition. St000331The number of upper interactions of a Dyck path. St000333The dez statistic, the number of descents of a permutation after replacing fixed points by zeros. St000338The number of pixed points of a permutation. St000360The number of occurrences of the pattern 32-1. St000365The number of double ascents of a permutation. St000375The number of non weak exceedences of a permutation that are mid-points of a decreasing subsequence of length $3$. St000461The rix statistic of a permutation. St000472The sum of the ascent bottoms of a permutation. St000650The number of 3-rises of a permutation. St000653The last descent of a permutation. St000677The standardized bi-alternating inversion number of a permutation. St000732The number of double deficiencies of a permutation. St000761The number of ascents in an integer composition. St000779The tier of a permutation. St000794The mak of a permutation. St000829The Ulam distance of a permutation to the identity permutation. St000836The number of descents of distance 2 of a permutation. St000837The number of ascents of distance 2 of a permutation. St000872The number of very big descents of a permutation. St000873The aix statistic of a permutation. St000961The shifted major index of a permutation. St000966Number of peaks minus the global dimension of the corresponding LNakayama algebra. St000989The number of final rises of a permutation. St001033The normalized area of the parallelogram polyomino associated with the Dyck path. St001036The number of inner corners of the parallelogram polyomino associated with the Dyck path. St001140Number of indecomposable modules with projective and injective dimension at least two in the corresponding Nakayama algebra. St001167The number of simple modules that appear as the top of an indecomposable non-projective modules that is reflexive in the corresponding Nakayama algebra. 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. St001253The number of non-projective indecomposable reflexive modules in the corresponding Nakayama algebra. St001269The sum of the minimum of the number of exceedances and deficiencies in each cycle of a permutation. St001298The number of repeated entries in the Lehmer code of a permutation. St001331The size of the minimal feedback vertex set. St001336The minimal number of vertices in a graph whose complement is triangle-free. St001388The number of non-attacking neighbors of a permutation. St001423The number of distinct cubes in a binary word. St001509The degree of the standard monomial associated to a Dyck path relative to the trivial lower boundary. St001520The number of strict 3-descents. St001549The number of restricted non-inversions between exceedances. St001552The number of inversions between excedances and fixed points of a permutation. St001559The number of transpositions that are smaller or equal to a permutation in Bruhat order while not being inversions. St001572The minimal number of edges to remove to make a graph bipartite. St001573The minimal number of edges to remove to make a graph triangle-free. St001575The minimal number of edges to add or remove to make a graph edge transitive. St001577The minimal number of edges to add or remove to make a graph a cograph. St001582The grades of the simple modules corresponding to the points in the poset of the symmetric group under the Bruhat order. St001640The number of ascent tops in the permutation such that all smaller elements appear before. St001665The number of pure excedances of a permutation. St001682The number of distinct positions of the pattern letter 1 in occurrences of 123 in a permutation. St001683The number of distinct positions of the pattern letter 3 in occurrences of 132 in a permutation. St001687The number of distinct positions of the pattern letter 2 in occurrences of 213 in a permutation. St001726The number of visible inversions of a permutation. St001729The number of visible descents of a permutation. St001744The number of occurrences of the arrow pattern 1-2 with an arrow from 1 to 2 in a permutation. St001761The maximal multiplicity of a letter in a reduced word of 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. St001811The Castelnuovo-Mumford regularity of a permutation. St001816Eigenvalues of the top-to-random operator acting on a simple module. St001822The number of alignments of a signed permutation. St001823The Stasinski-Voll length of a signed permutation. St001859The number of factors of the Stanley symmetric function associated with a permutation. St001866The nesting alignments of a signed permutation. St001871The number of triconnected components of a graph. St001874Lusztig's a-function for the symmetric group. St001882The number of occurrences of a type-B 231 pattern in a signed permutation. St001906Half of the difference between the total displacement and the number of inversions and the reflection length of a permutation. St001928The number of non-overlapping descents in a permutation. St001935The number of ascents in a parking function. St001946The number of descents in a parking function. St001948The number of augmented double ascents of a permutation. St000056The decomposition (or block) number of a permutation. St000089The absolute variation of a composition. St000105The number of blocks in the set partition. St000209Maximum difference of elements in cycles. St000213The number of weak exceedances (also weak excedences) of a permutation. St000236The number of cyclical small weak excedances. St000238The number of indices that are not small weak excedances. St000242The number of indices that are not cyclical small weak excedances. St000251The number of nonsingleton blocks of a set partition. St000253The crossing number of a set partition. St000272The treewidth of a graph. St000314The number of left-to-right-maxima of a permutation. St000316The number of non-left-to-right-maxima of a permutation. St000325The width of the tree associated to a permutation. St000340The number of non-final maximal constant sub-paths of length greater than one. St000362The size of a minimal vertex cover of a graph. St000387The matching number of a graph. St000470The number of runs in a permutation. St000488The number of cycles of a permutation of length at most 2. St000536The pathwidth of a graph. St000619The number of cyclic descents of a permutation. St000628The balance of a binary word. St000688The global dimension minus the dominant dimension of the LNakayama algebra associated to a Dyck path. St000723The maximal cardinality of a set of vertices with the same neighbourhood in a graph. St000774The maximal multiplicity of a Laplacian eigenvalue in a graph. St000776The maximal multiplicity of an eigenvalue in a graph. St000785The number of distinct colouring schemes of a graph. St000831The number of indices that are either descents or recoils. St000892The maximal number of nonzero entries on a diagonal of an alternating sign matrix. St000925The number of topologically connected components of a set partition. St000942The number of critical left to right maxima of the parking functions. St000956The maximal displacement of a permutation. St000964Gives the dimension of Ext^g(D(A),A) of the corresponding LNakayama algebra, when g denotes the global dimension of that algebra. St000965The sum of the dimension of Ext^i(D(A),A) for i=1,. St000985The number of positive eigenvalues of the adjacency matrix of the graph. St000986The multiplicity of the eigenvalue zero of the adjacency matrix of the graph. St001011Number of simple modules of projective dimension 2 in the Nakayama algebra corresponding to the Dyck path. St001026The maximum of the projective dimensions of the indecomposable non-projective injective modules minus the minimum in the Nakayama algebra corresponding to the Dyck path. St001066The number of simple reflexive modules in the corresponding Nakayama algebra. St001104The number of descents of the invariant in a tensor power of the adjoint representation of the rank two general linear group. St001125The number of simple modules that satisfy the 2-regular condition in the corresponding Nakayama algebra. St001126Number of simple module that are 1-regular in the corresponding Nakayama algebra. St001152The number of pairs with even minimum in a perfect matching. 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. St001220The width of a permutation. 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. St001230The number of simple modules with injective dimension equal to the dominant dimension equal to one and the dual property. 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. St001274The number of indecomposable injective modules with projective dimension equal to two. St001276The number of 2-regular indecomposable modules in the corresponding Nakayama algebra. St001277The degeneracy of a graph. St001278The number of indecomposable modules that are fixed by $\tau \Omega^1$ composed with its inverse in the corresponding Nakayama algebra. St001337The upper domination number of a graph. St001338The upper irredundance number 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. St001393The induced matching number of a graph. St001405The number of bonds in a permutation. St001461The number of topologically connected components of the chord diagram of a permutation. St001483The number of simple module modules that appear in the socle of the regular module but have no nontrivial selfextensions with the regular module. St001493The number of simple modules with maximal even projective dimension in the corresponding Nakayama algebra. St001503The largest distance of a vertex to a vertex in a cycle in the resolution quiver of the corresponding Nakayama algebra. 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. St001512The minimum rank of a graph. St001516The number of cyclic bonds of a permutation. St001524The degree of symmetry of a binary word. St001716The 1-improper chromatic number of a graph. St001734The lettericity of a graph. St001741The largest integer such that all patterns of this size are contained in the permutation. St001773The number of minimal elements in Bruhat order not less than the signed permutation. St001776The degree of the minimal polynomial of the largest Laplacian eigenvalue of a graph. St001778The largest greatest common divisor of an element and its image in a permutation. St001792The arboricity of a graph. St001806The upper middle entry of a permutation. St001807The lower middle entry of a permutation. St001812The biclique partition number of a graph. St001884The number of borders of a binary word. St000172The Grundy number of a graph. St000329The number of evenly positioned ascents of the Dyck path, with the initial position equal to 1. St000485The length of the longest cycle of a permutation. St000504The cardinality of the first block of a set partition. St000746The number of pairs with odd minimum in a perfect matching. St000820The number of compositions obtained by rotating the composition. St000822The Hadwiger number of the graph. St000844The size of the largest block in the direct sum decomposition of a permutation. St000904The maximal number of repetitions of an integer composition. St000918The 2-limited packing number of a graph. St001029The size of the core of a graph. St001108The 2-dynamic chromatic number of a graph. St001116The game chromatic number of a graph. St001245The cyclic maximal difference between two consecutive entries of a permutation. St001246The maximal difference between two consecutive entries of a permutation. St001261The Castelnuovo-Mumford regularity of a graph. St001285The number of primes in the column sums of the two line notation of a permutation. St001290The first natural number n such that the tensor product of n copies of D(A) is zero for the corresponding Nakayama algebra A. St001302The number of minimally dominating sets of vertices of a graph. St001304The number of maximally independent sets of vertices of a graph. St001346The number of parking functions that give the same permutation. St001494The Alon-Tarsi number of a graph. St001580The acyclic chromatic number of a graph. St001670The connected partition number of a graph. St001760The number of prefix or suffix reversals needed to sort a permutation. St001902The number of potential covers of a poset. St001963The tree-depth of a graph. St000638The number of up-down runs of a permutation. St001004The number of indices that are either left-to-right maxima or right-to-left minima. St001028Number of simple modules with injective dimension equal to the dominant dimension in the Nakayama algebra corresponding to the Dyck path. St001077The prefix exchange distance of a permutation. St001288The number of primes obtained by multiplying preimage and image of a permutation and adding one. St001505The number of elements generated by the Dyck path as a map in the full transformation monoid. St000882The number of connected components of short braid edges in the graph of braid moves of a permutation. St001399The distinguishing number of a poset.