St000149The number of cells of the partition whose leg is zero and arm is odd. St000256The number of parts from which one can substract 2 and still get an integer partition. St000377The dinv defect of an integer partition. St000473The number of parts of a partition that are strictly bigger than the number of ones. St000480The number of lower covers of a partition in dominance order. St000752The Grundy value for the game 'Couples are forever' on an integer partition. St000921The number of internal inversions of a binary word. St001092The number of distinct even parts of a partition. St001104The number of descents of the invariant in a tensor power of the adjoint representation of the rank two general linear group. St001115The number of even descents of a permutation. St001251The number of parts of a partition that are not congruent 1 modulo 3. St001311The cyclomatic number of a graph. St001317The minimal number of occurrences of the forest-pattern in a linear ordering of the vertices of the graph. St001319The minimal number of occurrences of the star-pattern in a linear ordering of the vertices of the graph. St001320The minimal number of occurrences of the path-pattern in a linear ordering of the vertices of the graph. St001328The minimal number of occurrences of the bipartite-pattern in a linear ordering of the vertices of the graph. St001331The size of the minimal feedback vertex set. St001335The cardinality of a minimal cycle-isolating set of a graph. St001336The minimal number of vertices in a graph whose complement is triangle-free. St001638The book thickness of a graph. St001736The total number of cycles in a graph. St001797The number of overfull subgraphs of a graph. St000179The product of the hook lengths of the integer partition. St000184The size of the centralizer of any permutation of given cycle type. St000201The number of leaf nodes in a binary tree. St000321The number of integer partitions of n that are dominated by an integer partition. St000345The number of refinements of a partition. St000346The number of coarsenings of a partition. St000352The Elizalde-Pak rank of a permutation. St000396The register function (or Horton-Strahler number) of a binary tree. St000470The number of runs in a permutation. St000482The (zero)-forcing number of a graph. St000531The leading coefficient of the rook polynomial of an integer partition. St000630The length of the shortest palindromic decomposition of a binary word. St000701The protection number of a binary tree. St000758The length of the longest staircase fitting into an integer composition. St000774The maximal multiplicity of a Laplacian eigenvalue in a graph. St000847The number of standard Young tableaux whose descent set is the binary word. St000862The number of parts of the shifted shape of a permutation. St000920The logarithmic height of a Dyck path. St000935The number of ordered refinements of an integer partition. St000983The length of the longest alternating subword. St000994The number of cycle peaks and the number of cycle valleys of a permutation. St001313The number of Dyck paths above the lattice path given by a binary word. St001359The number of permutations in the equivalence class of a permutation obtained by taking inverses of cycles. 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. St001710The number of permutations such that conjugation with a permutation of given cycle type yields the inverse permutation. St001732The number of peaks visible from the left. St001735The number of permutations with the same set of runs. St001741The largest integer such that all patterns of this size are contained in the permutation. St001758The number of orbits of promotion on a graph. St001917The order of toric promotion on the set of labellings of a graph. St000057The Shynar inversion number of a standard tableau. 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. St000196The number of occurrences of the contiguous pattern [[.,.],[.,. St000204The number of internal nodes of a binary tree. St000257The number of distinct parts of a partition that occur at least twice. St000291The number of descents of a binary word. St000292The number of ascents of a binary word. St000348The non-inversion sum of a binary word. St000386The number of factors DDU in a Dyck path. St000431The number of occurrences of the pattern 213 or of the pattern 321 in a permutation. St000433The number of occurrences of the pattern 132 or of the pattern 321 in a permutation. St000481The number of upper covers of a partition in dominance order. St000513The number of invariant subsets of size 2 when acting with a permutation of given cycle type. St000547The number of even non-empty partial sums of an integer partition. St000628The balance of a binary word. St000647The number of big descents of a permutation. St000648The number of 2-excedences of a permutation. St000660The number of rises of length at least 3 of a Dyck path. St000682The Grundy value of Welter's game on a binary word. St000691The number of changes of a binary word. St000875The semilength of the longest Dyck word in the Catalan factorisation of a binary word. St000884The number of isolated descents of a permutation. St001026The maximum of the projective dimensions of the indecomposable non-projective injective modules minus the minimum in the Nakayama algebra corresponding to the Dyck path. St001036The number of inner corners of the parallelogram polyomino associated with the Dyck path. St001037The number of inner corners of the upper path of the parallelogram polyomino associated with the Dyck path. St001252Half the sum of the even parts of a partition. St001382The number of boxes in the diagram of a partition that do not lie in its Durfee square. St001420Half the length of a longest factor which is its own reverse-complement of a binary word. St001421Half the length of a longest factor which is its own reverse-complement and begins with a one of a binary word. St001588The number of distinct odd parts smaller than the largest even part in an integer partition. St001665The number of pure excedances of a permutation. St001673The degree of asymmetry of an integer composition. St001699The major index of a standard tableau minus the weighted size of its shape. St001729The number of visible descents of a permutation. St001737The number of descents of type 2 in a permutation. St001810The number of fixed points of a permutation smaller than its largest moved point. St001928The number of non-overlapping descents in a permutation. St001035The convexity degree of the parallelogram polyomino associated with the Dyck path. St000568The hook number of a binary tree. St000619The number of cyclic descents of a permutation. St000652The maximal difference between successive positions of a permutation. St000659The number of rises of length at least 2 of a Dyck path. St000834The number of right outer peaks of a permutation. St000886The number of permutations with the same antidiagonal sums. St001499The number of indecomposable projective-injective modules of a magnitude 1 Nakayama algebra. St000293The number of inversions of a binary word. St000347The inversion sum of a binary word. St000353The number of inner valleys of a permutation. St000369The dinv deficit of a Dyck path. St000376The bounce deficit of a Dyck path. St000432The number of occurrences of the pattern 231 or of the pattern 312 in a permutation. St000434The number of occurrences of the pattern 213 or of the pattern 312 in a permutation. St000435The number of occurrences of the pattern 213 or of the pattern 231 in a permutation. St000436The number of occurrences of the pattern 231 or of the pattern 321 in a permutation. St000462The major index minus the number of excedences of a permutation. St000486The number of cycles of length at least 3 of a permutation. St000538The number of even inversions of a permutation. St000661The number of rises of length 3 of a Dyck path. St000710The number of big deficiencies of a permutation. St000791The number of pairs of left tunnels, one strictly containing the other, of a Dyck path. St000836The number of descents of distance 2 of a permutation. St000931The number of occurrences of the pattern UUU in a Dyck path. St001436The index of a given binary word in the lex-order among all its cyclic shifts. St000424The number of occurrences of the pattern 132 or of the pattern 231 in a permutation. St000662The staircase size of the code of a permutation. St000035The number of left outer peaks of a permutation. St000237The number of small exceedances. St000426The number of occurrences of the pattern 132 or of the pattern 312 in a permutation. St000624The normalized sum of the minimal distances to a greater element. St001727The number of invisible inversions of a permutation. St000883The number of longest increasing subsequences of a permutation. St000988The orbit size of a permutation under Foata's bijection. St001498The normalised height of a Nakayama algebra with magnitude 1. St000646The number of big ascents of a permutation. St000663The number of right floats of a permutation. St001078The minimal number of occurrences of (12) in a factorization of a permutation into transpositions (12) and cycles (1,. St001469The holeyness of a permutation. St000079The number of alternating sign matrices for a given Dyck path. St000092The number of outer peaks of a permutation. St000099The number of valleys of a permutation, including the boundary. St001476The evaluation of the Tutte polynomial of the graph at (x,y) equal to (1,-1). St000023The number of inner peaks of a permutation. St000095The number of triangles of a graph. 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. St001798The difference of the number of edges in a graph and the number of edges in the complement of the Turán graph. St000325The width of the tree associated to a permutation. St000387The matching number of a graph. St000955Number of times one has $Ext^i(D(A),A)>0$ for $i>0$ for the corresponding LNakayama algebra. St000959The number of strong Bruhat factorizations of a permutation. St000021The number of descents of a permutation. St000162The number of nontrivial cycles in the cycle decomposition of a permutation. St000222The number of alignments in the permutation. St000242The number of indices that are not cyclical small weak excedances. St000427The number of occurrences of the pattern 123 or of the pattern 231 in a permutation. St000428The number of occurrences of the pattern 123 or of the pattern 213 in a permutation. St000430The number of occurrences of the pattern 123 or of the pattern 312 in a permutation. St000437The number of occurrences of the pattern 312 or of the pattern 321 in a permutation. St000711The number of big exceedences of a permutation. 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. St001264The smallest index i such that the i-th simple module has projective dimension equal to the global dimension of the corresponding Nakayama algebra. St001471The magnitude of a Dyck path. St000771The largest multiplicity of a distance Laplacian eigenvalue in a connected graph. St000772The multiplicity of the largest distance Laplacian eigenvalue in a connected graph. St000837The number of ascents of distance 2 of a permutation. St001174The Gorenstein dimension of the algebra $A/I$ when $I$ is the tilting module corresponding to the permutation in the Auslander algebra of $K[x]/(x^n)$. St001731The factorization defect of a permutation. St001859The number of factors of the Stanley symmetric function associated with a permutation. St001640The number of ascent tops in the permutation such that all smaller elements appear before. St000258The burning number of a graph. St000299The number of nonisomorphic vertex-induced subtrees. St000452The number of distinct eigenvalues of a graph. St000453The number of distinct Laplacian eigenvalues of a graph. St000755The number of real roots of the characteristic polynomial of a linear recurrence associated with an integer partition. St000777The number of distinct eigenvalues of the distance Laplacian of a connected graph. St000918The 2-limited packing number of a graph. St001044The number of pairs whose larger element is at most one more than half the size of the perfect matching. St001093The detour number of a graph. St001261The Castelnuovo-Mumford regularity of a graph. St001315The dissociation number of a graph. St001318The number of vertices of the largest induced subforest with the same number of connected components of a graph. St001321The number of vertices of the largest induced subforest of a graph. St001608The number of coloured rooted trees such that the multiplicities of colours are given by a partition. St001674The number of vertices of the largest induced star graph in the graph. St001914The size of the orbit of an integer partition in Bulgarian solitaire. St000259The diameter of a connected graph. St000260The radius of a connected graph. St000535The rank-width of a graph. St000985The number of positive eigenvalues of the adjacency matrix of the graph. St001071The beta invariant of the graph. St001271The competition number of a graph. St001280The number of parts of an integer partition that are at least two. St001333The cardinality of a minimal edge-isolating set of a graph. St001340The cardinality of a minimal non-edge isolating set of a graph. St001349The number of different graphs obtained from the given graph by removing an edge. St001354The number of series nodes in the modular decomposition of a graph. St001393The induced matching number of a graph. St001512The minimum rank of a graph. St001587Half of the largest even part of an integer partition. 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. St000208Number of integral Gelfand-Tsetlin polytopes with prescribed top row and integer partition weight. St000460The hook length of the last cell along the main diagonal of an integer partition. St000476The sum of the semi-lengths of tunnels before a valley of a Dyck path. St000734The last entry in the first row of a standard tableau. St000870The product of the hook lengths of the diagonal cells in an integer partition. St001043The depth of the leaf closest to the root in the binary unordered tree associated with the perfect matching. St001199The dominant dimension of $eAe$ for the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. St001360The number of covering relations in Young's lattice below a partition. St001378The product of the cohook lengths of the integer partition. St001380The number of monomer-dimer tilings of a Ferrers diagram. St001389The number of partitions of the same length below the given integer partition. St001600The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on simple graphs. St001607The number of coloured graphs such that the multiplicities of colours are given by a partition. St001611The number of multiset partitions such that the multiplicities of elements are given by a partition. St001642The Prague dimension of a graph. St001746The coalition number of a graph. St001785The number of ways to obtain a partition as the multiset of antidiagonal lengths of the Ferrers diagram of a partition. St000319The spin of an integer partition. St000320The dinv adjustment of an integer partition. St000741The Colin de Verdière graph invariant. St001061The number of indices that are both descents and recoils of a permutation. St001384The number of boxes in the diagram of a partition that do not lie in the largest triangle it contains. St001411The number of patterns 321 or 3412 in a permutation. St001657The number of twos in an integer partition. St000668The least common multiple of the parts of the partition. St001514The dimension of the top of the Auslander-Reiten translate of the regular modules as a bimodule. St000155The number of exceedances (also excedences) of a permutation. St000243The number of cyclic valleys and cyclic peaks of a permutation. St000333The dez statistic, the number of descents of a permutation after replacing fixed points by zeros. St000958The number of Bruhat factorizations of a permutation. St001039The maximal height of a column in the parallelogram polyomino associated with a Dyck path. St001194The injective dimension of $A/AfA$ in the corresponding Nakayama algebra $A$ when $Af$ is the minimal faithful projective-injective left $A$-module St001220The width of a permutation. St001269The sum of the minimum of the number of exceedances and deficiencies in each cycle of a permutation. St001941The evaluation at 1 of the modified Kazhdan--Lusztig R polynomial (as in [1, Section 5. St000034The maximum defect over any reduced expression for a permutation and any subexpression. St000872The number of very big descents of a permutation. St001140Number of indecomposable modules with projective and injective dimension at least two in the corresponding Nakayama algebra. St001165Number of simple modules with even projective 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. St001258Gives the maximum of injective plus projective dimension of an indecomposable module over the corresponding Nakayama algebra. St001513The number of nested exceedences of a permutation. St001745The number of occurrences of the arrow pattern 13 with an arrow from 1 to 2 in a permutation. St001557The number of inversions of the second entry of a permutation. St000706The product of the factorials of the multiplicities of an integer partition. St000880The number of connected components of long braid edges in the graph of braid moves of a permutation. St000993The multiplicity of the largest part of an integer partition. St001568The smallest positive integer that does not appear twice in the partition. St000881The number of short braid edges in the graph of braid moves of a permutation. St000929The constant term of the character polynomial of an integer partition. St001960The number of descents of a permutation minus one if its first entry is not one. St001291The number of indecomposable summands of the tensor product of two copies of the dual of the Nakayama algebra associated to a Dyck path. St001645The pebbling number of a connected graph. St000466The Gutman (or modified Schultz) index of a connected graph. St001195The global dimension of the algebra $A/AfA$ of the corresponding Nakayama algebra $A$ with minimal left faithful projective-injective module $Af$. St001553The number of indecomposable summands of the square of the Jacobson radical as a bimodule in the Nakayama algebra corresponding to the Dyck path. St001171The vector space dimension of $Ext_A^1(I_o,A)$ when $I_o$ is the tilting module corresponding to the permutation $o$ in the Auslander algebra $A$ of $K[x]/(x^n)$. St001520The number of strict 3-descents. St001526The Loewy length of the Auslander-Reiten translate of the regular module as a bimodule of the Nakayama algebra corresponding to the Dyck path. 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. St000939The number of characters of the symmetric group whose value on the partition is positive. St001630The global dimension of the incidence algebra of the lattice over the rational numbers. St001704The size of the largest multi-subset-intersection of the deck of a graph with the deck of another graph. St001878The projective dimension of the simple modules corresponding to the minimum of L in the incidence algebra of the lattice L. St000264The girth of a graph, which is not a tree. St000284The Plancherel distribution on integer partitions. St000620The number of standard tableaux of shape equal to the given partition such that the minimal cyclic descent is odd. St000698The number of 2-rim hooks removed from an integer partition to obtain its associated 2-core. St000704The number of semistandard tableaux on a given integer partition with minimal maximal entry. St000813The number of zero-one matrices with weakly decreasing column sums and row sums given by the partition. St000901The cube of the number of standard Young tableaux with shape given by the partition. St000934The 2-degree of an integer partition. St001128The exponens consonantiae of a partition. St000567The sum of the products of all pairs of parts. St000621The number of standard tableaux of shape equal to the given partition such that the minimal cyclic descent is even. St000936The number of even values of the symmetric group character corresponding to the partition. St000938The number of zeros of the symmetric group character corresponding to the partition. St000940The number of characters of the symmetric group whose value on the partition is zero. St000941The number of characters of the symmetric group whose value on the partition is even. St001097The coefficient of the monomial symmetric function indexed by the partition in the formal group law for linear orders. St001098The 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 vertex labelled trees. 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. St001124The multiplicity of the standard representation in the Kronecker square corresponding to a partition. St000455The second largest eigenvalue of a graph if it is integral. St000707The product of the factorials of the parts. 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. St000510The number of invariant oriented cycles 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. St000681The Grundy value of Chomp on Ferrers diagrams. St000770The major index of an integer partition when read from bottom to top. St000815The number of semistandard Young tableaux of partition weight of given shape. St001123The multiplicity of the dual of the standard representation in the Kronecker square corresponding to a partition. St001200The number of simple modules in $eAe$ with projective dimension at most 2 in the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. St001207The Lowey length of the algebra $A/T$ when $T$ is the 1-tilting module corresponding to the permutation in the Auslander algebra of $K[x]/(x^n)$. St000379The number of Hamiltonian cycles in a graph. St000478Another weight of a partition according to Alladi. St000512The number of invariant subsets of size 3 when acting with a permutation of given cycle type. St000699The toughness times the least common multiple of 1,. St000928The sum of the coefficients of the character polynomial of an integer partition. St001281The normalized isoperimetric number of a graph. St001592The maximal number of simple paths between any two different vertices of a graph. St000716The dimension of the irreducible representation of Sp(6) labelled by an integer partition. St001942The number of loops of the quiver corresponding to the reduced incidence algebra of a poset. 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. St001095The number of non-isomorphic posets with precisely one further covering relation. St000980The number of boxes weakly below the path and above the diagonal that lie below at least two peaks. St001141The number of occurrences of hills of size 3 in a Dyck path. St001502The global dimension minus the dominant dimension of magnitude 1 Nakayama algebras. St001651The Frankl number of a lattice. St001060The distinguishing index of a graph. St000456The monochromatic index of a connected graph. St001632The number of indecomposable injective modules $I$ with $dim Ext^1(I,A)=1$ for the incidence algebra A of a poset. St000302The determinant of the distance matrix of a connected graph. St000467The hyper-Wiener index of a connected graph. St001232The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2. St001964The interval resolution global dimension of a poset. St001118The acyclic chromatic index of a graph. St000046The largest eigenvalue of the random to random operator acting on the simple module corresponding to the given partition. St000137The Grundy value of an integer partition. St000207Number of integral Gelfand-Tsetlin polytopes with prescribed top row and integer composition weight. St000618The number of self-evacuating tableaux of given shape. St000667The greatest common divisor of the parts of the partition. St000781The number of proper colouring schemes of a Ferrers diagram. St001122The multiplicity of the sign representation in the Kronecker square corresponding to a partition. St001247The number of parts of a partition that are not congruent 2 modulo 3. St001249Sum of the odd parts of a partition. St001250The number of parts of a partition that are not congruent 0 modulo 3. 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. St001364The number of permutations whose cube equals a fixed permutation of given cycle type. St001383The BG-rank of an integer partition. St001432The order dimension of the partition. St001442The number of standard Young tableaux whose major index is divisible by the size of a given integer partition. St001525The number of symmetric hooks on the diagonal of a partition. St001527The cyclic permutation representation number of an integer partition. St001529The number of monomials in the expansion of the nabla operator applied to the power-sum symmetric function indexed by the 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. St001571The Cartan determinant of the integer partition. 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. 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. 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. St001606The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on set partitions. 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. 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. St001629The coefficient of the integer composition in the quasisymmetric expansion of the relabelling action of the symmetric group on cycles. St001763The Hurwitz number of an integer partition. St001780The order of promotion on the set of standard tableaux of given shape. St001876The number of 2-regular simple modules in the incidence algebra of the lattice. 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. St001913The number of preimages of an integer partition in Bulgarian solitaire. St001924The number of cells in an integer partition whose arm and leg length coincide. St001933The largest multiplicity of a part in an integer partition. 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. St001939The number of parts that are equal to their multiplicity in the integer partition. St001940The number of distinct parts that are equal to their multiplicity in the integer partition. St001943The sum of the squares of the hook lengths of an integer partition. St000145The Dyson rank of a partition. St000175Degree of the polynomial counting the number of semistandard Young tableaux when stretching the shape. St000205Number of non-integral Gelfand-Tsetlin polytopes with prescribed top row and partition weight. St000206Number of non-integral Gelfand-Tsetlin polytopes with prescribed top row and integer composition weight. St000225Difference between largest and smallest parts in a partition. St000506The number of standard desarrangement tableaux of shape equal to the given partition. St000749The smallest integer d such that the restriction of the representation corresponding to a partition of n to the symmetric group on n-d letters has a constituent of odd degree. St000944The 3-degree of an integer partition. St001175The size of a partition minus the hook length of the base cell. St001176The size of a partition minus its first part. St001177Twice the mean value of the major index among all standard Young tableaux of a partition. St001178Twelve times the variance of the major index among all standard Young tableaux of a partition. St001248Sum of the even parts of a partition. St001279The sum of the parts of an integer partition that are at least two. St001392The largest nonnegative integer which is not a part and is smaller than the largest part of the partition. St001440The number of standard Young tableaux whose major index is congruent one modulo the size of a given integer partition. St001541The Gini index of an integer partition. St001570The minimal number of edges to add to make a graph Hamiltonian. St001586The number of odd parts smaller than the largest even part in an integer partition. St001714The number of subpartitions of an integer partition that do not dominate the conjugate subpartition. St001912The length of the preperiod in Bulgarian solitaire corresponding to an integer partition. St001961The sum of the greatest common divisors of all pairs of parts. St000474Dyson's crank of a partition. St000014The number of parking functions supported by a Dyck path. St000015The number of peaks 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. St000181The number of connected components of the Hasse diagram for the poset. St000289The decimal representation of a binary word. St000294The number of distinct factors of a binary word. St000318The number of addable cells of the Ferrers diagram of an integer partition. St000380Half of the maximal perimeter of a rectangle fitting into the diagram of an integer partition. St000393The number of strictly increasing runs in a binary word. St000395The sum of the heights of the peaks of a Dyck path. St000420The number of Dyck paths that are weakly above a Dyck path. St000439The position of the first down step of a Dyck path. St000464The Schultz index of a connected graph. St000511The number of invariant subsets when acting with a permutation of given cycle type. St000518The number of distinct subsequences in a binary word. St000529The number of permutations whose descent word is the given binary word. St000532The total number of rook placements on a Ferrers board. St000543The size of the conjugacy class of a binary word. St000626The minimal period of a binary word. St000674The number of hills of a Dyck path. St000678The number of up steps after the last double rise 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. St000759The smallest missing part in an integer partition. St000930The k-Gorenstein degree of the corresponding Nakayama algebra with linear quiver. St000949Gives the number of generalised tilting modules of the corresponding LNakayama algebra. St000950Number of tilting modules of the corresponding LNakayama algebra, where a tilting module is a generalised tilting module of projective dimension 1. St000952Gives the number of irreducible factors of the Coxeter polynomial of the Dyck path over the rational numbers. St000953The largest degree of an irreducible factor of the Coxeter polynomial of the Dyck path over the rational numbers. St000968We make a CNakayama algebra out of the LNakayama algebra (corresponding to the Dyck path) $[c_0,c_1,...,c_{n−1}]$ by adding $c_0$ to $c_{n−1}$. St000969We make a CNakayama algebra out of the LNakayama algebra (corresponding to the Dyck path) $[c_0,c_1,...,c_{n-1}]$ by adding $c_0$ to $c_{n-1}$. St000998Number of indecomposable projective modules with injective dimension smaller than or equal to the dominant dimension in the Nakayama algebra corresponding to the Dyck path. St001012Number of simple modules with projective dimension at most 2 in the Nakayama algebra corresponding to the Dyck path. St001018Sum of projective dimension of the indecomposable injective modules of the Nakayama algebra corresponding to the Dyck path. St001020Sum of the codominant dimensions of the non-projective indecomposable injective modules of the Nakayama algebra corresponding to the Dyck path. St001023Number of simple modules with projective dimension at most 3 in the Nakayama algebra corresponding to the Dyck path. St001024Maximum of dominant dimensions of the simple modules in the Nakayama algebra corresponding to the Dyck path. St001028Number of simple modules with injective dimension equal to the dominant dimension in the Nakayama algebra corresponding to the Dyck path. St001032The number of horizontal steps in the bicoloured Motzkin path associated with the Dyck path. St001038The minimal height of a column in the parallelogram polyomino associated with the Dyck path. St001065Number of indecomposable reflexive modules in the corresponding Nakayama algebra. St001068Number of torsionless simple modules in the corresponding Nakayama algebra. St001135The projective dimension of the first simple module in the Nakayama algebra corresponding to the Dyck path. St001166Number of indecomposable projective non-injective modules with dominant dimension equal to the global dimension plus the number of indecomposable projective injective modules in the corresponding Nakayama algebra. St001170Number of indecomposable injective modules whose socle has projective dimension at most g-1 when g denotes the global dimension in the corresponding Nakayama algebra. St001179Number of indecomposable injective modules with projective dimension at most 2 in the corresponding Nakayama algebra. St001180Number of indecomposable injective modules with projective dimension at most 1. St001190Number of simple modules with projective dimension at most 4 in the corresponding Nakayama algebra. 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 $eA$. St001201The grade of the simple module $S_0$ in the special CNakayama algebra corresponding to the Dyck path. 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. 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: 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 $eA$. St001211The number of simple modules in the corresponding Nakayama algebra that have vanishing second Ext-group with the regular module. St001213The number of indecomposable modules in the corresponding Nakayama algebra that have vanishing first Ext-group with the regular module. 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. 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. St001239The largest vector space dimension of the double dual of a simple module in the corresponding Nakayama algebra. St001240The number of indecomposable modules e_i J^2 that have injective dimension at most one in the corresponding Nakayama algebra St001242The toal dimension of certain Sn modules determined by LLT polynomials associated with a Dyck path. St001243The sum of coefficients in the Schur basis of certain LLT polynomials associated with a Dyck path. 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. St001257The dominant dimension of the double dual of A/J when A is the corresponding Nakayama algebra with Jacobson radical J. St001259The vector space dimension of the double dual of D(A) in the corresponding Nakayama algebra. St001267The length of the Lyndon factorization of the binary word. St001275The projective dimension of the second term in a minimal injective coresolution of the regular module. St001290The first natural number n such that the tensor product of n copies of D(A) is zero for the corresponding Nakayama algebra A. St001299The product of all non-zero projective dimensions of simple modules of the corresponding Nakayama algebra. St001348The bounce of the parallelogram polyomino associated with the Dyck path. St001361The number of lattice paths of the same length that stay weakly above a Dyck path. St001365The number of lattice paths of the same length weakly above the path given by a binary word. St001400The total number of Littlewood-Richardson tableaux of given shape. St001437The flex of a binary word. St001492The number of simple modules that do not appear in the socle of the regular module or have no nontrivial selfextensions with the regular module in the corresponding Nakayama algebra. St001500The global dimension of magnitude 1 Nakayama algebras. St001501The dominant dimension of magnitude 1 Nakayama algebras. St001504The sum of all indegrees of vertices with indegree at least two in the resolution quiver of a Nakayama algebra corresponding to the Dyck path. St001505The number of elements generated by the Dyck path as a map in the full transformation monoid. St001523The degree of symmetry of a Dyck path. St001530The depth of a Dyck path. St001545The second Elser number of a connected graph. St001650The order of Ringel's homological bijection associated to the linear Nakayama algebra corresponding to the Dyck path. St001658The total number of rook placements on a Ferrers board. St001669The number of single rises in a Dyck path. St001688The sum of the squares of the heights of the peaks of a Dyck path. St001733The number of weak left to right maxima of a Dyck path. St001808The box weight or horizontal decoration of a Dyck path. St001814The number of partitions interlacing the given partition. St001885The number of binary words with the same proper border set. St001890The maximum magnitude of the Möbius function of a poset. St001915The size of the component corresponding to a necklace in Bulgarian solitaire. St000003The number of standard Young tableaux of the partition. St000005The bounce statistic of a Dyck path. St000006The dinv of a Dyck path. St000010The length of the partition. St000026The position of the first return of a Dyck path. St000032The number of elements smaller than the given Dyck path in the Tamari Order. St000038The product of the heights of the descending steps of a Dyck path. St000045The number of linear extensions of a binary tree. St000048The multinomial of the parts of a partition. St000049The number of set partitions whose sorted block sizes correspond to the partition. St000053The number of valleys of the Dyck path. St000075The orbit size of a standard tableau under promotion. St000088The row sums of the character table of the symmetric group. St000117The number of centered tunnels of a Dyck path. St000120The number of left tunnels of a Dyck path. St000147The largest part of an integer partition. St000148The number of odd parts of a partition. St000159The number of distinct parts of the integer partition. St000160The multiplicity of the smallest part of a partition. St000182The number of permutations whose cycle type is the given integer partition. St000183The side length of the Durfee square of an integer partition. St000212The number of standard Young tableaux for an integer partition such that no two consecutive entries appear in the same row. St000228The size of a partition. St000275Number of permutations whose sorted list of non zero multiplicities of the Lehmer code is the given partition. St000278The size of the preimage of the map 'to partition' from Integer compositions to Integer partitions. St000288The number of ones in a binary word. St000290The major index of a binary word. St000296The length of the symmetric border of a binary word. St000297The number of leading ones in a binary word. St000306The bounce count of a Dyck path. St000326The position of the first one in a binary word after appending a 1 at the end. St000331The number of upper interactions of a Dyck path. St000335The difference of lower and upper interactions. St000378The diagonal inversion number of an integer partition. St000384The maximal part of the shifted composition of an integer partition. St000389The number of runs of ones of odd length in a binary word. St000390The number of runs of ones in a binary word. St000391The sum of the positions of the ones in a binary word. St000392The length of the longest run of ones in a binary word. St000418The number of Dyck paths that are weakly below a Dyck path. St000419The number of Dyck paths that are weakly above the Dyck path, except for the path itself. St000438The position of the last up step in a Dyck path. St000443The number of long tunnels of a Dyck path. St000444The length of the maximal rise of a Dyck path. St000459The hook length of the base cell of a partition. St000475The number of parts equal to 1 in a partition. St000517The Kreweras number of an integer partition. St000519The largest length of a factor maximising the subword complexity. St000533The minimum of the number of parts and the size of the first part of an integer partition. St000548The number of different non-empty partial sums of an integer partition. St000549The number of odd partial sums of an integer partition. St000627The exponent of a binary word. St000631The number of distinct palindromic decompositions of a binary word. St000655The length of the minimal rise of a Dyck path. St000675The number of centered multitunnels of a Dyck path. St000689The maximal n such that the minimal generator-cogenerator module in the LNakayama algebra of a Dyck path is n-rigid. St000705The number of semistandard tableaux on a given integer partition of n with maximal entry n. St000712The number of semistandard Young tableau of given shape, with entries at most 4. St000715The number of semistandard Young tableaux of given shape and entries at most 3. St000733The row containing the largest entry of a standard tableau. St000738The first entry in the last row of a standard tableau. St000753The Grundy value for the game of Kayles on a binary word. St000782The indicator function of whether a given perfect matching is an L & P matching. St000783The side length of the largest staircase partition fitting into a partition. St000784The maximum of the length and the largest part of the integer partition. St000792The Grundy value for the game of ruler on a binary word. St000810The sum of the entries in the column specified by the partition of the change of basis matrix from powersum symmetric functions to monomial symmetric functions. 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. St000812The sum of the entries in the column specified by the partition of the change of basis matrix from complete homogeneous symmetric functions to monomial symmetric functions. 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. St000827The decimal representation of a binary word with a leading 1. St000835The minimal difference in size when partitioning the integer partition into two subpartitions. St000867The sum of the hook lengths in the first row of an integer partition. St000869The sum of the hook lengths of an integer partition. St000876The number of factors in the Catalan decomposition of a binary word. St000878The number of ones minus the number of zeros of a binary word. St000885The number of critical steps in the Catalan decomposition of a binary word. St000897The number of different multiplicities of parts of an integer partition. St000913The number of ways to refine the partition into singletons. St000922The minimal number such that all substrings of this length are unique. St000932The number of occurrences of the pattern UDU in a Dyck path. St000947The major index east count of a Dyck path. St000951The dimension of $Ext^{1}(D(A),A)$ of the corresponding LNakayama algebra. St000954Number of times the corresponding LNakayama algebra has $Ext^i(D(A),A)=0$ for $i>0$. 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,. St000967The value p(1) for the Coxeterpolynomial p of the corresponding LNakayama algebra. St000982The length of the longest constant subword. St000992The alternating sum of the parts of an integer partition. St000999Number of indecomposable projective module with injective dimension equal to the global dimension in the Nakayama algebra corresponding to the Dyck path. St001000Number of indecomposable modules with projective dimension equal to the global dimension in the Nakayama algebra corresponding to the Dyck path. St001002Number of indecomposable modules with projective and injective dimension at most 1 in the Nakayama algebra corresponding to the Dyck path. St001003The number of indecomposable modules with projective dimension at most 1 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. St001008Number of indecomposable injective 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. 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. 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. 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. St001019Sum of the projective dimensions of the simple modules in 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. St001055The Grundy value for the game of removing cells of a row in an integer partition. St001063Numbers of 3-torsionfree simple modules in the corresponding Nakayama algebra. St001064Number of simple modules in the corresponding Nakayama algebra that are 3-syzygy modules. St001066The number of simple reflexive modules in the corresponding Nakayama algebra. St001067The number of simple modules of dominant dimension at least two in the corresponding Nakayama algebra. St001088Number of indecomposable projective non-injective modules with dominant dimension equal to the injective dimension in the corresponding Nakayama algebra. St001103The number of words with multiplicities of the letters given by the partition, avoiding the consecutive pattern 123. St001121The multiplicity of the irreducible representation indexed by the partition in the Kronecker square corresponding to the partition. 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. St001127The sum of the squares of the parts of a partition. St001129The product of the squares of the parts of a partition. St001138The number of indecomposable modules with projective dimension or injective dimension at most one in the corresponding Nakayama algebra. St001142The projective dimension of the socle of the regular module as a bimodule in the Nakayama algebra corresponding to the Dyck path. St001159Number of simple modules with dominant dimension equal to the global dimension in the corresponding Nakayama algebra. St001161The major index north count of a Dyck path. St001169Number of simple modules with projective dimension at least two in the corresponding Nakayama algebra. St001182Number of indecomposable injective modules with codominant dimension at least two in the corresponding Nakayama algebra. St001184Number of indecomposable injective modules with grade at least 1 in the corresponding Nakayama algebra. St001185The number of indecomposable injective modules of grade at least 2 in the corresponding Nakayama algebra. St001187The number of simple modules with grade at least one 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 $A$. 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 $eA$. St001204Call a CNakayama algebra (a Nakayama algebra with a cyclic quiver) with Kupisch series $L=[c_0,c_1,...,c_{n−1}]$ such that $n=c_0 < c_i$ for all $i > 0$ a special CNakayama algebra. 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 $eA$. 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. 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. St001217The projective dimension of the indecomposable injective module I[n-2] in the corresponding Nakayama algebra with simples enumerated from 0 to n-1. St001218Smallest index k greater than or equal to one such that the Coxeter matrix C of the corresponding Nakayama algebra has C^k=1. St001222Number of simple modules in the corresponding LNakayama algebra that have a unique 2-extension with the regular module. 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. St001224Let X be the direct sum of all simple modules of the corresponding Nakayama algebra. 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. 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. St001241The number of non-zero radicals of the indecomposable projective modules that have injective dimension and projective dimension at most one. St001244The number of simple modules of projective dimension one that are not 1-regular for the Nakayama algebra associated to a Dyck path. St001255The vector space dimension of the double dual of A/J when A is the corresponding Nakayama algebra with Jacobson radical J. St001256Number of simple reflexive modules that are 2-stable reflexive. St001273The projective dimension of the first term in an injective coresolution of the regular module. 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. St001289The vector space dimension of the n-fold tensor product of D(A), where n is maximal such that this n-fold tensor product is nonzero. 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. 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. St001355Number of non-empty prefixes of a binary word that contain equally many 0's and 1's. St001372The length of a longest cyclic run of ones of a binary word. St001387Number of standard Young tableaux of the skew shape tracing the border of the given partition. 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. St001462The number of factors of a standard tableaux under concatenation. St001473The absolute value of the sum of all entries of the Coxeter matrix of the corresponding LNakayama algebra. St001481The minimal height of a peak 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. St001484The number of singletons of an integer partition. St001485The modular major index of a binary word. St001487The number of inner corners of a skew partition. St001488The number of corners of a skew partition. St001490The number of connected components of a skew partition. St001491The number of indecomposable projective-injective modules in the algebra corresponding to a subset. 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. St001509The degree of the standard monomial associated to a Dyck path relative to the trivial lower boundary. St001515The vector space dimension of the socle of the first syzygy module of the regular module (as a bimodule). St001531Number of partial orders contained in the poset determined by the Dyck path. St001594The number of indecomposable projective modules in the Nakayama algebra corresponding to the Dyck path such that the UC-condition is satisfied. St001595The number of standard Young tableaux of the skew partition. St001597The Frobenius rank of a skew partition. St001614The cyclic permutation representation number of a skew partition. St001643The Frobenius dimension of the Nakayama algebra corresponding to the Dyck path. St001660The number of ways to place as many non-attacking rooks as possible on a skew Ferrers board. St001711The number of permutations such that conjugation with a permutation of given cycle type yields the squared permutation. St001721The degree of a binary word. St001722The number of minimal chains with small intervals between a binary word and the top element. St001786The number of total orderings of the north steps of a Dyck path such that steps after the k-th east step are not among the first k positions in the order. St001804The minimal height of the rectangular inner shape in a cylindrical tableau associated to a tableau. St001809The index of the step at the first peak of maximal height in a Dyck path. St001838The number of nonempty primitive factors of a binary word. St001872The number of indecomposable injective modules with even projective dimension in the corresponding Nakayama algebra. St001884The number of borders of a binary word. St001910The height of the middle non-run of a Dyck path. St001929The number of meanders with top half given by the noncrossing matching corresponding to the Dyck path. St001930The weak major index of a binary word. St001932The number of pairs of singleton blocks in the noncrossing set partition corresponding to a Dyck path, that can be merged to create another noncrossing set 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. St000012The area of a Dyck path. St000016The number of attacking pairs of a standard tableau. St000017The number of inversions of a standard tableau. St000146The Andrews-Garvan crank of a partition. St000185The weighted size of a partition. St000219The number of occurrences of the pattern 231 in a permutation. St000295The length of the border of a binary word. St000329The number of evenly positioned ascents of the Dyck path, with the initial position equal to 1. St000340The number of non-final maximal constant sub-paths of length greater than one. St000394The sum of the heights of the peaks of a Dyck path minus the number of peaks. St000421The number of Dyck paths that are weakly below a Dyck path, except for the path itself. St000442The maximal area to the right of an up step of a Dyck path. St000629The defect of a binary word. 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. St000687The dimension of $Hom(I,P)$ for the LNakayama algebra of a Dyck path. St000688The global dimension minus the dominant dimension of the LNakayama algebra associated to a Dyck path. St000697The number of 3-rim hooks removed from an integer partition to obtain its associated 3-core. St000790The number of pairs of centered tunnels, one strictly containing the other, of a Dyck path. St000874The position of the last double rise in a Dyck path. St000877The depth of the binary word interpreted as a path. St000946The sum of the skew hook positions in a Dyck path. St000966Number of peaks minus the global dimension of the corresponding LNakayama algebra. St000970Number of peaks minus the dominant dimension of the corresponding LNakayama algebra. St000976The sum of the positions of double up-steps of a Dyck path. St000977MacMahon's equal index of a Dyck path. St000978The sum of the positions of double down-steps of a Dyck path. St000981The length of the longest zigzag subpath. St000984The number of boxes below precisely one peak. St000995The largest even part of an integer partition. St001001The number of indecomposable modules with projective and injective dimension equal to the global dimension of the Nakayama algebra corresponding to the Dyck path. St001021Sum of the differences between projective and codominant dimension of the non-projective indecomposable injective modules in the Nakayama algebra corresponding to the Dyck path. St001022Number of simple modules with projective dimension 3 in the Nakayama algebra corresponding to the Dyck path. St001025Number of simple modules with projective dimension 4 in the Nakayama algebra corresponding to the Dyck path. St001031The height of the bicoloured Motzkin path associated with the Dyck path. 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. St001091The number of parts in an integer partition whose next smaller part has the same size. 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. St001113Number of indecomposable projective non-injective modules with reflexive Auslander-Reiten sequences in the corresponding Nakayama algebra. St001137Number of simple modules that are 3-regular in the corresponding Nakayama algebra. St001139The number of occurrences of hills of size 2 in a Dyck path. 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. St001172The number of 1-rises at odd height of a Dyck path. St001181Number of indecomposable injective modules with grade at least 3 in the corresponding Nakayama algebra. St001186Number of simple modules with grade at least 3 in the corresponding Nakayama algebra. St001189The number of simple modules with dominant and codominant dimension equal to zero in the Nakayama algebra corresponding to the Dyck path. St001193The dimension of $Ext_A^1(A/AeA,A)$ in the corresponding Nakayama algebra $A$ such that $eA$ is a minimal faithful projective-injective module. St001214The aft of an integer partition. 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. St001221The number of simple modules in the corresponding LNakayama algebra that have 2 dimensional second Extension group with the regular module. St001229The vector space dimension of the first extension group between the Jacobson radical J and J^2. St001233The number of indecomposable 2-dimensional modules with projective dimension one. St001253The number of non-projective indecomposable reflexive modules in the corresponding Nakayama algebra. St001265The maximal i such that the i-th simple module has projective dimension equal to the global dimension in the corresponding Nakayama algebra. St001266The largest vector space dimension of an indecomposable non-projective module that is reflexive in the corresponding Nakayama algebra. St001292The injective dimension of the tensor product of two copies of the dual of the Nakayama algebra associated to a Dyck path. St001295Gives the vector space dimension of the homomorphism space between J^2 and J^2. St001314The number of tilting modules of arbitrary projective dimension that have no simple modules as a direct summand in the corresponding Nakayama algebra. St001371The length of the longest Yamanouchi prefix of a binary word. St001413Half the length of the longest even length palindromic prefix of a binary word. St001418Half of the global dimension of the stable Auslander algebra of the Nakayama algebra corresponding to the Dyck path. St001423The number of distinct cubes in a binary word. St001424The number of distinct squares in 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. St001435The number of missing boxes in the first row. St001438The number of missing boxes of a skew partition. 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. St001524The degree of symmetry of a binary word. St001584The area statistic between a Dyck path and its bounce path. St001596The number of two-by-two squares inside a skew partition. St001695The natural comajor index of a standard Young tableau. St001697The shifted natural comajor index of a standard Young tableau. St001698The comajor index of a standard tableau minus the weighted size of its shape. St001712The number of natural descents of a standard Young tableau. St001730The number of times the path corresponding to a binary word crosses the base line. St001803The maximal overlap of the cylindrical tableau associated with a tableau. 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). St001916The number of transient elements in the orbit of Bulgarian solitaire corresponding to a necklace. St001956The comajor index for set-valued two-row standard Young tableaux. St000826The stopping time of the decimal representation of the binary word for the 3x+1 problem. St000281The size of the preimage of the map 'to poset' from Binary trees to Posets. St000477The weight of a partition according to Alladi. St000656The number of cuts of a poset. St000680The Grundy value for Hackendot on posets. St000717The number of ordinal summands of a poset. St000817The sum of the entries in the column specified by the composition of the change of basis matrix from dual immaculate quasisymmetric functions to monomial quasisymmetric functions. St000818The sum of the entries in the column specified by the composition of the change of basis matrix from quasisymmetric Schur functions to monomial quasisymmetric functions. St000906The length of the shortest maximal chain in a poset. St000997The even-odd crank of an integer partition. St000100The number of linear extensions of a poset. St000282The size of the preimage of the map 'to poset' from Ordered trees to Posets. St000285The size of the preimage of the map 'to inverse des composition' from Parking functions to Integer compositions. St000327The number of cover relations in a poset. St000509The diagonal index (content) of a partition. 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. St000633The size of the automorphism group of a poset. St000634The number of endomorphisms of a poset. St000635The number of strictly order preserving maps of a poset into itself. St000639The number of relations in a poset. St000640The rank of the largest boolean interval in a poset. St000641The number of non-empty boolean intervals in a poset. St000642The size of the smallest orbit of antichains under Panyushev complementation. St000643The size of the largest orbit of antichains under Panyushev complementation. St000714The number of semistandard Young tableau of given shape, with entries at most 2. St000762The sum of the positions of the weak records of an integer composition. St000806The semiperimeter of the associated bargraph. St000910The number of maximal chains of minimal length in a poset. St000914The sum of the values of the Möbius function of a poset. St000927The alternating sum of the coefficients of the character polynomial of an integer partition. St001105The number of greedy linear extensions of a poset. St001106The number of supergreedy linear extensions of a poset. St001637The number of (upper) dissectors of a poset. St001668The number of points of the poset minus the width of the poset. St000848The balance constant multiplied with the number of linear extensions of a poset. St000849The number of 1/3-balanced pairs in a poset. St000850The number of 1/2-balanced pairs in a poset. St000713The dimension of the irreducible representation of Sp(4) labelled by an integer partition. St001208The number of connected components of the quiver of $A/T$ when $T$ is the 1-tilting module corresponding to the permutation in the Auslander algebra $A$ of $K[x]/(x^n)$. St001236The dominant dimension of the corresponding Comp-Nakayama algebra. St001569The maximal modular displacement of a permutation. St000102The charge of a semistandard tableau. St001556The number of inversions of the third entry of a permutation. St001857The number of edges in the reduced word graph of a signed permutation. St001948The number of augmented double ascents of a permutation.