St001385The number of conjugacy classes of subgroups with connected subgroups of sizes prescribed by an integer partition. St001918The degree of the cyclic sieving polynomial corresponding to an integer partition. St001934The number of monotone factorisations of genus zero of a permutation of given cycle type. St000118The number of occurrences of the contiguous pattern [.,[.,[.,.]]] in a binary tree. St000752The Grundy value for the game 'Couples are forever' on an integer partition. St001718The number of non-empty open intervals in a poset. St000521The number of distinct subtrees of an ordered tree. St000010The length of the partition. St000013The height of a Dyck path. St000097The order of the largest clique of the graph. St000098The chromatic number of a graph. St000172The Grundy number of a graph. St000382The first part of an integer composition. St000444The length of the maximal rise of a Dyck path. St000504The cardinality of the first block of a set partition. St000507The number of ascents of a standard tableau. St000676The number of odd rises of a Dyck path. St000734The last entry in the first row of a standard tableau. St000808The number of up steps of the associated bargraph. St000972The composition number of a graph. St001029The size of the core of a graph. St001039The maximal height of a column in the parallelogram polyomino associated with a Dyck path. St001058The breadth of the ordered tree. St001062The maximal size of a block of a set partition. St001116The game chromatic number of a graph. St001474The evaluation of the Tutte polynomial of the graph at (x,y) equal to (2,-1). St001494The Alon-Tarsi number of a graph. St001580The acyclic chromatic number of a graph. St001581The achromatic number of a graph. St001626The number of maximal proper sublattices of a lattice. St001670The connected partition number of a graph. St001720The minimal length of a chain of small intervals in a lattice. St001883The mutual visibility number of a graph. St001963The tree-depth of a graph. St000001The number of reduced words for a permutation. St000272The treewidth of a graph. St000326The position of the first one in a binary word after appending a 1 at the end. St000392The length of the longest run of ones in a binary word. St000442The maximal area to the right of an up step of a Dyck path. St000536The pathwidth of a graph. St000537The cutwidth of a graph. St000729The minimal arc length of a set partition. St000730The maximal arc length of a set partition. St000920The logarithmic height of a Dyck path. St001066The number of simple reflexive modules in the corresponding Nakayama algebra. St001270The bandwidth of a graph. St001277The degeneracy of a graph. St001358The largest degree of a regular subgraph of a graph. St001418Half of the global dimension of the stable Auslander algebra of the Nakayama algebra corresponding to the Dyck path. St001475The evaluation of the Tutte polynomial of the graph at (x,y) equal to (1,0). St001568The smallest positive integer that does not appear twice in the partition. St001592The maximal number of simple paths between any two different vertices of a graph. St001644The dimension of a graph. St001743The discrepancy of a graph. St001792The arboricity of a graph. St001820The size of the image of the pop stack sorting operator. St001962The proper pathwidth of a graph. St000052The number of valleys of a Dyck path not on the x-axis. St000119The number of occurrences of the pattern 321 in a permutation. St000123The difference in Coxeter length of a permutation and its image under the Simion-Schmidt map. St000143The largest repeated part of a partition. St000149The number of cells of the partition whose leg is zero and arm is odd. St000150The floored half-sum of the multiplicities of a partition. St000223The number of nestings in the permutation. St000256The number of parts from which one can substract 2 and still get an integer partition. St000257The number of distinct parts of a partition that occur at least twice. St000344The number of strongly connected outdegree sequences of a graph. St000360The number of occurrences of the pattern 32-1. St000366The number of double descents of a permutation. St000367The number of simsun double descents of a permutation. St000371The number of mid points of decreasing subsequences of length 3 in a permutation. St000373The number of weak exceedences of a permutation that are also mid-points of a decreasing subsequence of length $3$. 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. St000491The number of inversions of a set partition. St000496The rcs statistic of a set partition. St000497The lcb statistic of a set partition. St000555The number of occurrences of the pattern {{1,3},{2}} in a set partition. St000561The number of occurrences of the pattern {{1,2,3}} in a set partition. St000572The dimension exponent of a set partition. St000581The number of occurrences of the pattern {{1,3},{2}} such that 1 is minimal, 2 is maximal. St000582The number of occurrences of the pattern {{1,3},{2}} such that 1 is minimal, 3 is maximal, (1,3) are consecutive in a block. St000585The number of occurrences of the pattern {{1,3},{2}} such that 2 is maximal, (1,3) are consecutive in a block. St000594The number of occurrences of the pattern {{1,3},{2}} such that 1,2 are minimal, (1,3) are consecutive in a block. St000600The number of occurrences of the pattern {{1,3},{2}} such that 1 is minimal, (1,3) are consecutive in a block. St000602The number of occurrences of the pattern {{1,3},{2}} such that 1 is minimal. St000610The number of occurrences of the pattern {{1,3},{2}} such that 2 is maximal. St000613The number of occurrences of the pattern {{1,3},{2}} such that 2 is minimal, 3 is maximal, (1,3) are consecutive in a block. St000660The number of rises of length at least 3 of a Dyck path. St000661The number of rises of length 3 of a Dyck path. St000931The number of occurrences of the pattern UUU in a Dyck path. St001022Number of simple modules with projective dimension 3 in the Nakayama algebra corresponding to the Dyck path. St001033The normalized area of the parallelogram polyomino associated with the Dyck path. St001070The absolute value of the derivative of the chromatic polynomial of the graph at 1. St001071The beta invariant of the graph. St001137Number of simple modules that are 3-regular in the corresponding Nakayama algebra. St001141The number of occurrences of hills of size 3 in a Dyck path. St001167The number of simple modules that appear as the top of an indecomposable non-projective modules that is reflexive in the corresponding Nakayama algebra. St001253The number of non-projective indecomposable reflexive modules in the corresponding Nakayama algebra. 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. 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. St001411The number of patterns 321 or 3412 in a permutation. St001413Half the length of the longest even length palindromic prefix of a binary word. St001552The number of inversions between excedances and fixed points of a permutation. St001588The number of distinct odd parts smaller than the largest even part in an integer partition. St001638The book thickness of a graph. St001651The Frankl number of a lattice. St001657The number of twos in an integer partition. St001728The number of invisible descents of a permutation. St001736The total number of cycles in a graph. St001781The interlacing number of a set partition. St001797The number of overfull subgraphs of a graph. St001839The number of excedances of a set partition. St001840The number of descents of a set partition. St001841The number of inversions of a set partition. St001843The Z-index of a set partition. St001846The number of elements which do not have a complement in the lattice. St000054The first entry of the permutation. St000063The number of linear extensions of a certain poset defined for an integer partition. St000088The row sums of the character table of the symmetric group. St000108The number of partitions contained in the given partition. St000380Half of the maximal perimeter of a rectangle fitting into the diagram of an integer partition. St000384The maximal part of the shifted composition of an integer partition. St000421The number of Dyck paths that are weakly below a Dyck path, except for the path itself. St000439The position of the first down step of a Dyck path. St000459The hook length of the base cell of a partition. St000532The total number of rook placements on a Ferrers board. St001028Number of simple modules with injective dimension equal to the dominant dimension 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. 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. 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. St001875The number of simple modules with projective dimension at most 1. St000007The number of saliances of the permutation. St000008The major index of the composition. St000009The charge of a standard tableau. St000012The area of a Dyck path. St000025The number of initial rises of a Dyck path. St000032The number of elements smaller than the given Dyck path in the Tamari Order. St000058The order of a permutation. St000087The number of induced subgraphs. St000105The number of blocks in the set partition. St000141The maximum drop size of a permutation. St000167The number of leaves of an ordered tree. St000169The cocharge of a standard tableau. St000184The size of the centralizer of any permutation of given cycle type. St000228The size of a partition. St000288The number of ones in a binary word. St000289The decimal representation of a binary word. St000330The (standard) major index of a standard tableau. St000345The number of refinements of a partition. St000378The diagonal inversion number of an integer partition. St000383The last part of an integer composition. St000391The sum of the positions of the ones in a binary word. St000394The sum of the heights of the peaks of a Dyck path minus the number of peaks. St000418The number of Dyck paths that are weakly below a Dyck path. St000451The length of the longest pattern of the form k 1 2. St000460The hook length of the last cell along the main diagonal of an integer partition. St000469The distinguishing number of a graph. St000470The number of runs in a permutation. St000476The sum of the semi-lengths of tunnels before a valley of a Dyck path. St000505The biggest entry in the block containing the 1. St000531The leading coefficient of the rook polynomial of an integer partition. St000550The number of modular elements of a lattice. St000551The number of left modular elements of a lattice. St000566The number of ways to select a row of a Ferrers shape and two cells in this row. St000636The hull number of a graph. St000684The global dimension of the LNakayama algebra associated to a Dyck path. St000686The finitistic dominant dimension of a Dyck path. St000691The number of changes of a binary word. St000702The number of weak deficiencies of a permutation. St000708The product of the parts of an integer partition. St000718The largest Laplacian eigenvalue of a graph if it is integral. St000723The maximal cardinality of a set of vertices with the same neighbourhood in a graph. St000725The smallest label of a leaf of the increasing binary tree associated to a permutation. St000733The row containing the largest entry of a standard tableau. St000738The first entry in the last row of a standard tableau. St000740The last entry of a permutation. St000745The index of the last row whose first entry is the row number in a standard Young tableau. 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. St000822The Hadwiger number of the graph. St000823The number of unsplittable factors of the set partition. St000833The comajor index of a permutation. St000870The product of the hook lengths of the diagonal cells in an integer partition. St000877The depth of the binary word interpreted as a path. St000907The number of maximal antichains of minimal length in a poset. St000926The clique-coclique number of a graph. St000933The number of multipartitions of sizes given by an integer partition. St000935The number of ordered refinements of an integer partition. St000947The major index east count of a Dyck path. St000969We make a CNakayama algebra out of the LNakayama algebra (corresponding to the Dyck path) $[c_0,c_1,...,c_{n-1}]$ by adding $c_0$ to $c_{n-1}$. St000971The smallest closer of a set partition. St000983The length of the longest alternating subword. St000984The number of boxes below precisely one peak. St001007Number of simple modules with projective dimension 1 in the Nakayama algebra corresponding to the Dyck path. St001068Number of torsionless simple modules in the corresponding Nakayama algebra. St001088Number of indecomposable projective non-injective modules with dominant dimension equal to the injective dimension in the corresponding Nakayama algebra. St001108The 2-dynamic chromatic number of a graph. St001110The 3-dynamic chromatic number of a graph. St001203We associate to a CNakayama algebra (a Nakayama algebra with a cyclic quiver) with Kupisch series $L=[c_0,c_1,...,c_{n-1}]$ such that $n=c_0 < c_i$ for all $i > 0$ a Dyck path as follows: St001249Sum of the odd parts of a partition. St001279The sum of the parts of an integer partition that are at least two. St001330The hat guessing number of a graph. St001342The number of vertices in the center of a graph. St001360The number of covering relations in Young's lattice below a partition. St001366The maximal multiplicity of a degree of a vertex of a graph. St001368The number of vertices of maximal degree in a graph. St001380The number of monomer-dimer tilings of a Ferrers diagram. St001389The number of partitions of the same length below the given integer partition. St001415The length of the longest palindromic prefix of a binary word. St001461The number of topologically connected components of the chord diagram of a permutation. St001462The number of factors of a standard tableaux under concatenation. St001611The number of multiset partitions such that the multiplicities of elements are given by a partition. St001612The number of coloured multisets of cycles such that the multiplicities of colours are given by a partition. St001621The number of atoms of a lattice. St001622The number of join-irreducible elements of a lattice. St001623The number of doubly irreducible elements of a lattice. St001654The monophonic hull number of a graph. St001655The general position number of a graph. St001656The monophonic position number of a graph. St001659The number of ways to place as many non-attacking rooks as possible on a Ferrers board. St001697The shifted natural comajor index of a standard Young tableau. St001706The number of closed sets in a graph. St001721The degree of a binary word. St001746The coalition number of a graph. St001809The index of the step at the first peak of maximal height in a Dyck path. St001844The maximal degree of a generator of the invariant ring of the automorphism group of a graph. St000024The number of double up and double down steps of a Dyck path. St000028The number of stack-sorts needed to sort a permutation. St000040The number of regions of the inversion arrangement of a permutation. St000048The multinomial of the parts of a partition. St000053The number of valleys of the Dyck path. St000078The number of alternating sign matrices whose left key is the permutation. St000157The number of descents of a standard tableau. St000160The multiplicity of the smallest part of a partition. St000171The degree of the graph. St000182The number of permutations whose cycle type is the given integer partition. St000201The number of leaf nodes in a binary tree. St000268The number of strongly connected orientations of a graph. St000292The number of ascents of a binary word. St000295The length of the border of a binary word. St000346The number of coarsenings of a partition. St000374The number of exclusive right-to-left minima of a permutation. St000377The dinv defect of an integer partition. St000396The register function (or Horton-Strahler number) of a binary tree. St000453The number of distinct Laplacian eigenvalues of a graph. St000454The largest eigenvalue of a graph if it is integral. St000485The length of the longest cycle of a permutation. St000502The number of successions of a set partitions. St000503The maximal difference between two elements in a common block. St000510The number of invariant oriented cycles when acting with a permutation of given cycle type. St000519The largest length of a factor maximising the subword complexity. St000539The number of odd inversions of a permutation. St000548The number of different non-empty partial sums of an integer partition. St000617The number of global maxima of a Dyck path. St000619The number of cyclic descents of a permutation. St000651The maximal size of a rise in a permutation. St000652The maximal difference between successive positions of a permutation. St000662The staircase size of the code of a permutation. St000670The reversal length of a permutation. St000675The number of centered multitunnels of a Dyck path. St000678The number of up steps after the last double rise of a Dyck path. St000679The pruning number of an ordered tree. St000681The Grundy value of Chomp on Ferrers diagrams. St000695The number of blocks in the first part of the atomic decomposition of a set partition. St000697The number of 3-rim hooks removed from an integer partition to obtain its associated 3-core. St000701The protection number of a binary tree. St000703The number of deficiencies of a permutation. St000741The Colin de Verdière graph invariant. St000753The Grundy value for the game of Kayles on a binary word. St000755The number of real roots of the characteristic polynomial of a linear recurrence associated with an integer partition. St000773The multiplicity of the largest Laplacian eigenvalue in a graph. St000778The metric dimension of a graph. 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. St000844The size of the largest block in the direct sum decomposition of a permutation. St000862The number of parts of the shifted shape of a permutation. St000874The position of the last double rise in a Dyck path. St000883The number of longest increasing subsequences of a permutation. St000886The number of permutations with the same antidiagonal sums. St000913The number of ways to refine the partition into singletons. St000988The orbit size of a permutation under Foata's bijection. St000996The number of exclusive left-to-right maxima of a permutation. St001038The minimal height of a column in the parallelogram polyomino associated with the Dyck path. St001073The number of nowhere zero 3-flows of a graph. St001081The number of minimal length factorizations of a permutation into star transpositions. St001090The number of pop-stack-sorts needed to sort a permutation. St001093The detour number of a graph. St001103The number of words with multiplicities of the letters given by the partition, avoiding the consecutive pattern 123. St001120The length of a longest path in a graph. St001189The number of simple modules with dominant and codominant dimension equal to zero in the Nakayama algebra corresponding to the Dyck path. St001197The global dimension of $eAe$ for the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. St001199The dominant dimension of $eAe$ for the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. St001246The maximal difference between two consecutive entries of a permutation. St001250The number of parts of a partition that are not congruent 0 modulo 3. St001261The Castelnuovo-Mumford regularity of a graph. St001267The length of the Lyndon factorization of the binary word. St001313The number of Dyck paths above the lattice path given by a binary word. St001345The Hamming dimension of a graph. St001359The number of permutations in the equivalence class of a permutation obtained by taking inverses of cycles. St001372The length of a longest cyclic run of ones of a binary word. St001382The number of boxes in the diagram of a partition that do not lie in its Durfee square. St001384The number of boxes in the diagram of a partition that do not lie in the largest triangle it contains. St001387Number of standard Young tableaux of the skew shape tracing the border of the given partition. St001419The length of the longest palindromic factor beginning with a one of a binary word. St001437The flex of a binary word. St001464The number of bases of the positroid corresponding to the permutation, with all fixed points counterclockwise. St001483The number of simple module modules that appear in the socle of the regular module but have no nontrivial selfextensions with the regular module. St001499The number of indecomposable projective-injective modules of a magnitude 1 Nakayama algebra. St001506Half the projective dimension of the unique simple module with even projective dimension in a magnitude 1 Nakayama algebra. St001599The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on rooted trees. St001608The number of coloured rooted trees such that the multiplicities of colours are given by a partition. St001619The number of non-isomorphic sublattices of a lattice. St001625The Möbius invariant of a lattice. St001627The number of coloured connected graphs such that the multiplicities of colours are given by a partition. St001666The number of non-isomorphic subposets of a lattice which are lattices. St001674The number of vertices of the largest induced star graph in the graph. St001716The 1-improper chromatic number of a graph. 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. St001761The maximal multiplicity of a letter in a reduced word of a permutation. St001777The number of weak descents in an integer composition. 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. St001884The number of borders of a binary word. St001933The largest multiplicity of a part in an integer partition. St001938The number of transitive monotone factorizations of genus zero of a permutation of given cycle type. St001949The rigidity index of a graph. St000002The number of occurrences of the pattern 123 in a permutation. St000065The number of entries equal to -1 in an alternating sign matrix. St000095The number of triangles of a graph. St000137The Grundy value of an integer partition. St000142The number of even parts of a partition. St000148The number of odd parts of a partition. St000185The weighted size of a partition. St000196The number of occurrences of the contiguous pattern [[.,.],[.,. 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. St000209Maximum difference of elements in cycles. St000290The major index of a binary word. St000291The number of descents of a binary word. St000293The number of inversions of a binary word. St000297The number of leading ones in a binary word. St000303The determinant of the product of the incidence matrix and its transpose of a graph divided by $4$. St000347The inversion sum of a binary word. St000348The non-inversion sum of a binary word. St000353The number of inner valleys of a permutation. St000354The number of recoils of a permutation. St000356The number of occurrences of the pattern 13-2. St000358The number of occurrences of the pattern 31-2. St000359The number of occurrences of the pattern 23-1. St000379The number of Hamiltonian cycles in a graph. St000386The number of factors DDU in a Dyck path. St000387The matching number of a graph. St000389The number of runs of ones of odd length in a binary word. 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. St000437The number of occurrences of the pattern 312 or of the pattern 321 in a permutation. St000463The number of admissible inversions of a permutation. St000473The number of parts of a partition that are strictly bigger than the number of ones. St000475The number of parts equal to 1 in a partition. St000480The number of lower covers of a partition in dominance order. St000481The number of upper covers of a partition in dominance order. St000486The number of cycles of length at least 3 of a permutation. St000494The number of inversions of distance at most 3 of a permutation. St000495The number of inversions of distance at most 2 of a permutation. St000506The number of standard desarrangement tableaux of shape equal to the given partition. St000512The number of invariant subsets of size 3 when acting with a permutation of given cycle type. St000523The number of 2-protected nodes of a rooted tree. St000535The rank-width of a graph. St000565The major index of a set partition. St000586The number of occurrences of the pattern {{1},{2,3}} such that 2 is minimal. St000588The number of occurrences of the pattern {{1},{2},{3}} such that 1,3 are minimal, 2 is maximal. St000589The number of occurrences of the pattern {{1},{2,3}} such that 1 is maximal, (2,3) are consecutive in a block. St000590The number of occurrences of the pattern {{1},{2,3}} such that 2 is minimal, 1 is maximal, (2,3) are consecutive in a block. St000592The number of occurrences of the pattern {{1},{2},{3}} such that 1 is maximal. St000597The number of occurrences of the pattern {{1},{2,3}} such that 2 is minimal, (2,3) are consecutive in a block. St000598The number of occurrences of the pattern {{1},{2,3}} such that 1,2 are minimal, 3 is maximal, (2,3) are consecutive in a block. St000601The number of occurrences of the pattern {{1},{2,3}} such that 1,2 are minimal, (2,3) are consecutive in a block. St000604The number of occurrences of the pattern {{1},{2},{3}} such that 3 is minimal, 2 is maximal. St000606The number of occurrences of the pattern {{1},{2,3}} such that 1,3 are maximal, (2,3) are consecutive in a block. St000607The number of occurrences of the pattern {{1},{2,3}} such that 2 is minimal, 3 is maximal, (2,3) are consecutive in a block. St000609The number of occurrences of the pattern {{1},{2,3}} such that 1,2 are minimal. St000611The number of occurrences of the pattern {{1},{2,3}} such that 1 is maximal. St000615The number of occurrences of the pattern {{1},{2},{3}} such that 1,3 are maximal. St000624The normalized sum of the minimal distances to a greater element. St000647The number of big descents of a permutation. St000648The number of 2-excedences of a permutation. St000682The Grundy value of Welter's game on a binary word. St000710The number of big deficiencies of a permutation. St000711The number of big exceedences of a permutation. St000731The number of double exceedences of a permutation. St000732The number of double deficiencies of a permutation. St000779The tier of a permutation. St000791The number of pairs of left tunnels, one strictly containing the other, of a Dyck path. St000795The mad of a permutation. St000803The number of occurrences of the vincular pattern |132 in a permutation. St000809The reduced reflection length of the permutation. St000829The Ulam distance of a permutation to the identity permutation. St000831The number of indices that are either descents or recoils. St000875The semilength of the longest Dyck word in the Catalan factorisation of a binary word. St000884The number of isolated descents of a permutation. St000932The number of occurrences of the pattern UDU in a Dyck path. St000934The 2-degree of an integer partition. St000944The 3-degree of an integer partition. St000956The maximal displacement of a permutation. St000957The number of Bruhat lower covers of a permutation. St000985The number of positive eigenvalues of the adjacency matrix of the graph. St000994The number of cycle peaks and the number of cycle valleys of a permutation. St001037The number of inner corners of the upper path of the parallelogram polyomino associated with the Dyck path. St001061The number of indices that are both descents and recoils of a permutation. St001067The number of simple modules of dominant dimension at least two in the corresponding Nakayama algebra. St001076The minimal length of a factorization of a permutation into transpositions that are cyclic shifts of (12). St001078The minimal number of occurrences of (12) in a factorization of a permutation into transpositions (12) and cycles (1,. St001083The number of boxed occurrences of 132 in a permutation. St001086The number of occurrences of the consecutive pattern 132 in a permutation. St001087The number of occurrences of the vincular pattern |12-3 in a permutation. St001091The number of parts in an integer partition whose next smaller part has the same size. St001092The number of distinct even parts of a partition. St001107The number of times one can erase the first up and the last down step in a Dyck path and still remain a Dyck path. St001121The multiplicity of the irreducible representation indexed by the partition in the Kronecker square corresponding to the partition. St001172The number of 1-rises at odd height of a Dyck path. St001176The size of a partition minus its first part. St001251The number of parts of a partition that are not congruent 1 modulo 3. St001252Half the sum of the even parts of a partition. St001269The sum of the minimum of the number of exceedances and deficiencies in each cycle of a permutation. St001280The number of parts of an integer partition that are at least two. St001319The minimal number of occurrences of the star-pattern in a linear ordering of the vertices of the graph. St001333The cardinality of a minimal 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. St001383The BG-rank of an integer partition. St001393The induced matching number of a graph. St001394The genus of a permutation. St001412Number of minimal entries in the Bruhat order matrix of a permutation. 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. St001436The index of a given binary word in the lex-order among all its cyclic shifts. St001440The number of standard Young tableaux whose major index is congruent one modulo the size of a given integer partition. St001442The number of standard Young tableaux whose major index is divisible by the size of a given integer partition. St001465The number of adjacent transpositions in the cycle decomposition of a permutation. St001466The number of transpositions swapping cyclically adjacent numbers in a permutation. St001469The holeyness of a permutation. St001484The number of singletons of an integer partition. St001485The modular major index of a binary word. St001489The maximum of the number of descents and the number of inverse descents. St001512The minimum rank of a graph. St001558The number of transpositions that are smaller or equal to a permutation in Bruhat order. 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. St001579The number of cyclically simple transpositions decreasing the number of cyclic descents needed to sort a permutation. St001584The area statistic between a Dyck path and its bounce path. St001587Half of the largest even part of an integer partition. St001593This is the number of standard Young tableaux of the given shifted shape. St001601The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on trees. St001618The cardinality of the Frattini sublattice of a lattice. St001663The number of occurrences of the Hertzsprung pattern 132 in a permutation. St001665The number of pure excedances of a permutation. St001683The number of distinct positions of the pattern letter 3 in occurrences of 132 in a permutation. St001714The number of subpartitions of an integer partition that do not dominate the conjugate subpartition. St001723The differential of a graph. St001724The 2-packing differential of a graph. St001726The number of visible inversions of a permutation. St001727The number of invisible inversions of a permutation. St001729The number of visible descents of a permutation. St001737The number of descents of type 2 in a permutation. St001744The number of occurrences of the arrow pattern 1-2 with an arrow from 1 to 2 in a permutation. St001801Half the number of preimage-image pairs of different parity in a permutation. St001816Eigenvalues of the top-to-random operator acting on a simple module. St001842The major index of a set partition. St001845The number of join irreducibles minus the rank of a lattice. St001912The length of the preperiod in Bulgarian solitaire corresponding to an integer partition. St001928The number of non-overlapping descents in a permutation. 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. St001961The sum of the greatest common divisors of all pairs of parts. St000997The even-odd crank of an integer partition. St000845The maximal number of elements covered by an element in a poset. St000110The number of permutations less than or equal to a permutation in left weak order. St000772The multiplicity of the largest distance Laplacian eigenvalue in a connected graph. St000018The number of inversions of a permutation. St000019The cardinality of the support of a permutation. St000035The number of left outer peaks of a permutation. St000214The number of adjacencies of a permutation. St000215The number of adjacencies of a permutation, zero appended. St000237The number of small exceedances. St000337The lec statistic, the sum of the inversion numbers of the hook factors of a permutation. St001687The number of distinct positions of the pattern letter 2 in occurrences of 213 in a permutation. St000846The maximal number of elements covering an element of a poset. St000527The width of the poset. St000245The number of ascents of a permutation. St000796The stat' of a permutation. St000798The makl of a permutation. St001337The upper domination number of a graph. St001338The upper irredundance number of a graph. St000299The number of nonisomorphic vertex-induced subtrees. St000306The bounce count of a Dyck path. St001294The maximal torsionfree index of a simple non-projective module in the corresponding Nakayama algebra. St001597The Frobenius rank of a skew partition. St000234The number of global ascents of a permutation. St000802The number of occurrences of the vincular pattern |321 in a permutation. St001085The number of occurrences of the vincular pattern |21-3 in a permutation. St001113Number of indecomposable projective non-injective modules with reflexive Auslander-Reiten sequences in the corresponding Nakayama algebra. 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. St001596The number of two-by-two squares inside a skew partition. St001291The number of indecomposable summands of the tensor product of two copies of the dual of the Nakayama algebra associated to a Dyck path. 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. St000538The number of even inversions of a permutation. St000836The number of descents of distance 2 of a permutation. St000068The number of minimal elements in a poset. St000990The first ascent of a permutation. St000069The number of maximal elements of a poset. St000081The number of edges of a graph. St000672The number of minimal elements in Bruhat order not less than the permutation. St000665The number of rafts of a permutation. St001497The position of the largest weak excedence of a permutation. St000316The number of non-left-to-right-maxima of a permutation. St000653The last descent of a permutation. St000991The number of right-to-left minima of a permutation. St001184Number of indecomposable injective modules with grade at least 1 in the corresponding Nakayama algebra. St001480The number of simple summands of the module J^2/J^3. St000120The number of left tunnels of a Dyck path. St000667The greatest common divisor of the parts of the partition. St000989The number of final rises of a permutation. St001571The Cartan determinant of the integer partition. St001640The number of ascent tops in the permutation such that all smaller elements appear before. 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). St000546The number of global descents of a permutation. St000649The number of 3-excedences of a permutation. St001084The number of occurrences of the vincular pattern |1-23 in a permutation. St001114The number of odd descents of a permutation. St001115The number of even descents of a permutation. St001221The number of simple modules in the corresponding LNakayama algebra that have 2 dimensional second Extension group with the regular module. St001392The largest nonnegative integer which is not a part and is smaller than the largest part of the partition. St000329The number of evenly positioned ascents of the Dyck path, with the initial position equal to 1. St001257The dominant dimension of the double dual of A/J when A is the corresponding Nakayama algebra with Jacobson radical J. St001508The degree of the standard monomial associated to a Dyck path relative to the diagonal boundary. St001089Number of indecomposable projective non-injective modules minus the number of indecomposable projective non-injective modules with dominant dimension equal to the injective dimension in the corresponding Nakayama algebra. St001229The vector space dimension of the first extension group between the Jacobson radical J and J^2. St000446The disorder of a permutation. St001005The number of indices for a permutation that are either left-to-right maxima or right-to-left minima but not both. St000632The jump number of the poset. St000534The number of 2-rises of a permutation. St001810The number of fixed points of a permutation smaller than its largest moved point. St001180Number of indecomposable injective modules with projective dimension at most 1. St000031The number of cycles in the cycle decomposition of a permutation. St000235The number of indices that are not cyclical small weak excedances. St000443The number of long tunnels of a Dyck path. St000891The number of distinct diagonal sums of a permutation matrix. St000912The number of maximal antichains in a poset. St001187The number of simple modules with grade at least one in the corresponding Nakayama algebra. St001210Gives the maximal vector space dimension of the first Ext-group between an indecomposable module X and the regular module A, when A is the Nakayama algebra corresponding to the Dyck path. St001224Let X be the direct sum of all simple modules of 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. St000079The number of alternating sign matrices for a given Dyck path. St000083The number of left oriented leafs of a binary tree except the first one. St001128The exponens consonantiae of a partition. St001192The maximal dimension of $Ext_A^2(S,A)$ for a simple module $S$ over the corresponding Nakayama algebra $A$. St001233The number of indecomposable 2-dimensional modules with projective dimension one. St001295Gives the vector space dimension of the homomorphism space between J^2 and J^2. St001876The number of 2-regular simple modules in the incidence algebra of the lattice. St000220The number of occurrences of the pattern 132 in a permutation. St000424The number of occurrences of the pattern 132 or of the pattern 231 in a permutation. St000426The number of occurrences of the pattern 132 or of the pattern 312 in a permutation. St000800The number of occurrences of the vincular pattern |231 in a permutation. St000801The number of occurrences of the vincular pattern |312 in a permutation. 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. 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. St001247The number of parts of a partition that are not congruent 2 modulo 3. St001586The number of odd parts smaller than the largest even part in an integer partition. St000255The number of reduced Kogan faces with the permutation as type. St000225Difference between largest and smallest parts in a partition. St001124The multiplicity of the standard representation in the Kronecker square corresponding to a partition. St001396Number of triples of incomparable elements in a finite poset. St000849The number of 1/3-balanced pairs in a poset. St001397Number of pairs of incomparable elements in a finite poset. St001533The largest coefficient of the Poincare polynomial of the poset cone. St000542The number of left-to-right-minima of a permutation. St000541The number of indices greater than or equal to 2 of a permutation such that all smaller indices appear to its right. St000864The number of circled entries of the shifted recording tableau of a permutation. St000124The cardinality of the preimage of the Simion-Schmidt map. St000218The number of occurrences of the pattern 213 in a permutation. St000308The height of the tree associated to a permutation. St000264The girth of a graph, which is not a tree. St000365The number of double ascents of a permutation. St000372The number of mid points of increasing subsequences of length 3 in a permutation. St000799The number of occurrences of the vincular pattern |213 in a permutation. St001682The number of distinct positions of the pattern letter 1 in occurrences of 123 in a permutation. St000246The number of non-inversions of a permutation. St000553The number of blocks of a graph. St000673The number of non-fixed points of a permutation. St001118The acyclic chromatic index of a graph. St001645The pebbling number of a connected graph. St000706The product of the factorials of the multiplicities of an integer partition. St000707The product of the factorials of the parts. St000770The major index of an integer partition when read from bottom to top. St000771The largest multiplicity of a distance Laplacian eigenvalue in a connected graph. St000815The number of semistandard Young tableaux of partition weight of given shape. St000937The number of positive values of the symmetric group character corresponding to the partition. St000939The number of characters of the symmetric group whose value on the partition is positive. St000993The multiplicity of the largest part of an integer partition. St000478Another weight of a partition according to Alladi. 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. St000621The number of standard tableaux of shape equal to the given partition such that the minimal cyclic descent is even. St000646The number of big ascents of a permutation. St000866The number of admissible inversions of a permutation in the sense of Shareshian-Wachs. St000929The constant term of the character polynomial of an integer partition. 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. St000928The sum of the coefficients of the character polynomial of an integer partition. St001427The number of descents of a signed permutation. St000355The number of occurrences of the pattern 21-3. St000654The first descent of a permutation. St001685The number of distinct positions of the pattern letter 1 in occurrences of 132 in a permutation. St000062The length of the longest increasing subsequence of the permutation. St000357The number of occurrences of the pattern 12-3. St001082The number of boxed occurrences of 123 in a permutation. St001130The number of two successive successions in a permutation. St000080The rank of the poset. St000882The number of connected components of short braid edges in the graph of braid moves 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. St000430The number of occurrences of the pattern 123 or of the pattern 312 in a permutation. St000804The number of occurrences of the vincular pattern |123 in a permutation. St000879The number of long braid edges in the graph of braid moves of a permutation. St000086The number of subgraphs. St000094The depth of an ordered tree. St000004The major index of a permutation. St000067The inversion number of the alternating sign matrix. St000166The depth minus 1 of an ordered tree. St000213The number of weak exceedances (also weak excedences) of a permutation. St000224The sorting index of a permutation. St000314The number of left-to-right-maxima of a permutation. St000325The width of the tree associated to a permutation. St000328The maximum number of child nodes in a tree. St000332The positive inversions of an alternating sign matrix. St000448The number of pairs of vertices of a graph with distance 2. St001235The global dimension of the corresponding Comp-Nakayama algebra. St001390The number of bumps occurring when Schensted-inserting the letter 1 of a permutation. St001428The number of B-inversions of a signed permutation. St001646The number of edges that can be added without increasing the maximal degree of a graph. St000021The number of descents of a permutation. St000099The number of valleys of a permutation, including the boundary. St001220The width of a permutation. 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. St001503The largest distance of a vertex to a vertex in a cycle in the resolution quiver of the corresponding Nakayama algebra. St000023The number of inner peaks of a permutation. St000039The number of crossings of a permutation. St000217The number of occurrences of the pattern 312 in a permutation. St000219The number of occurrences of the pattern 231 in a permutation. St000317The cycle descent number of a permutation. St000423The number of occurrences of the pattern 123 or of the pattern 132 in a permutation. St000427The number of occurrences of the pattern 123 or of the pattern 231 in a permutation. 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. St001266The largest vector space dimension of an indecomposable non-projective module that is reflexive in the corresponding Nakayama algebra. St001745The number of occurrences of the arrow pattern 13 with an arrow from 1 to 2 in a permutation. St000300The number of independent sets of vertices of a graph. St000301The number of facets of the stable set polytope of a graph. St000341The non-inversion sum of a permutation. 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. St000015The number of peaks of a Dyck path. St000061The number of nodes on the left branch of a binary tree. St000154The sum of the descent bottoms of a permutation. St000156The Denert index of a permutation. St000238The number of indices that are not small weak excedances. St000239The number of small weak excedances. St000286The number of connected components of the complement of a graph. St000304The load of a permutation. St000305The inverse major index of a permutation. St000335The difference of lower and upper interactions. St000363The number of minimal vertex covers of a graph. St000628The balance of a binary word. St000720The size of the largest partition in the oscillating tableau corresponding to the perfect matching. St000722The number of different neighbourhoods in a graph. St000724The label of the leaf of the path following the smaller label in the increasing binary tree associated to a permutation. St000727The largest label of a leaf in the binary search tree associated with the permutation. St000887The maximal number of nonzero entries on a diagonal of a permutation matrix. St000930The k-Gorenstein degree of the corresponding Nakayama algebra with linear quiver. St000982The length of the longest constant subword. St001024Maximum of dominant dimensions of the simple modules in the Nakayama algebra corresponding to the Dyck path. St001239The largest vector space dimension of the double dual of a simple module in the corresponding Nakayama algebra. St001302The number of minimally dominating sets of vertices of a graph. St001304The number of maximally independent sets of vertices of a graph. St001316The domatic number of a graph. St001341The number of edges in the center of a graph. St001346The number of parking functions that give the same permutation. St001458The rank of the adjacency matrix of a graph. St001459The number of zero columns in the nullspace of a graph. St001530The depth of a Dyck path. St001652The length of a longest interval of consecutive numbers. St001662The length of the longest factor of consecutive numbers in a permutation. St001707The length of a longest path in a graph such that the remaining vertices can be partitioned into two sets of the same size without edges between them. St001725The harmonious chromatic number of a graph. St001959The product of the heights of the peaks of a Dyck path. St000056The decomposition (or block) number of a permutation. St000092The number of outer peaks of a permutation. St000109The number of elements less than or equal to the given element in Bruhat order. St000133The "bounce" of a permutation. St000155The number of exceedances (also excedences) of a permutation. St000168The number of internal nodes of an ordered tree. St000216The absolute length of a permutation. St000261The edge connectivity of a graph. St000262The vertex connectivity of a graph. St000310The minimal degree of a vertex of a graph. St000362The size of a minimal vertex cover of a graph. St000450The number of edges minus the number of vertices plus 2 of a graph. St000472The sum of the ascent bottoms of a permutation. St000482The (zero)-forcing number of a graph. St000774The maximal multiplicity of a Laplacian eigenvalue in a graph. St000776The maximal multiplicity of an eigenvalue in a graph. St000889The number of alternating sign matrices with the same antidiagonal sums. St000948The chromatic discriminant of a graph. St000987The number of positive eigenvalues of the Laplacian matrix of the graph. St001031The height of the bicoloured Motzkin path associated with the Dyck path. St001046The maximal number of arcs nesting a given arc of a perfect matching. St001119The length of a shortest maximal path in a graph. 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. St001196The global dimension of $A$ minus the global dimension of $eAe$ for the corresponding Nakayama algebra with minimal faithful projective-injective module $eA$. St001205The number of non-simple indecomposable projective-injective modules of the algebra $eAe$ in the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. St001215Let X be the direct sum of all simple modules of the corresponding Nakayama algebra. St001281The normalized isoperimetric number of a graph. St001296The maximal torsionfree index of an indecomposable non-projective module in the corresponding Nakayama algebra. St001298The number of repeated entries in the Lehmer code of a permutation. St001357The maximal degree of a regular spanning subgraph of a graph. St001391The disjunction number of a graph. St001702The absolute value of the determinant of the adjacency matrix of a graph. St001812The biclique partition number of a graph. St001869The maximum cut size of a graph. St000029The depth of a permutation. St000030The sum of the descent differences of a permutations. St000055The inversion sum of a permutation. St000162The number of nontrivial cycles in the cycle decomposition of a permutation. St000241The number of cyclical small excedances. St000242The number of indices that are not cyclical small weak excedances. St000338The number of pixed points of a permutation. St000425The number of occurrences of the pattern 132 or of the pattern 213 in a permutation. St000428The number of occurrences of the pattern 123 or of the pattern 213 in a permutation. St000663The number of right floats of a permutation. St000837The number of ascents of distance 2 of a permutation. St001163The number of simple modules with dominant dimension at least three in the corresponding Nakayama algebra. St001174The Gorenstein dimension of the algebra $A/I$ when $I$ is the tilting module corresponding to the permutation in the Auslander algebra of $K[x]/(x^n)$. St001185The number of indecomposable injective modules of grade at least 2 in the corresponding Nakayama algebra. 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. St001217The projective dimension of the indecomposable injective module I[n-2] in the corresponding Nakayama algebra with simples enumerated from 0 to n-1. 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. St001264The smallest index i such that the i-th simple module has projective dimension equal to the global dimension of 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. St001309The number of four-cliques in a graph. St001329The minimal number of occurrences of the outerplanar pattern in a linear ordering of the vertices of the graph. St001334The minimal number of occurrences of the 3-colorable pattern in a linear ordering of the vertices of the graph. St001398Number of subsets of size 3 of elements in a poset that form a "v". St001511The minimal number of transpositions needed to sort a permutation in either direction. St001546The number of monomials in the Tutte polynomial of a graph. St001731The factorization defect of a permutation. St001859The number of factors of the Stanley symmetric function associated with a permutation. St001874Lusztig's a-function for the symmetric group. 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. St000422The energy of a graph, if it is integral. St000282The size of the preimage of the map 'to poset' from Ordered trees to Posets. St001432The order dimension of the partition. St000199The column of the unique '1' in the last row of the alternating sign matrix. St000200The row of the unique '1' in the last column of the alternating sign matrix. St000746The number of pairs with odd minimum in a perfect matching. St000840The number of closers smaller than the largest opener in a perfect matching. St001323The independence gap of a graph. St001431Half of the Loewy length minus one of a modified stable Auslander algebra of the Nakayama algebra corresponding to the Dyck path. St001553The number of indecomposable summands of the square of the Jacobson radical as a bimodule in the Nakayama algebra corresponding to the Dyck path. St000689The maximal n such that the minimal generator-cogenerator module in the LNakayama algebra of a Dyck path is n-rigid. St001314The number of tilting modules of arbitrary projective dimension that have no simple modules as a direct summand in the corresponding Nakayama algebra. St000455The second largest eigenvalue of a graph if it is integral. St000806The semiperimeter of the associated bargraph. St000046The largest eigenvalue of the random to random operator acting on the simple module corresponding to the given partition. St000207Number of integral Gelfand-Tsetlin polytopes with prescribed top row and integer composition weight. St000208Number of integral Gelfand-Tsetlin polytopes with prescribed top row and integer partition weight. St000618The number of self-evacuating tableaux of given shape. St000781The number of proper colouring schemes of a Ferrers diagram. St001122The multiplicity of the sign representation in the Kronecker square corresponding to a partition. St001232The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2. 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. St001378The product of the cohook lengths of the 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. St001600The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on simple graphs. 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. 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. 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. St001780The order of promotion on the set of standard tableaux of given shape. St001785The number of ways to obtain a partition as the multiset of antidiagonal lengths of the Ferrers diagram of a partition. 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. St001914The size of the orbit of an integer partition in Bulgarian solitaire. St001924The number of cells in an integer partition whose arm and leg length coincide. St001936The number of transitive factorisations of a permutation of given cycle type into star transpositions. 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. 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. St001175The size of a partition minus the hook length of the base cell. 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. St001498The normalised height of a Nakayama algebra with magnitude 1. St001541The Gini index of an integer partition. St001767The largest minimal number of arrows pointing to a cell in the Ferrers diagram in any assignment. St000474Dyson's crank of a partition. St001526The Loewy length of the Auslander-Reiten translate of the regular module as a bimodule of the Nakayama algebra corresponding to the Dyck path. St001907The number of Bastidas - Hohlweg - Saliola excedances of a signed permutation. 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. St001282The number of graphs with the same chromatic polynomial. St001198The number of simple modules in the algebra $eAe$ with projective dimension at most 1 in the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. St001206The maximal dimension of an indecomposable projective $eAe$-module (that is the height of the corresponding Dyck path) of the corresponding Nakayama algebra with minimal faithful projective-injective module $eA$. St001182Number of indecomposable injective modules with codominant dimension at least two in the corresponding Nakayama algebra. St001255The vector space dimension of the double dual of A/J when A is the corresponding Nakayama algebra with Jacobson radical J. St001290The first natural number n such that the tensor product of n copies of D(A) is zero for the corresponding Nakayama algebra A. 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 $eA$. 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. St000075The orbit size of a standard tableau under promotion. St000331The number of upper interactions of a Dyck path. St000390The number of runs of ones in a binary word. St000529The number of permutations whose descent word is the given binary word. St000543The size of the conjugacy class of a binary word. St000626The minimal period of a binary word. St000627The exponent of a binary word. St000630The length of the shortest palindromic decomposition of a binary word. St000955Number of times one has $Ext^i(D(A),A)>0$ for $i>0$ for the corresponding LNakayama 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. St001278The number of indecomposable modules that are fixed by $\tau \Omega^1$ composed with its inverse in the corresponding Nakayama algebra. St001420Half the length of a longest factor which is its own reverse-complement of a binary word. St001509The degree of the standard monomial associated to a Dyck path relative to the trivial lower boundary. St001514The dimension of the top of the Auslander-Reiten translate of the regular modules as a bimodule. St001595The number of standard Young tableaux of the skew partition. St001804The minimal height of the rectangular inner shape in a cylindrical tableau associated to a tableau. St001929The number of meanders with top half given by the noncrossing matching corresponding to the Dyck path. St000117The number of centered tunnels of a Dyck path. St000688The global dimension minus the dominant dimension of the LNakayama algebra associated to a Dyck path. St000970Number of peaks minus the dominant dimension of the corresponding LNakayama algebra. 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. 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. St001355Number of non-empty prefixes of a binary word that contain equally many 0's and 1's. St001695The natural comajor index of a standard Young tableau. St001698The comajor index of a standard tableau minus the weighted size of its shape. St001699The major index of a standard tableau minus the weighted size of its shape. St001712The number of natural descents of a standard Young tableau. St001910The height of the middle non-run of a Dyck path. St001060The distinguishing index of a graph. St001123The multiplicity of the dual of the standard representation in the Kronecker square corresponding to a partition. St001878The projective dimension of the simple modules corresponding to the minimum of L in the incidence algebra of the lattice L. St001811The Castelnuovo-Mumford regularity of a permutation. St001856The number of edges in the reduced word graph of a permutation. St001948The number of augmented double ascents of a permutation. St001960The number of descents of a permutation minus one if its first entry is not one. St001589The nesting number of a perfect matching. St000177The number of free tiles in the pattern. St000178Number of free entries. St001195The global dimension of the algebra $A/AfA$ of the corresponding Nakayama algebra $A$ with minimal left faithful projective-injective module $Af$. St001569The maximal modular displacement of a permutation. St001604The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on polygons. St001684The reduced word complexity of a permutation. St001866The nesting alignments of a signed permutation. St001871The number of triconnected components of a graph. St000813The number of zero-one matrices with weakly decreasing column sums and row sums given by the partition. St000464The Schultz index of a connected graph. 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. St000927The alternating sum of the coefficients of the character polynomial of an integer partition. 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. St001545The second Elser number of a connected graph. 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. St000260The radius of a connected graph. St000284The Plancherel distribution on integer partitions. St000456The monochromatic index of a connected graph. 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. St000713The dimension of the irreducible representation of Sp(4) labelled by an integer partition. St000714The number of semistandard Young tableau of given shape, with entries at most 2. St000901The cube of the number of standard Young tableaux with shape given by the partition. St001877Number of indecomposable injective modules with projective dimension 2. St000699The toughness times the least common multiple of 1,. 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. St001570The minimal number of edges to add to make a graph Hamiltonian. St000477The weight of a partition according to Alladi. St000509The diagonal index (content) of a partition. St000716The dimension of the irreducible representation of Sp(6) labelled by an integer partition. St001882The number of occurrences of a type-B 231 pattern in a signed permutation. St001862The number of crossings of a signed permutation. St001896The number of right descents of a signed permutations. St001851The number of Hecke atoms of a signed permutation. St000259The diameter of a connected graph. St000369The dinv deficit of a Dyck path. St000376The bounce deficit of a Dyck path. St001035The convexity degree of the parallelogram polyomino associated with the Dyck path. St001502The global dimension minus the dominant dimension of magnitude 1 Nakayama algebras. St001603The number of colourings of a polygon such that the multiplicities of a colour are given by a partition. St001605The number of colourings of a cycle such that the multiplicities of colours are given by a partition. St001868The number of alignments of type NE of a signed permutation. St001491The number of indecomposable projective-injective modules in the algebra corresponding to a subset. St001863The number of weak excedances of a signed permutation. St001889The size of the connectivity set of a signed permutation. St001583The projective dimension of the simple module corresponding to the point in the poset of the symmetric group under bruhat order. St000136The dinv of a parking function. St000194The number of primary dinversion pairs of a labelled dyck path corresponding to a parking function. St001772The number of occurrences of the signed pattern 12 in a signed permutation. St001404The number of distinct entries in a Gelfand Tsetlin pattern. St001822The number of alignments of a signed permutation. St001935The number of ascents in a parking function. St000777The number of distinct eigenvalues of the distance Laplacian of a connected graph. St000441The number of successions of a permutation. St000942The number of critical left to right maxima of the parking functions. St001433The flag major index of a signed permutation. St001773The number of minimal elements in Bruhat order not less than the signed permutation. St001821The sorting index of a signed permutation. St001892The flag excedance statistic of a signed permutation. St001207The Lowey length of the algebra $A/T$ when $T$ is the 1-tilting module corresponding to the permutation in the Auslander algebra of $K[x]/(x^n)$. St001768The number of reduced words of a signed permutation. St001823The Stasinski-Voll length of a signed permutation. St001860The number of factors of the Stanley symmetric function associated with a signed permutation. St001904The length of the initial strictly increasing segment of a parking function. St001946The number of descents in a parking function. 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 $K[x]/(x^n)$. St001771The number of occurrences of the signed pattern 1-2 in a signed permutation. St001895The oddness of a signed permutation. St001632The number of indecomposable injective modules $I$ with $dim Ext^1(I,A)=1$ for the incidence algebra A of a poset. St000906The length of the shortest maximal chain in a poset. St001624The breadth of a lattice. St001633The number of simple modules with projective dimension two in the incidence algebra of the poset. St001095The number of non-isomorphic posets with precisely one further covering relation. St001268The size of the largest ordinal summand in the poset. St001300The rank of the boundary operator in degree 1 of the chain complex of the order complex of the poset. St000656The number of cuts of a poset.