Your data matches 208 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St000197
(load all 12 compositions to match this statistic)
Mapping
St000197: Alternating sign matrices ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[[1]]
 => 1
[[1,0],[0,1]]
 => 2
[[0,1],[1,0]]
 => 2
[[1,0,0],[0,1,0],[0,0,1]]
 => 3
[[0,1,0],[1,0,0],[0,0,1]]
 => 3
[[1,0,0],[0,0,1],[0,1,0]]
 => 3
[[0,1,0],[1,-1,1],[0,1,0]]
 => 4
[[0,0,1],[1,0,0],[0,1,0]]
 => 3
[[0,1,0],[0,0,1],[1,0,0]]
 => 3
[[0,0,1],[0,1,0],[1,0,0]]
 => 3
Description
The number of entries equal to positive one in the alternating sign matrix.
Matching statistic: St001348
(load all 23 compositions to match this statistic)
Mapping
Mp00007: Alternating sign matrices —to Dyck path⟶ Dyck paths
St001348: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[[1]]
 => [1,0]
 => 1
[[1,0],[0,1]]
 => [1,0,1,0]
 => 2
[[0,1],[1,0]]
 => [1,1,0,0]
 => 2
[[1,0,0],[0,1,0],[0,0,1]]
 => [1,0,1,0,1,0]
 => 3
[[0,1,0],[1,0,0],[0,0,1]]
 => [1,1,0,0,1,0]
 => 3
[[1,0,0],[0,0,1],[0,1,0]]
 => [1,0,1,1,0,0]
 => 4
[[0,1,0],[1,-1,1],[0,1,0]]
 => [1,1,0,1,0,0]
 => 3
[[0,0,1],[1,0,0],[0,1,0]]
 => [1,1,1,0,0,0]
 => 3
[[0,1,0],[0,0,1],[1,0,0]]
 => [1,1,0,1,0,0]
 => 3
[[0,0,1],[0,1,0],[1,0,0]]
 => [1,1,1,0,0,0]
 => 3
Description
The bounce of the parallelogram polyomino associated with the Dyck path. A bijection due to Delest and Viennot [1] associates a Dyck path with a parallelogram polyomino. The bounce statistic is defined in [2].
Matching statistic: St000030
(load all 8 compositions to match this statistic)
Mapping
Mp00007: Alternating sign matrices —to Dyck path⟶ Dyck paths
Mp00201: Dyck paths —Ringel⟶ Permutations
St000030: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[[1]]
 => [1,0]
 => [2,1] => 1
[[1,0],[0,1]]
 => [1,0,1,0]
 => [3,1,2] => 2
[[0,1],[1,0]]
 => [1,1,0,0]
 => [2,3,1] => 2
[[1,0,0],[0,1,0],[0,0,1]]
 => [1,0,1,0,1,0]
 => [4,1,2,3] => 3
[[0,1,0],[1,0,0],[0,0,1]]
 => [1,1,0,0,1,0]
 => [2,4,1,3] => 3
[[1,0,0],[0,0,1],[0,1,0]]
 => [1,0,1,1,0,0]
 => [3,1,4,2] => 4
[[0,1,0],[1,-1,1],[0,1,0]]
 => [1,1,0,1,0,0]
 => [4,3,1,2] => 3
[[0,0,1],[1,0,0],[0,1,0]]
 => [1,1,1,0,0,0]
 => [2,3,4,1] => 3
[[0,1,0],[0,0,1],[1,0,0]]
 => [1,1,0,1,0,0]
 => [4,3,1,2] => 3
[[0,0,1],[0,1,0],[1,0,0]]
 => [1,1,1,0,0,0]
 => [2,3,4,1] => 3
Description
The sum of the descent differences of a permutations. This statistic is given by $$\pi \mapsto \sum_{i\in\operatorname{Des}(\pi)} (\pi_i-\pi_{i+1}).$$ See [[St000111]] and [[St000154]] for the sum of the descent tops and the descent bottoms, respectively. This statistic was studied in [1] and [2] where is was called the ''drop'' of a permutation.
Matching statistic: St000176
(load all 2 compositions to match this statistic)
Mapping
Mp00001: Alternating sign matrices —to semistandard tableau via monotone triangles⟶ Semistandard tableaux
Mp00076: Semistandard tableaux —to Gelfand-Tsetlin pattern⟶ Gelfand-Tsetlin patterns
St000176: Gelfand-Tsetlin patterns ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[[1]]
 => [[1]]
 => [[1]]
 => 1
[[1,0],[0,1]]
 => [[1,1],[2]]
 => [[2,1],[2]]
 => 2
[[0,1],[1,0]]
 => [[1,2],[2]]
 => [[2,1],[1]]
 => 2
[[1,0,0],[0,1,0],[0,0,1]]
 => [[1,1,1],[2,2],[3]]
 => [[3,2,1],[3,2],[3]]
 => 3
[[0,1,0],[1,0,0],[0,0,1]]
 => [[1,1,2],[2,2],[3]]
 => [[3,2,1],[3,2],[2]]
 => 3
[[1,0,0],[0,0,1],[0,1,0]]
 => [[1,1,1],[2,3],[3]]
 => [[3,2,1],[3,1],[3]]
 => 3
[[0,1,0],[1,-1,1],[0,1,0]]
 => [[1,1,2],[2,3],[3]]
 => [[3,2,1],[3,1],[2]]
 => 4
[[0,0,1],[1,0,0],[0,1,0]]
 => [[1,1,3],[2,3],[3]]
 => [[3,2,1],[2,1],[2]]
 => 3
[[0,1,0],[0,0,1],[1,0,0]]
 => [[1,2,2],[2,3],[3]]
 => [[3,2,1],[3,1],[1]]
 => 3
[[0,0,1],[0,1,0],[1,0,0]]
 => [[1,2,3],[2,3],[3]]
 => [[3,2,1],[2,1],[1]]
 => 3
Description
The total number of tiles in the Gelfand-Tsetlin pattern. The tiling of a Gelfand-Tsetlin pattern is the finest partition of the entries in the pattern, such that adjacent (NW,NE,SW,SE) entries that are equal belong to the same part. These parts are called tiles, and each entry in a pattern belongs to exactly one tile.
Matching statistic: St000229
(load all 9 compositions to match this statistic)
Mapping
Mp00002: Alternating sign matrices —to left key permutation⟶ Permutations
Mp00151: Permutations —to cycle type⟶ Set partitions
St000229: Set partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[[1]]
 => [1] => {{1}}
 => 1
[[1,0],[0,1]]
 => [1,2] => {{1},{2}}
 => 2
[[0,1],[1,0]]
 => [2,1] => {{1,2}}
 => 2
[[1,0,0],[0,1,0],[0,0,1]]
 => [1,2,3] => {{1},{2},{3}}
 => 3
[[0,1,0],[1,0,0],[0,0,1]]
 => [2,1,3] => {{1,2},{3}}
 => 3
[[1,0,0],[0,0,1],[0,1,0]]
 => [1,3,2] => {{1},{2,3}}
 => 3
[[0,1,0],[1,-1,1],[0,1,0]]
 => [1,3,2] => {{1},{2,3}}
 => 3
[[0,0,1],[1,0,0],[0,1,0]]
 => [3,1,2] => {{1,2,3}}
 => 3
[[0,1,0],[0,0,1],[1,0,0]]
 => [2,3,1] => {{1,2,3}}
 => 3
[[0,0,1],[0,1,0],[1,0,0]]
 => [3,2,1] => {{1,3},{2}}
 => 4
Description
Sum of the difference between the maximal and the minimal elements of the blocks plus the number of blocks of a set partition. This is, for a set partition $P = \{B_1,\ldots,B_k\}$ of $\{1,\ldots,n\}$, the statistic is $$d(P) = \sum_i \big(\operatorname{max}(B_i)-\operatorname{min}(B_i)+1\big).$$ This statistic is called ''dimension index'' in [2]
Matching statistic: St000384
(load all 3 compositions to match this statistic)
Mapping
Mp00001: Alternating sign matrices —to semistandard tableau via monotone triangles⟶ Semistandard tableaux
Mp00225: Semistandard tableaux —weight⟶ Integer partitions
St000384: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[[1]]
 => [[1]]
 => [1]
 => 1
[[1,0],[0,1]]
 => [[1,1],[2]]
 => [2,1]
 => 2
[[0,1],[1,0]]
 => [[1,2],[2]]
 => [2,1]
 => 2
[[1,0,0],[0,1,0],[0,0,1]]
 => [[1,1,1],[2,2],[3]]
 => [3,2,1]
 => 3
[[0,1,0],[1,0,0],[0,0,1]]
 => [[1,1,2],[2,2],[3]]
 => [3,2,1]
 => 3
[[1,0,0],[0,0,1],[0,1,0]]
 => [[1,1,1],[2,3],[3]]
 => [3,2,1]
 => 3
[[0,1,0],[1,-1,1],[0,1,0]]
 => [[1,1,2],[2,3],[3]]
 => [2,2,2]
 => 4
[[0,0,1],[1,0,0],[0,1,0]]
 => [[1,1,3],[2,3],[3]]
 => [3,2,1]
 => 3
[[0,1,0],[0,0,1],[1,0,0]]
 => [[1,2,2],[2,3],[3]]
 => [3,2,1]
 => 3
[[0,0,1],[0,1,0],[1,0,0]]
 => [[1,2,3],[2,3],[3]]
 => [3,2,1]
 => 3
Description
The maximal part of the shifted composition of an integer partition. A partition $\lambda = (\lambda_1,\ldots,\lambda_k)$ is shifted into a composition by adding $i-1$ to the $i$-th part. The statistic is then $\operatorname{max}_i\{ \lambda_i + i - 1 \}$. See also [[St000380]].
Matching statistic: St000395
(load all 23 compositions to match this statistic)
Mapping
Mp00002: Alternating sign matrices —to left key permutation⟶ Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
St000395: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[[1]]
 => [1] => [1,0]
 => 1
[[1,0],[0,1]]
 => [1,2] => [1,0,1,0]
 => 2
[[0,1],[1,0]]
 => [2,1] => [1,1,0,0]
 => 2
[[1,0,0],[0,1,0],[0,0,1]]
 => [1,2,3] => [1,0,1,0,1,0]
 => 3
[[0,1,0],[1,0,0],[0,0,1]]
 => [2,1,3] => [1,1,0,0,1,0]
 => 3
[[1,0,0],[0,0,1],[0,1,0]]
 => [1,3,2] => [1,0,1,1,0,0]
 => 3
[[0,1,0],[1,-1,1],[0,1,0]]
 => [1,3,2] => [1,0,1,1,0,0]
 => 3
[[0,0,1],[1,0,0],[0,1,0]]
 => [3,1,2] => [1,1,1,0,0,0]
 => 3
[[0,1,0],[0,0,1],[1,0,0]]
 => [2,3,1] => [1,1,0,1,0,0]
 => 4
[[0,0,1],[0,1,0],[1,0,0]]
 => [3,2,1] => [1,1,1,0,0,0]
 => 3
Description
The sum of the heights of the peaks of a Dyck path.
Matching statistic: St001018
(load all 22 compositions to match this statistic)
Mapping
Mp00002: Alternating sign matrices —to left key permutation⟶ Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
St001018: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[[1]]
 => [1] => [1,0]
 => 1
[[1,0],[0,1]]
 => [1,2] => [1,0,1,0]
 => 2
[[0,1],[1,0]]
 => [2,1] => [1,1,0,0]
 => 2
[[1,0,0],[0,1,0],[0,0,1]]
 => [1,2,3] => [1,0,1,0,1,0]
 => 3
[[0,1,0],[1,0,0],[0,0,1]]
 => [2,1,3] => [1,1,0,0,1,0]
 => 3
[[1,0,0],[0,0,1],[0,1,0]]
 => [1,3,2] => [1,0,1,1,0,0]
 => 3
[[0,1,0],[1,-1,1],[0,1,0]]
 => [1,3,2] => [1,0,1,1,0,0]
 => 3
[[0,0,1],[1,0,0],[0,1,0]]
 => [3,1,2] => [1,1,1,0,0,0]
 => 3
[[0,1,0],[0,0,1],[1,0,0]]
 => [2,3,1] => [1,1,0,1,0,0]
 => 4
[[0,0,1],[0,1,0],[1,0,0]]
 => [3,2,1] => [1,1,1,0,0,0]
 => 3
Description
Sum of projective dimension of the indecomposable injective modules of the Nakayama algebra corresponding to the Dyck path.
Matching statistic: St001034
(load all 19 compositions to match this statistic)
Mapping
Mp00007: Alternating sign matrices —to Dyck path⟶ Dyck paths
Mp00118: Dyck paths —swap returns and last descent⟶ Dyck paths
St001034: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[[1]]
 => [1,0]
 => [1,0]
 => 1
[[1,0],[0,1]]
 => [1,0,1,0]
 => [1,1,0,0]
 => 2
[[0,1],[1,0]]
 => [1,1,0,0]
 => [1,0,1,0]
 => 2
[[1,0,0],[0,1,0],[0,0,1]]
 => [1,0,1,0,1,0]
 => [1,1,1,0,0,0]
 => 4
[[0,1,0],[1,0,0],[0,0,1]]
 => [1,1,0,0,1,0]
 => [1,1,0,1,0,0]
 => 3
[[1,0,0],[0,0,1],[0,1,0]]
 => [1,0,1,1,0,0]
 => [1,0,1,1,0,0]
 => 3
[[0,1,0],[1,-1,1],[0,1,0]]
 => [1,1,0,1,0,0]
 => [1,1,0,0,1,0]
 => 3
[[0,0,1],[1,0,0],[0,1,0]]
 => [1,1,1,0,0,0]
 => [1,0,1,0,1,0]
 => 3
[[0,1,0],[0,0,1],[1,0,0]]
 => [1,1,0,1,0,0]
 => [1,1,0,0,1,0]
 => 3
[[0,0,1],[0,1,0],[1,0,0]]
 => [1,1,1,0,0,0]
 => [1,0,1,0,1,0]
 => 3
Description
The area of the parallelogram polyomino associated with the Dyck path. The (bivariate) generating function is given in [1].
Matching statistic: St000380
(load all 2 compositions to match this statistic)
Mapping
Mp00001: Alternating sign matrices —to semistandard tableau via monotone triangles⟶ Semistandard tableaux
Mp00225: Semistandard tableaux —weight⟶ Integer partitions
St000380: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[[1]]
 => [[1]]
 => [1]
 => 2 = 1 + 1
[[1,0],[0,1]]
 => [[1,1],[2]]
 => [2,1]
 => 3 = 2 + 1
[[0,1],[1,0]]
 => [[1,2],[2]]
 => [2,1]
 => 3 = 2 + 1
[[1,0,0],[0,1,0],[0,0,1]]
 => [[1,1,1],[2,2],[3]]
 => [3,2,1]
 => 4 = 3 + 1
[[0,1,0],[1,0,0],[0,0,1]]
 => [[1,1,2],[2,2],[3]]
 => [3,2,1]
 => 4 = 3 + 1
[[1,0,0],[0,0,1],[0,1,0]]
 => [[1,1,1],[2,3],[3]]
 => [3,2,1]
 => 4 = 3 + 1
[[0,1,0],[1,-1,1],[0,1,0]]
 => [[1,1,2],[2,3],[3]]
 => [2,2,2]
 => 5 = 4 + 1
[[0,0,1],[1,0,0],[0,1,0]]
 => [[1,1,3],[2,3],[3]]
 => [3,2,1]
 => 4 = 3 + 1
[[0,1,0],[0,0,1],[1,0,0]]
 => [[1,2,2],[2,3],[3]]
 => [3,2,1]
 => 4 = 3 + 1
[[0,0,1],[0,1,0],[1,0,0]]
 => [[1,2,3],[2,3],[3]]
 => [3,2,1]
 => 4 = 3 + 1
Description
Half of the maximal perimeter of a rectangle fitting into the diagram of an integer partition. Put differently, this is the smallest number $n$ such that the partition fits into the triangular partition $(n-1,n-2,\dots,1)$.
The following 198 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
St000473The number of parts of a partition that are strictly bigger than the number of ones. St001065Number of indecomposable reflexive modules in the corresponding Nakayama algebra. St001251The number of parts of a partition that are not congruent 1 modulo 3. St001280The number of parts of an integer partition that are at least two. St000474Dyson's crank of a partition. St001218Smallest index k greater than or equal to one such that the Coxeter matrix C of the corresponding Nakayama algebra has C^k=1. St001650The order of Ringel's homological bijection associated to the linear Nakayama algebra corresponding to the Dyck path. St000013The height of a Dyck path. St000029The depth of a permutation. St000062The length of the longest increasing subsequence of the permutation. St000155The number of exceedances (also excedences) of a permutation. St000189The number of elements in the poset. St000238The number of indices that are not small weak excedances. St000308The height of the tree associated to a permutation. St000337The lec statistic, the sum of the inversion numbers of the hook factors of a permutation. St000354The number of recoils of a permutation. St000394The sum of the heights of the peaks of a Dyck path minus the number of peaks. St000443The number of long tunnels of a Dyck path. St000451The length of the longest pattern of the form k 1 2. St000476The sum of the semi-lengths of tunnels before a valley of a Dyck path. St000519The largest length of a factor maximising the subword complexity. St000645The sum of the areas of the rectangles formed by two consecutive peaks and the valley in between. St000670The reversal length of a permutation. St000702The number of weak deficiencies of a permutation. St000703The number of deficiencies of a permutation. St000728The dimension of a set partition. St000730The maximal arc length of a set partition. St000829The Ulam distance of a permutation to the identity permutation. St000922The minimal number such that all substrings of this length are unique. St001007Number of simple modules with projective dimension 1 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. St001116The game chromatic number of a graph. St001187The number of simple modules with grade at least one in the corresponding Nakayama algebra. St001224Let X be the direct sum of all simple modules of the corresponding Nakayama algebra. St001286The annihilation number of a graph. 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. St001343The dimension of the reduced incidence algebra of a poset. St001405The number of bonds in a permutation. St001489The maximum of the number of descents and the number of inverse descents. St001515The vector space dimension of the socle of the first syzygy module of the regular module (as a bimodule). St001526The Loewy length of the Auslander-Reiten translate of the regular module as a bimodule of the Nakayama algebra corresponding to the Dyck path. St001566The length of the longest arithmetic progression in a permutation. St001717The largest size of an interval in a poset. St001861The number of Bruhat lower covers of a permutation. St000024The number of double up and double down steps of a Dyck path. St000070The number of antichains in a poset. St000104The number of facets in the order polytope of this poset. St000108The number of partitions contained in the given partition. St000144The pyramid weight of the Dyck path. St000151The number of facets in the chain polytope of the poset. St000245The number of ascents of a permutation. St000316The number of non-left-to-right-maxima of a permutation. St000319The spin of an integer partition. St000320The dinv adjustment of an integer partition. St000393The number of strictly increasing runs in a binary word. St000532The total number of rook placements on a Ferrers board. St000624The normalized sum of the minimal distances to a greater element. St000625The sum of the minimal distances to a greater element. St000663The number of right floats of a permutation. St000672The number of minimal elements in Bruhat order not less than the permutation. St000710The number of big deficiencies of a permutation. St000711The number of big exceedences of a permutation. St000809The reduced reflection length of the permutation. St000834The number of right outer peaks of a permutation. St000863The length of the first row of the shifted shape of a permutation. St000935The number of ordered refinements of an integer partition. St001020Sum of the codominant dimensions of the non-projective indecomposable injective modules of the Nakayama algebra corresponding to the Dyck path. St001076The minimal length of a factorization of a permutation into transpositions that are cyclic shifts of (12). St001077The prefix exchange distance of a permutation. 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. St001180Number of indecomposable injective modules with projective dimension at most 1. St001211The number of simple modules in the corresponding Nakayama algebra that have vanishing second Ext-group with the regular module. St001267The length of the Lyndon factorization of the binary word. St001269The sum of the minimum of the number of exceedances and deficiencies in each cycle of a permutation. St001298The number of repeated entries in the Lehmer code of a permutation. St001300The rank of the boundary operator in degree 1 of the chain complex of the order complex of the poset. St001345The Hamming dimension of a graph. St001403The number of vertical separators in a permutation. 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. St001554The number of distinct nonempty subtrees of a binary tree. St001565The number of arithmetic progressions of length 2 in a permutation. St001664The number of non-isomorphic subposets of a poset. St001792The arboricity of a graph. St001882The number of occurrences of a type-B 231 pattern in a signed permutation. St000058The order of a permutation. St000146The Andrews-Garvan crank of a partition. 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. St001190Number of simple modules with projective dimension at most 4 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 St000967The value p(1) for the Coxeterpolynomial p of the corresponding LNakayama algebra. St001604The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on polygons. St000444The length of the maximal rise of a Dyck path. St000619The number of cyclic descents of a permutation. St000656The number of cuts of a poset. St000923The minimal number with no two order isomorphic substrings of this length in a permutation. St000208Number of integral Gelfand-Tsetlin polytopes with prescribed top row and integer partition weight. St000243The number of cyclic valleys and cyclic peaks of a permutation. St000442The maximal area to the right of an up step of a Dyck path. St000520The number of patterns in a permutation. St000646The number of big ascents of a permutation. St000744The length of the path to the largest entry in a standard Young tableau. St001220The width of a permutation. St001389The number of partitions of the same length below the given integer partition. St001419The length of the longest palindromic factor beginning with a one of a binary word. St001915The size of the component corresponding to a necklace in Bulgarian solitaire. St000486The number of cycles of length at least 3 of a permutation. St000516The number of stretching pairs of a permutation. 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. St000779The tier of a permutation. St000837The number of ascents of distance 2 of a permutation. St000872The number of very big descents of a permutation. St000931The number of occurrences of the pattern UUU in a Dyck path. St001176The size of a partition minus its first part. St001394The genus of a permutation. St001657The number of twos in an integer partition. St001745The number of occurrences of the arrow pattern 13 with an arrow from 1 to 2 in a permutation. St001961The sum of the greatest common divisors of all pairs of parts. St000080The rank of the poset. St000307The number of rowmotion orbits of a poset. 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 $eA$. St000718The largest Laplacian eigenvalue of a graph if it is integral. St001199The dominant dimension of $eAe$ for the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. St001875The number of simple modules with projective dimension at most 1. St000219The number of occurrences of the pattern 231 in a permutation. St000045The number of linear extensions of a binary tree. St001605The number of colourings of a cycle such that the multiplicities of colours are given by a partition. St000815The number of semistandard Young tableaux of partition weight of given shape. St001812The biclique partition number of a graph. St001880The number of 2-Gorenstein indecomposable injective modules in the incidence algebra of the lattice. St000566The number of ways to select a row of a Ferrers shape and two cells in this row. St000706The product of the factorials of the multiplicities of an integer partition. St000937The number of positive values of the symmetric group character corresponding to the partition. St000938The number of zeros of the symmetric group character corresponding to the partition. St000993The multiplicity of the largest part of an integer partition. St000997The even-odd crank of an integer partition. St001097The coefficient of the monomial symmetric function indexed by the partition in the formal group law for linear orders. St001603The number of colourings of a polygon such that the multiplicities of a colour are given by a partition. St001629The coefficient of the integer composition in the quasisymmetric expansion of the relabelling action of the symmetric group on cycles. St000777The number of distinct eigenvalues of the distance Laplacian of a connected graph. St000259The diameter of a connected graph. St000741The Colin de Verdière graph invariant. St001232The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2. St001645The pebbling number of a connected graph. St001621The number of atoms of a lattice. St001623The number of doubly irreducible elements of a lattice. St001626The number of maximal proper sublattices of a lattice. St000260The radius of a connected graph. St000466The Gutman (or modified Schultz) index of a connected graph. St000550The number of modular elements of a lattice. St000551The number of left modular elements of a lattice. St001644The dimension of a graph. St000739The first entry in the last row of a semistandard tableau. St001401The number of distinct entries in a semistandard tableau. St000101The cocharge of a semistandard tableau. St000736The last entry in the first row of a semistandard tableau. St000102The charge of a semistandard tableau. St001556The number of inversions of the third entry of a permutation. St001582The grades of the simple modules corresponding to the points in the poset of the symmetric group under the Bruhat order. St001960The number of descents of a permutation minus one if its first entry is not one. St000134The size of the orbit of an alternating sign matrix under gyration. St000264The girth of a graph, which is not a tree. St000454The largest eigenvalue of a graph if it is integral. St000762The sum of the positions of the weak records of an integer composition. St000806The semiperimeter of the associated bargraph. St000942The number of critical left to right maxima of the parking functions. St001060The distinguishing index of a graph. St001207The Lowey length of the algebra $A/T$ when $T$ is the 1-tilting module corresponding to the permutation in the Auslander algebra of $K[x]/(x^n)$. St001330The hat guessing number of a graph. St001491The number of indecomposable projective-injective modules in the algebra corresponding to a subset. St001569The maximal modular displacement of a permutation. St001624The breadth of a lattice. St001637The number of (upper) dissectors of a poset. St001668The number of points of the poset minus the width of the poset. St001686The order of promotion on a Gelfand-Tsetlin pattern. St001769The reflection length of a signed permutation. St001773The number of minimal elements in Bruhat order not less than the signed permutation. St001863The number of weak excedances of a signed permutation. St001864The number of excedances of a signed permutation. St001879The number of indecomposable summands of the top of the first syzygy of the dual of the regular module in the incidence algebra of the lattice. St001896The number of right descents of a signed permutations. St001905The number of preferred parking spots in a parking function less than the index of the car. St001946The number of descents in a parking function. St000074The number of special entries. St000152The number of boxed plus the number of special entries. 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. St001553The number of indecomposable summands of the square of the Jacobson radical as a bimodule in the Nakayama algebra corresponding to the Dyck path. St001684The reduced word complexity of a permutation. St001738The minimal order of a graph which is not an induced subgraph of the given graph. St001754The number of tolerances of a finite lattice. St001811The Castelnuovo-Mumford regularity of a permutation. St001823The Stasinski-Voll length of a signed permutation. St001856The number of edges in the reduced word graph of a permutation. St001926Sparre Andersen's position of the maximum of a signed permutation. St001935The number of ascents in a parking function. St001948The number of augmented double ascents of a permutation.