Your data matches 74 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St001146
Mapping
St001146: Finite Cartan types ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
['A',2]
 => 5
['B',2]
 => 7
['G',2]
 => 11
Description
The number of Grassmannian elements in the Coxeter group of the given type. An element is Grassmannian if it has at most one descent.
Matching statistic: St001653
Mapping
St001653: Finite Cartan types ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
['A',2]
 => 5
['B',2]
 => 7
['G',2]
 => 11
Description
The number of fully commutative elements of the Weyl group of the given Cartan type. An element $w$ of a Weyl group is fully commutative if any reduced expression for $w$ can be obtained from any other one by using only commutation relations.
Matching statistic: St000106
Mapping
St000106: Finite Cartan types ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
['A',2]
 => 6 = 5 + 1
['B',2]
 => 8 = 7 + 1
['G',2]
 => 12 = 11 + 1
Description
The size of the associated Weyl group.
Matching statistic: St001888
Mapping
St001888: Finite Cartan types ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
['A',2]
 => 3 = 5 - 2
['B',2]
 => 5 = 7 - 2
['G',2]
 => 9 = 11 - 2
Description
The number of connected elements in the Coxeter group corresponding to a finite Cartan type. Let $(W, S)$ be a Coxeter system. Then, according to [1], the connectivity set of $w\in W$ is the cardinality of $S \setminus S(w)$, where $S(w)$ is the set of generators appearing in any reduced word for $w$. For $A_n$, this is [2], for $B_n$ this is [3] and for $D_n$ this is [4].
Matching statistic: St001148
Mapping
St001148: Finite Cartan types ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
['A',2]
 => 8 = 5 + 3
['B',2]
 => 10 = 7 + 3
['G',2]
 => 14 = 11 + 3
Description
The dimension of the adjoint representation of the Lie group of given type.
Matching statistic: St000641
(load all 3 compositions to match this statistic)
Mapping
Mp00148: Finite Cartan types —to root poset⟶ Posets
St000641: Posets ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
['A',2]
 => ([(0,2),(1,2)],3)
 => 5
['B',2]
 => ([(0,3),(1,3),(3,2)],4)
 => 7
['G',2]
 => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
 => 11
Description
The number of non-empty boolean intervals in a poset.
Matching statistic: St001664
(load all 2 compositions to match this statistic)
Mapping
Mp00148: Finite Cartan types —to root poset⟶ Posets
St001664: Posets ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
['A',2]
 => ([(0,2),(1,2)],3)
 => 5
['B',2]
 => ([(0,3),(1,3),(3,2)],4)
 => 7
['G',2]
 => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
 => 11
Description
The number of non-isomorphic subposets of a poset.
Matching statistic: St000108
(load all 2 compositions to match this statistic)
Mapping
Mp00148: Finite Cartan types —to root poset⟶ Posets
Mp00110: Posets —Greene-Kleitman invariant⟶ Integer partitions
St000108: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
['A',2]
 => ([(0,2),(1,2)],3)
 => [2,1]
 => 5
['B',2]
 => ([(0,3),(1,3),(3,2)],4)
 => [3,1]
 => 7
['G',2]
 => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
 => [5,1]
 => 11
Description
The number of partitions contained in the given partition.
Matching statistic: St000301
(load all 2 compositions to match this statistic)
Mapping
Mp00148: Finite Cartan types —to root poset⟶ Posets
Mp00198: Posets —incomparability graph⟶ Graphs
St000301: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
['A',2]
 => ([(0,2),(1,2)],3)
 => ([(1,2)],3)
 => 5
['B',2]
 => ([(0,3),(1,3),(3,2)],4)
 => ([(2,3)],4)
 => 7
['G',2]
 => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
 => ([(4,5)],6)
 => 11
Description
The number of facets of the stable set polytope of a graph. The stable set polytope of a graph $G$ is the convex hull of the characteristic vectors of stable (or independent) sets of vertices of $G$ inside $\mathbb{R}^{V(G)}$.
Matching statistic: St000532
(load all 2 compositions to match this statistic)
Mapping
Mp00148: Finite Cartan types —to root poset⟶ Posets
Mp00110: Posets —Greene-Kleitman invariant⟶ Integer partitions
St000532: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
['A',2]
 => ([(0,2),(1,2)],3)
 => [2,1]
 => 5
['B',2]
 => ([(0,3),(1,3),(3,2)],4)
 => [3,1]
 => 7
['G',2]
 => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
 => [5,1]
 => 11
Description
The total number of rook placements on a Ferrers board.
The following 64 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
St001389The number of partitions of the same length below the given integer partition. St001619The number of non-isomorphic sublattices of a lattice. St001666The number of non-isomorphic subposets of a lattice which are lattices. St000063The number of linear extensions of a certain poset defined for an integer partition. St000087The number of induced subgraphs. St000184The size of the centralizer of any permutation of given cycle type. St000350The sum of the vertex degrees of a graph. St000531The leading coefficient of the rook polynomial of an integer partition. St000567The sum of the products of all pairs of parts. St000708The product of the parts of an integer partition. St000926The clique-coclique number of a graph. St001562The value of the complete homogeneous symmetric function evaluated at 1. St001659The number of ways to place as many non-attacking rooks as possible on a Ferrers board. St001814The number of partitions interlacing the given partition. St001936The number of transitive factorisations of a permutation of given cycle type into star transpositions. St001177Twice the mean value of the major index among all standard Young tableaux of a partition. St001522The total irregularity of a graph. St001571The Cartan determinant of the integer partition. St001708The number of pairs of vertices of different degree in a graph. St001710The number of permutations such that conjugation with a permutation of given cycle type yields the inverse permutation. St001521Half the total irregularity of a graph. St000477The weight of a partition according to Alladi. St000420The number of Dyck paths that are weakly above a Dyck path. St000438The position of the last up step in a Dyck path. St000978The sum of the positions of double down-steps of a Dyck path. St001213The number of indecomposable modules in the corresponding Nakayama algebra that have vanishing first Ext-group with the regular module. St001259The vector space dimension of the double dual of D(A) in the corresponding Nakayama algebra. St001658The total number of rook placements on a Ferrers board. St000300The number of independent sets of vertices of a graph. St000419The number of Dyck paths that are weakly above the Dyck path, except for the path itself. St000468The Hosoya index of a graph. St000979Half of MacMahon's equal index of a Dyck path. St001065Number of indecomposable reflexive modules in the corresponding Nakayama algebra. St001541The Gini index of an integer partition. St001643The Frobenius dimension of the Nakayama algebra corresponding to the Dyck path. St001808The box weight or horizontal decoration of a Dyck path. St001809The index of the step at the first peak of maximal height in a Dyck path. St000395The sum of the heights of the peaks of a Dyck path. St000874The position of the last double rise in a Dyck path. St000976The sum of the positions of double up-steps of a Dyck path. St000981The length of the longest zigzag subpath. St001018Sum of projective dimension of the indecomposable injective modules of the Nakayama algebra corresponding to the Dyck path. St001161The major index north count of a Dyck path. St001711The number of permutations such that conjugation with a permutation of given cycle type yields the squared permutation. St001721The degree of a binary word. St000175Degree of the polynomial counting the number of semistandard Young tableaux when stretching the shape. St000514The number of invariant simple graphs when acting with a permutation of given cycle type. St000644The number of graphs with given frequency partition. St000915The Ore degree of a graph. St001351The Albertson index of a graph. St001374The Padmakar-Ivan index of a graph. St001500The global dimension of magnitude 1 Nakayama algebras. St001669The number of single rises in a Dyck path. St000345The number of refinements of a partition. St000933The number of multipartitions of sizes given by an integer partition. St000935The number of ordered refinements of an integer partition. St001502The global dimension minus the dominant dimension of magnitude 1 Nakayama algebras. St000212The number of standard Young tableaux for an integer partition such that no two consecutive entries appear in the same row. St000394The sum of the heights of the peaks of a Dyck path minus the number of peaks. St000403The Szeged index minus the Wiener index of a graph. St000940The number of characters of the symmetric group whose value on the partition is zero. St000984The number of boxes below precisely one peak. St001307The number of induced stars on four vertices in a graph. St001714The number of subpartitions of an integer partition that do not dominate the conjugate subpartition.