Your data matches 33 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',1]
 => 2
['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',1]
 => 2
['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: 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',1]
 => ([],1)
 => 2
['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',1]
 => ([],1)
 => [1]
 => 2
['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 4 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',1]
 => ([],1)
 => ([],1)
 => 2
['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',1]
 => ([],1)
 => [1]
 => 2
['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.
Matching statistic: St001389
Mapping
Mp00148: Finite Cartan types —to root poset⟶ Posets
Mp00306: Posets —rowmotion cycle type⟶ Integer partitions
St001389: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
['A',1]
 => ([],1)
 => [2]
 => 2
['A',2]
 => ([(0,2),(1,2)],3)
 => [3,2]
 => 5
['B',2]
 => ([(0,3),(1,3),(3,2)],4)
 => [4,2]
 => 7
['G',2]
 => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
 => [6,2]
 => 11
Description
The number of partitions of the same length below the given integer partition. For a partition $\lambda_1 \geq \dots \lambda_k > 0$, this number is $$ \det\left( \binom{\lambda_{k+1-i}}{j-i+1} \right)_{1 \le i,j \le k}.$$
Matching statistic: St001619
(load all 2 compositions to match this statistic)
Mapping
Mp00148: Finite Cartan types —to root poset⟶ Posets
Mp00282: Posets —Dedekind-MacNeille completion⟶ Lattices
St001619: Lattices ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
['A',1]
 => ([],1)
 => ([],1)
 => 2
['A',2]
 => ([(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 5
['B',2]
 => ([(0,3),(1,3),(3,2)],4)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 7
['G',2]
 => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
 => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
 => 11
Description
The number of non-isomorphic sublattices of a lattice.
Matching statistic: St001666
(load all 2 compositions to match this statistic)
Mapping
Mp00148: Finite Cartan types —to root poset⟶ Posets
Mp00282: Posets —Dedekind-MacNeille completion⟶ Lattices
St001666: Lattices ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
['A',1]
 => ([],1)
 => ([],1)
 => 2
['A',2]
 => ([(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 5
['B',2]
 => ([(0,3),(1,3),(3,2)],4)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 7
['G',2]
 => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
 => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
 => 11
Description
The number of non-isomorphic subposets of a lattice which are lattices.
Matching statistic: St000087
(load all 3 compositions to match this statistic)
Mapping
Mp00148: Finite Cartan types —to root poset⟶ Posets
Mp00198: Posets —incomparability graph⟶ Graphs
St000087: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
['A',1]
 => ([],1)
 => ([],1)
 => 1 = 2 - 1
['A',2]
 => ([(0,2),(1,2)],3)
 => ([(1,2)],3)
 => 4 = 5 - 1
['B',2]
 => ([(0,3),(1,3),(3,2)],4)
 => ([(2,3)],4)
 => 6 = 7 - 1
['G',2]
 => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
 => ([(4,5)],6)
 => 10 = 11 - 1
Description
The number of induced subgraphs. A subgraph $H \subseteq G$ is induced if $E(H)$ consists of all edges in $E(G)$ that connect the vertices of $H$.
The following 23 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
St000926The clique-coclique number of a graph. St000420The number of Dyck paths that are weakly above 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. St000419The number of Dyck paths that are weakly above the Dyck path, except for the path itself. St001643The Frobenius dimension of the Nakayama algebra corresponding to the Dyck path. St001809The index of the step at the first peak of maximal height in a Dyck path. St000641The number of non-empty boolean intervals in a poset. St001834The number of non-isomorphic minors of a graph. St000978The sum of the positions of double down-steps of a Dyck path. St000438The position of the last up step in a Dyck path. St001345The Hamming dimension of a graph. St001645The pebbling number of a connected graph. St001869The maximum cut size of a graph. 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. St000514The number of invariant simple graphs when acting with a permutation of given cycle type. St001500The global dimension of magnitude 1 Nakayama algebras. St000933The number of multipartitions of sizes given by an integer partition. St001502The global dimension minus the dominant dimension of magnitude 1 Nakayama algebras. St000940The number of characters of the symmetric group whose value on the partition is zero.