Your data matches 24 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St001146
St001146: Finite Cartan types ⟶ ℤResult quality: 100% values known / values provided: 100%distinct values known / distinct values provided: 100%
Values
['A',1]
=> 2 = 1 + 1
['A',2]
=> 5 = 4 + 1
['B',2]
=> 7 = 6 + 1
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
St001653: Finite Cartan types ⟶ ℤResult quality: 100% values known / values provided: 100%distinct values known / distinct values provided: 100%
Values
['A',1]
=> 2 = 1 + 1
['A',2]
=> 5 = 4 + 1
['B',2]
=> 7 = 6 + 1
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.
Mp00148: Finite Cartan types to root posetPosets
St001664: Posets ⟶ ℤResult quality: 100% values known / values provided: 100%distinct values known / distinct values provided: 100%
Values
['A',1]
=> ([],1)
=> 2 = 1 + 1
['A',2]
=> ([(0,2),(1,2)],3)
=> 5 = 4 + 1
['B',2]
=> ([(0,3),(1,3),(3,2)],4)
=> 7 = 6 + 1
Description
The number of non-isomorphic subposets of a poset.
Mp00148: Finite Cartan types to root posetPosets
Mp00198: Posets incomparability graphGraphs
St000087: Graphs ⟶ ℤResult quality: 100% values known / values provided: 100%distinct values known / distinct values provided: 100%
Values
['A',1]
=> ([],1)
=> ([],1)
=> 1
['A',2]
=> ([(0,2),(1,2)],3)
=> ([(1,2)],3)
=> 4
['B',2]
=> ([(0,3),(1,3),(3,2)],4)
=> ([(2,3)],4)
=> 6
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 $H$.
Mp00148: Finite Cartan types to root posetPosets
Mp00198: Posets incomparability graphGraphs
St000926: Graphs ⟶ ℤResult quality: 100% values known / values provided: 100%distinct values known / distinct values provided: 100%
Values
['A',1]
=> ([],1)
=> ([],1)
=> 1
['A',2]
=> ([(0,2),(1,2)],3)
=> ([(1,2)],3)
=> 4
['B',2]
=> ([(0,3),(1,3),(3,2)],4)
=> ([(2,3)],4)
=> 6
Description
The clique-coclique number of a graph. This is the product of the size of a maximal clique [[St000097]] and the size of a maximal independent set [[St000093]].
Mp00148: Finite Cartan types to root posetPosets
Mp00110: Posets Greene-Kleitman invariantInteger 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 = 1 + 1
['A',2]
=> ([(0,2),(1,2)],3)
=> [2,1]
=> 5 = 4 + 1
['B',2]
=> ([(0,3),(1,3),(3,2)],4)
=> [3,1]
=> 7 = 6 + 1
Description
The number of partitions contained in the given partition.
Mp00148: Finite Cartan types to root posetPosets
Mp00198: Posets incomparability graphGraphs
St000301: Graphs ⟶ ℤResult quality: 100% values known / values provided: 100%distinct values known / distinct values provided: 100%
Values
['A',1]
=> ([],1)
=> ([],1)
=> 2 = 1 + 1
['A',2]
=> ([(0,2),(1,2)],3)
=> ([(1,2)],3)
=> 5 = 4 + 1
['B',2]
=> ([(0,3),(1,3),(3,2)],4)
=> ([(2,3)],4)
=> 7 = 6 + 1
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 $\mathbb{R}^{V(G)}$.
Mp00148: Finite Cartan types to root posetPosets
Mp00110: Posets Greene-Kleitman invariantInteger 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 = 1 + 1
['A',2]
=> ([(0,2),(1,2)],3)
=> [2,1]
=> 5 = 4 + 1
['B',2]
=> ([(0,3),(1,3),(3,2)],4)
=> [3,1]
=> 7 = 6 + 1
Description
The total number of rook placements on a Ferrers board.
Matching statistic: St000620
Mp00148: Finite Cartan types to root posetPosets
Mp00306: Posets rowmotion cycle typeInteger partitions
St000620: Integer partitions ⟶ ℤResult quality: 100% values known / values provided: 100%distinct values known / distinct values provided: 100%
Values
['A',1]
=> ([],1)
=> [2]
=> 0 = 1 - 1
['A',2]
=> ([(0,2),(1,2)],3)
=> [3,2]
=> 3 = 4 - 1
['B',2]
=> ([(0,3),(1,3),(3,2)],4)
=> [4,2]
=> 5 = 6 - 1
Description
The number of standard tableaux of shape equal to the given partition such that the minimal cyclic descent is odd. To be precise, this is given for a partition $\lambda \vdash n$ by the number of standard tableaux $T$ of shape $\lambda$ such that $\min\big( \operatorname{Des}(T) \cup \{n\} \big)$ is odd. The case of an even minimum is [[St000621]].
Matching statistic: St001389
Mp00148: Finite Cartan types to root posetPosets
Mp00306: Posets rowmotion cycle typeInteger 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 = 1 + 1
['A',2]
=> ([(0,2),(1,2)],3)
=> [3,2]
=> 5 = 4 + 1
['B',2]
=> ([(0,3),(1,3),(3,2)],4)
=> [4,2]
=> 7 = 6 + 1
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 $$ \det\left( \binom{\lambda_{k+1-i}}{j-i+1} \right)_{1 \le i,j \le k}.$$
The following 14 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
St001619The number of non-isomorphic sublattices of a lattice. St001666The number of non-isomorphic subposets of a lattice which are lattices. St000046The largest eigenvalue of the random to random operator acting on the simple module corresponding to the given partition. St000419The number of Dyck paths that are weakly above the Dyck path, except for the path itself. St001345The Hamming dimension of a graph. St001592The maximal number of simple paths between any two different vertices of a graph. 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. St001869The maximum cut size 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. St001798The difference of the number of edges in a graph and the number of edges in the complement of the Turán graph.