Your data matches 4 different statistics following compositions of up to 3 maps.
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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
['A',3]
 => ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)
 => 21
Description
The number of non-isomorphic subposets of a poset.
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
Mp00203: Graphs —cone⟶ Graphs
St000301: Graphs ⟶ ℤResult quality: 60% ●values known / values provided: 60%●distinct values known / distinct values provided: 60%
Values
['A',1]
 => ([],1)
 => ([],1)
 => ([(0,1)],2)
 => 3 = 2 + 1
['A',2]
 => ([(0,2),(1,2)],3)
 => ([(1,2)],3)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 6 = 5 + 1
['B',2]
 => ([(0,3),(1,3),(3,2)],4)
 => ([(2,3)],4)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 8 = 7 + 1
['G',2]
 => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
 => ([(4,5)],6)
 => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 11 + 1
['A',3]
 => ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,6),(1,2),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 21 + 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 $\mathbb{R}^{V(G)}$.
Matching statistic: St001345
Mapping
Mp00148: Finite Cartan types —to root poset⟶ Posets
Mp00198: Posets —incomparability graph⟶ Graphs
Mp00203: Graphs —cone⟶ Graphs
St001345: Graphs ⟶ ℤResult quality: 60% ●values known / values provided: 60%●distinct values known / distinct values provided: 60%
Values
['A',1]
 => ([],1)
 => ([],1)
 => ([(0,1)],2)
 => 1 = 2 - 1
['A',2]
 => ([(0,2),(1,2)],3)
 => ([(1,2)],3)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 4 = 5 - 1
['B',2]
 => ([(0,3),(1,3),(3,2)],4)
 => ([(2,3)],4)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 6 = 7 - 1
['G',2]
 => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
 => ([(4,5)],6)
 => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 11 - 1
['A',3]
 => ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,6),(1,2),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 21 - 1
Description
The Hamming dimension of a graph. Let $H(n, k)$ be the graph whose vertices are the subsets of $\{1,\dots,n\}$, and $(u,v)$ being an edge, for $u\neq v$, if the symmetric difference of $u$ and $v$ has cardinality at most $k$. This statistic is the smallest $n$ such that the graph is an induced subgraph of $H(n, k)$ for some $k$.
Matching statistic: St001869
Mapping
Mp00148: Finite Cartan types —to root poset⟶ Posets
Mp00074: Posets —to graph⟶ Graphs
Mp00203: Graphs —cone⟶ Graphs
St001869: Graphs ⟶ ℤResult quality: 60% ●values known / values provided: 60%●distinct values known / distinct values provided: 60%
Values
['A',1]
 => ([],1)
 => ([],1)
 => ([(0,1)],2)
 => 1 = 2 - 1
['A',2]
 => ([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 4 = 5 - 1
['B',2]
 => ([(0,3),(1,3),(3,2)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 6 = 7 - 1
['G',2]
 => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 11 - 1
['A',3]
 => ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ? = 21 - 1
Description
The maximum cut size of a graph. A '''cut''' is a set of edges which connect different sides of a vertex partition $V = A \sqcup B$.