Your data matches 7 different statistics following compositions of up to 3 maps.
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Matching statistic: St000960
Mapping
St000960: 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
['G',2]
 => 7 = 6 + 1
Description
The permanent of the Cartan matrix of a finite Cartan type.
Matching statistic: St000915
Mapping
Mp00148: Finite Cartan types —to root poset⟶ Posets
Mp00074: Posets —to graph⟶ Graphs
St000915: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
['A',1]
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
['A',2]
 => ([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => 3 = 4 - 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)
 => 5 = 6 - 1
Description
The Ore degree of a graph. This is the maximal Ore degree of an edge, which is the sum of the degrees of its two endpoints.
Matching statistic: St000207
Mapping
Mp00148: Finite Cartan types —to root poset⟶ Posets
Mp00110: Posets —Greene-Kleitman invariant⟶ Integer partitions
Mp00322: Integer partitions —Loehr-Warrington⟶ Integer partitions
St000207: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
['A',1]
 => ([],1)
 => [1]
 => [1]
 => 1
['A',2]
 => ([(0,2),(1,2)],3)
 => [2,1]
 => [3]
 => 4
['G',2]
 => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
 => [5,1]
 => [2,1,1,1,1]
 => 6
Description
Number of integral Gelfand-Tsetlin polytopes with prescribed top row and integer composition weight. Given $\lambda$ count how many ''integer compositions'' $w$ (weight) there are, such that $P_{\lambda,w}$ is integral, i.e., $w$ such that the Gelfand-Tsetlin polytope $P_{\lambda,w}$ has all vertices in integer lattice points.
Matching statistic: St001118
Mapping
Mp00148: Finite Cartan types —to root poset⟶ Posets
Mp00074: Posets —to graph⟶ Graphs
Mp00203: Graphs —cone⟶ Graphs
St001118: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
['A',1]
 => ([],1)
 => ([],1)
 => ([(0,1)],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
['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)
 => 6
Description
The acyclic chromatic index of a graph. An acyclic edge coloring of a graph is a proper colouring of the edges of a graph such that the union of the edges colored with any two given colours is a forest. The smallest number of colours such that such a colouring exists is the acyclic chromatic index.
Matching statistic: St001645
Mapping
Mp00148: Finite Cartan types —to root poset⟶ Posets
Mp00198: Posets —incomparability graph⟶ Graphs
Mp00111: Graphs —complement⟶ Graphs
St001645: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
['A',1]
 => ([],1)
 => ([],1)
 => ([],1)
 => 1
['A',2]
 => ([(0,2),(1,2)],3)
 => ([(1,2)],3)
 => ([(0,2),(1,2)],3)
 => 4
['G',2]
 => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
 => ([(4,5)],6)
 => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 6
Description
The pebbling number of a connected graph.
Matching statistic: St001345
Mapping
Mp00148: Finite Cartan types —to root poset⟶ Posets
Mp00074: Posets —to graph⟶ Graphs
Mp00111: Graphs —complement⟶ Graphs
St001345: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
['A',1]
 => ([],1)
 => ([],1)
 => ([],1)
 => 0 = 1 - 1
['A',2]
 => ([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => ([(1,2)],3)
 => 3 = 4 - 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)
 => ([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => 5 = 6 - 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: St001541
Mapping
Mp00148: Finite Cartan types —to root poset⟶ Posets
Mp00110: Posets —Greene-Kleitman invariant⟶ Integer partitions
Mp00322: Integer partitions —Loehr-Warrington⟶ Integer partitions
St001541: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
['A',1]
 => ([],1)
 => [1]
 => [1]
 => 0 = 1 - 1
['A',2]
 => ([(0,2),(1,2)],3)
 => [2,1]
 => [3]
 => 3 = 4 - 1
['G',2]
 => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
 => [5,1]
 => [2,1,1,1,1]
 => 5 = 6 - 1
Description
The Gini index of an integer partition. As discussed in [1], this statistic is equal to [[St000567]] applied to the conjugate partition.