Your data matches 3 different statistics following compositions of up to 3 maps.
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Matching statistic: St001680
Mapping
St001680: Finite Cartan types ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
['A',1]
 => 1
['A',2]
 => 5
['B',2]
 => 10
['G',2]
 => 26
['A',3]
 => 14
['B',3]
 => 35
['C',3]
 => 35
Description
The sum of the squares of the exponents of the Weyl group of the finite Cartan type. According to Suter [1], this equals $\frac{1}{6}n(h^2 + \gamma - h)$, where $n$ is the rank, $h$ is the Coxeter number and $\gamma$ the gamma number.
Matching statistic: St001127
Mapping
Mp00148: Finite Cartan types —to root poset⟶ Posets
Mp00110: Posets —Greene-Kleitman invariant⟶ Integer partitions
St001127: Integer partitions ⟶ 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)
 => [2,1]
 => 5
['B',2]
 => ([(0,3),(1,3),(3,2)],4)
 => [3,1]
 => 10
['G',2]
 => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
 => [5,1]
 => 26
['A',3]
 => ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)
 => [3,2,1]
 => 14
['B',3]
 => ([(0,7),(1,8),(2,7),(2,8),(4,5),(5,3),(6,5),(7,6),(8,4),(8,6)],9)
 => [5,3,1]
 => 35
['C',3]
 => ([(0,7),(1,8),(2,7),(2,8),(4,5),(5,3),(6,5),(7,6),(8,4),(8,6)],9)
 => [5,3,1]
 => 35
Description
The sum of the squares of the parts of a partition.
Matching statistic: St001706
Mapping
Mp00148: Finite Cartan types —to root poset⟶ Posets
Mp00198: Posets —incomparability graph⟶ Graphs
Mp00203: Graphs —cone⟶ Graphs
St001706: Graphs ⟶ ℤResult quality: 43% ●values known / values provided: 43%●distinct values known / distinct values provided: 50%
Values
['A',1]
 => ([],1)
 => ([],1)
 => ([(0,1)],2)
 => 4 = 1 + 3
['A',2]
 => ([(0,2),(1,2)],3)
 => ([(1,2)],3)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 8 = 5 + 3
['B',2]
 => ([(0,3),(1,3),(3,2)],4)
 => ([(2,3)],4)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 13 = 10 + 3
['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)
 => ? = 26 + 3
['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)
 => ? ∊ {14,35,35} + 3
['B',3]
 => ([(0,7),(1,8),(2,7),(2,8),(4,5),(5,3),(6,5),(7,6),(8,4),(8,6)],9)
 => ([(2,7),(3,5),(3,8),(4,6),(4,8),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(0,9),(1,9),(2,7),(2,9),(3,5),(3,8),(3,9),(4,6),(4,8),(4,9),(5,6),(5,7),(5,9),(6,8),(6,9),(7,8),(7,9),(8,9)],10)
 => ? ∊ {14,35,35} + 3
['C',3]
 => ([(0,7),(1,8),(2,7),(2,8),(4,5),(5,3),(6,5),(7,6),(8,4),(8,6)],9)
 => ([(2,7),(3,5),(3,8),(4,6),(4,8),(5,6),(5,7),(6,8),(7,8)],9)
 => ([(0,9),(1,9),(2,7),(2,9),(3,5),(3,8),(3,9),(4,6),(4,8),(4,9),(5,6),(5,7),(5,9),(6,8),(6,9),(7,8),(7,9),(8,9)],10)
 => ? ∊ {14,35,35} + 3
Description
The number of closed sets in a graph. A subset $S$ of the set of vertices is a closed set, if for any pair of distinct elements of $S$ the intersection of the corresponding neighbourhoods is a subset of $S$: $$ \forall a, b\in S: N(a)\cap N(b) \subseteq S. $$