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
['A',4]
 => 30
['D',4]
 => 44
['A',5]
 => 55
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
['A',4]
 => ([(0,8),(1,7),(2,7),(2,9),(3,8),(3,9),(5,4),(6,4),(7,5),(8,6),(9,5),(9,6)],10)
 => [4,3,2,1]
 => 30
['D',4]
 => ([(0,10),(1,9),(2,8),(3,8),(3,9),(3,10),(5,11),(6,11),(7,11),(8,5),(8,6),(9,5),(9,7),(10,6),(10,7),(11,4)],12)
 => [5,3,3,1]
 => 44
['A',5]
 => ([(0,11),(1,10),(2,10),(2,13),(3,11),(3,14),(4,13),(4,14),(6,8),(7,9),(8,5),(9,5),(10,6),(11,7),(12,8),(12,9),(13,6),(13,12),(14,7),(14,12)],15)
 => [5,4,3,2,1]
 => 55
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: 30% ●values known / values provided: 30%●distinct values known / distinct values provided: 33%
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 + 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)
 => ? = 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)
 => ? = 35 + 3
['A',4]
 => ([(0,8),(1,7),(2,7),(2,9),(3,8),(3,9),(5,4),(6,4),(7,5),(8,6),(9,5),(9,6)],10)
 => ([(1,2),(1,7),(1,9),(2,6),(2,8),(3,4),(3,6),(3,8),(3,9),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,7),(6,9),(7,8),(8,9)],10)
 => ([(0,10),(1,2),(1,7),(1,9),(1,10),(2,6),(2,8),(2,10),(3,4),(3,6),(3,8),(3,9),(3,10),(4,7),(4,8),(4,9),(4,10),(5,6),(5,7),(5,8),(5,9),(5,10),(6,7),(6,9),(6,10),(7,8),(7,10),(8,9),(8,10),(9,10)],11)
 => ? = 30 + 3
['D',4]
 => ([(0,10),(1,9),(2,8),(3,8),(3,9),(3,10),(5,11),(6,11),(7,11),(8,5),(8,6),(9,5),(9,7),(10,6),(10,7),(11,4)],12)
 => ([(2,9),(2,10),(2,11),(3,4),(3,5),(3,8),(3,11),(4,5),(4,7),(4,10),(5,6),(5,9),(6,7),(6,8),(6,10),(6,11),(7,8),(7,9),(7,11),(8,9),(8,10),(9,10),(9,11),(10,11)],12)
 => ([(0,12),(1,12),(2,9),(2,10),(2,11),(2,12),(3,4),(3,5),(3,8),(3,11),(3,12),(4,5),(4,7),(4,10),(4,12),(5,6),(5,9),(5,12),(6,7),(6,8),(6,10),(6,11),(6,12),(7,8),(7,9),(7,11),(7,12),(8,9),(8,10),(8,12),(9,10),(9,11),(9,12),(10,11),(10,12),(11,12)],13)
 => ? = 44 + 3
['A',5]
 => ([(0,11),(1,10),(2,10),(2,13),(3,11),(3,14),(4,13),(4,14),(6,8),(7,9),(8,5),(9,5),(10,6),(11,7),(12,8),(12,9),(13,6),(13,12),(14,7),(14,12)],15)
 => ([(1,2),(1,10),(1,12),(1,14),(2,9),(2,11),(2,13),(3,7),(3,8),(3,11),(3,12),(3,13),(3,14),(4,9),(4,10),(4,11),(4,12),(4,13),(4,14),(5,6),(5,8),(5,9),(5,11),(5,12),(5,13),(5,14),(6,7),(6,10),(6,11),(6,12),(6,13),(6,14),(7,8),(7,9),(7,11),(7,13),(7,14),(8,10),(8,12),(8,13),(8,14),(9,10),(9,12),(9,14),(10,11),(10,13),(11,12),(11,14),(12,13),(13,14)],15)
 => ([(0,15),(1,2),(1,10),(1,12),(1,14),(1,15),(2,9),(2,11),(2,13),(2,15),(3,7),(3,8),(3,11),(3,12),(3,13),(3,14),(3,15),(4,9),(4,10),(4,11),(4,12),(4,13),(4,14),(4,15),(5,6),(5,8),(5,9),(5,11),(5,12),(5,13),(5,14),(5,15),(6,7),(6,10),(6,11),(6,12),(6,13),(6,14),(6,15),(7,8),(7,9),(7,11),(7,13),(7,14),(7,15),(8,10),(8,12),(8,13),(8,14),(8,15),(9,10),(9,12),(9,14),(9,15),(10,11),(10,13),(10,15),(11,12),(11,14),(11,15),(12,13),(12,15),(13,14),(13,15),(14,15)],16)
 => ? = 55 + 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 $S$: $$ \forall a, b\in S: N(a)\cap N(b) \subseteq S. $$