Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St001917
Mapping
St001917: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],1)
 => 1
([],2)
 => 1
([(0,1)],2)
 => 1
([],3)
 => 2
([(1,2)],3)
 => 4
([(0,2),(1,2)],3)
 => 2
([(0,1),(0,2),(1,2)],3)
 => 1
([],4)
 => 3
([(2,3)],4)
 => 3
([(1,3),(2,3)],4)
 => 9
([(0,3),(1,3),(2,3)],4)
 => 3
([(0,3),(1,2)],4)
 => 3
([(0,3),(1,2),(2,3)],4)
 => 3
([(1,2),(1,3),(2,3)],4)
 => 9
([(0,3),(1,2),(1,3),(2,3)],4)
 => 3
([(0,2),(0,3),(1,2),(1,3)],4)
 => 2
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
([],5)
 => 4
([(3,4)],5)
 => 8
([(2,4),(3,4)],5)
 => 12
([(1,4),(2,4),(3,4)],5)
 => 16
([(0,4),(1,4),(2,4),(3,4)],5)
 => 4
([(1,4),(2,3)],5)
 => 8
([(1,4),(2,3),(3,4)],5)
 => 16
([(0,1),(2,4),(3,4)],5)
 => 24
([(2,3),(2,4),(3,4)],5)
 => 12
([(0,4),(1,4),(2,3),(3,4)],5)
 => 4
([(1,4),(2,3),(2,4),(3,4)],5)
 => 16
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 4
([(1,3),(1,4),(2,3),(2,4)],5)
 => 32
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => 8
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 32
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 4
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 8
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => 6
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 6
([(0,4),(1,3),(2,3),(2,4)],5)
 => 4
([(0,1),(2,3),(2,4),(3,4)],5)
 => 24
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => 4
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => 4
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => 24
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 15
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => 6
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => 8
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 16
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 4
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 6
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => 6
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => 2
Description
The order of toric promotion on the set of labellings of a graph. In the context of toric promotion, a labelling of a graph $(V, E)$ with $n=|V|$ vertices is a bijection $\sigma: V \to [n]$. In particular, any graph has $n!$ labellings.