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Statistic identifier: St001917
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Collection: Graphs
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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.
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References: [1] Defant, C. Toric Promotion [[arXiv:2112.06843]]
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Code:
from sage.combinat.cyclic_sieving_phenomenon import orbit_decomposition
def toggle_labelling(G, pi, i, j):
if G.has_edge(pi.index(i), pi.index(j)):
return pi
sigma = [j if e == i else i if e == j else e for e in pi]
return Permutation(sigma)
def toric_promotion_labelling(G, pi):
n = G.num_verts()
assert set(G.vertices()) == set(range(n))
for i in range(1, n):
pi = toggle_labelling(G, pi, i, i+1)
return toggle_labelling(G, pi, n, 1)
def toric_promotion_labelling_orbits(G):
G = G.canonical_label().copy(immutable=True)
return toric_promotion_labelling_orbits_aux(G)
@cached_function
def toric_promotion_labelling_orbits_aux(G):
n = G.num_verts()
return orbit_decomposition(Permutations(n),
lambda pi: toric_promotion_labelling(G, pi))
def statistic(G):
return lcm(len(o) for o in toric_promotion_labelling_orbits(G))
-----------------------------------------------------------------------------
Statistic 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
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 1
([],6) => 5
([(4,5)],6) => 5
([(3,5),(4,5)],6) => 5
([(2,5),(3,5),(4,5)],6) => 10
([(1,5),(2,5),(3,5),(4,5)],6) => 25
([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
([(2,5),(3,4)],6) => 5
([(2,5),(3,4),(4,5)],6) => 10
([(1,2),(3,5),(4,5)],6) => 5
([(3,4),(3,5),(4,5)],6) => 5
([(1,5),(2,5),(3,4),(4,5)],6) => 25
([(0,1),(2,5),(3,5),(4,5)],6) => 10
([(2,5),(3,4),(3,5),(4,5)],6) => 10
([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 5
([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 25
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 5
([(2,4),(2,5),(3,4),(3,5)],6) => 20
([(0,5),(1,5),(2,4),(3,4)],6) => 5
([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 25
([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 5
([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 20
([(1,5),(2,4),(3,4),(3,5),(4,5)],6) => 25
([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 5
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 10
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 25
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => 5
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 10
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 25
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => 10
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 15
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 25
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 10
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 15
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 12
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 12
([(0,5),(1,4),(2,3)],6) => 5
([(1,5),(2,4),(3,4),(3,5)],6) => 25
([(0,1),(2,5),(3,4),(4,5)],6) => 10
([(1,2),(3,4),(3,5),(4,5)],6) => 5
([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 5
([(1,4),(2,3),(2,5),(3,5),(4,5)],6) => 25
([(0,1),(2,5),(3,4),(3,5),(4,5)],6) => 10
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 5
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 25
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 5
([(1,4),(1,5),(2,3),(2,5),(3,4)],6) => 25
([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 10
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => 125
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6) => 30
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => 25
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6) => 5
([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => 75
([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 10
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6) => 25
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6) => 15
([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 5
([(0,1),(2,4),(2,5),(3,4),(3,5)],6) => 20
([(0,5),(1,5),(2,3),(2,4),(3,4)],6) => 5
([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) => 10
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6) => 5
([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6) => 5
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 20
([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6) => 5
([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6) => 10
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6) => 10
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 5
([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 10
([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 10
([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => 10
([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 25
([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => 924
([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6) => 2184
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 15
([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => 15
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 84
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6) => 840
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => 15
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 25
([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 15
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => 12
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 12
([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 15
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => 25
([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => 15
([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => 25
([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => 5
([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6) => 60
([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6) => 1092
([(0,5),(1,2),(1,4),(2,3),(3,4),(3,5),(4,5)],6) => 75
([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => 10032
([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => 10
([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => 75
([(0,1),(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 60
([(0,4),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => 15
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 132
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => 60
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => 24
([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 15
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 24
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 24
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 168
([(0,5),(1,2),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 25
([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 15
([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5),(3,4),(3,5),(4,5)],6) => 336
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => 24
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 168
([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 24
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 6
([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => 24
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => 6
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6) => 5
([(0,2),(1,4),(1,5),(2,3),(3,4),(3,5),(4,5)],6) => 10
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6) => 5
([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 10
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => 10
([(0,1),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6) => 132
([(0,4),(0,5),(1,2),(1,3),(1,4),(2,3),(2,5),(3,5),(4,5)],6) => 1092
([(0,3),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 15
([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 60
([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 84
([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 420
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 12
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 12
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4)],6) => 840
([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => 462
([(0,3),(0,4),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 120
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 15
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6) => 462
([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 24
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => 420
([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 30
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => 24
([(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 12
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 84
([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 25
([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
([(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) => 12
([(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
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => 6
([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => 12
([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 6
([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => 6
([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 2
([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
([(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) => 2
([(0,1),(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) => 1
([],7) => 6
([(5,6)],7) => 12
([(4,6),(5,6)],7) => 18
([(3,6),(4,6),(5,6)],7) => 24
([(2,6),(3,6),(4,6),(5,6)],7) => 30
([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 36
([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 6
([(3,6),(4,5)],7) => 12
([(3,6),(4,5),(5,6)],7) => 24
([(2,3),(4,6),(5,6)],7) => 36
([(4,5),(4,6),(5,6)],7) => 18
([(2,6),(3,6),(4,5),(5,6)],7) => 30
([(1,2),(3,6),(4,6),(5,6)],7) => 24
([(3,6),(4,5),(4,6),(5,6)],7) => 24
([(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 36
([(0,1),(2,6),(3,6),(4,6),(5,6)],7) => 60
([(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 30
([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 6
([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 36
([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 6
([(3,5),(3,6),(4,5),(4,6)],7) => 48
([(1,6),(2,6),(3,5),(4,5)],7) => 18
([(2,6),(3,4),(3,5),(4,6),(5,6)],7) => 60
([(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 36
([(0,6),(1,6),(2,6),(3,5),(4,5)],7) => 72
([(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 48
([(2,6),(3,5),(4,5),(4,6),(5,6)],7) => 30
([(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 36
([(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => 72
([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 6
([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 60
([(1,6),(2,6),(3,5),(4,5),(4,6),(5,6)],7) => 36
([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 6
([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 12
([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 72
([(0,6),(1,6),(2,6),(3,5),(4,5),(4,6),(5,6)],7) => 6
([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 12
([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 90
([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => 72
([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => 6
([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 108
([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => 12
([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 90
([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 72
([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6),(5,6)],7) => 6
([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 18
([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 108
([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 12
([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 18
([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 432
([(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 18
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 72
([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 432
([(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 18
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 72
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 60
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 60
([(1,6),(2,5),(3,4)],7) => 12
([(2,6),(3,5),(4,5),(4,6)],7) => 30
([(1,2),(3,6),(4,5),(5,6)],7) => 24
([(0,3),(1,2),(4,6),(5,6)],7) => 36
([(2,3),(4,5),(4,6),(5,6)],7) => 36
([(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 36
([(0,1),(2,6),(3,6),(4,5),(5,6)],7) => 60
([(2,5),(3,4),(3,6),(4,6),(5,6)],7) => 30
([(1,2),(3,6),(4,5),(4,6),(5,6)],7) => 24
([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 6
([(1,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => 36
([(0,1),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 60
([(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => 30
([(0,6),(1,6),(2,3),(3,6),(4,5),(4,6),(5,6)],7) => 6
([(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => 36
([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => 6
([(2,5),(2,6),(3,4),(3,6),(4,5)],7) => 180
([(1,6),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => 72
([(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7) => 450
([(1,6),(2,3),(2,5),(3,4),(4,6),(5,6)],7) => 216
([(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => 60
([(1,6),(2,5),(3,4),(4,5),(4,6),(5,6)],7) => 36
([(1,6),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7) => 540
([(1,6),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 72
([(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => 90
([(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => 108
([(1,6),(2,5),(3,4),(3,5),(4,6)],7) => 36
([(1,2),(3,5),(3,6),(4,5),(4,6)],7) => 48
([(1,6),(2,6),(3,4),(3,5),(4,5)],7) => 18
([(1,5),(2,3),(2,4),(3,6),(4,6),(5,6)],7) => 72
([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 60
([(1,5),(2,3),(2,6),(3,6),(4,5),(4,6)],7) => 36
([(1,5),(2,3),(3,6),(4,5),(4,6),(5,6)],7) => 36
([(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 48
([(0,1),(2,6),(3,5),(4,5),(4,6),(5,6)],7) => 60
([(1,5),(2,5),(3,4),(3,6),(4,6),(5,6)],7) => 36
([(0,5),(1,6),(2,3),(2,4),(3,6),(4,6),(5,6)],7) => 12
([(1,4),(1,5),(2,3),(2,6),(3,6),(4,6),(5,6)],7) => 72
([(1,4),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7) => 72
([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 60
([(1,5),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 36
([(0,4),(1,6),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7) => 12
([(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 72
([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5)],7) => 72
([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 24
([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5),(5,6)],7) => 6
([(1,6),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => 72
([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 30
([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => 12
([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 36
([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
([(1,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => 4752
([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 18
([(1,4),(1,6),(2,4),(2,6),(3,5),(3,6),(4,5),(5,6)],7) => 11232
([(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 108
([(1,6),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => 108
([(1,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 432
([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 18
([(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => 864
([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5)],7) => 12
([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 180
([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,6)],7) => 18
([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(5,6)],7) => 12
([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 180
([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7) => 18
([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => 108
([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 90
([(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 36
([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 108
([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 72
([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 72
([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => 432
([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 432
([(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => 108
([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => 90
([(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => 108
([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => 30
([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => 36
([(1,5),(1,6),(2,3),(2,4),(3,6),(4,5)],7) => 432
([(1,4),(1,6),(2,3),(2,6),(3,5),(4,5),(5,6)],7) => 5616
([(1,6),(2,3),(2,5),(3,4),(4,5),(4,6),(5,6)],7) => 540
([(1,2),(1,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7) => 361152
([(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => 72
([(1,6),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => 540
([(1,2),(1,6),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 432
([(0,6),(1,2),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 12
([(1,5),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => 108
([(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => 4752
([(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => 432
([(0,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => 18
([(0,6),(1,4),(2,5),(2,6),(3,4),(3,5),(5,6)],7) => 6
([(0,5),(1,4),(2,4),(2,6),(3,5),(3,6),(4,6),(5,6)],7) => 6
([(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => 864
([(0,6),(1,5),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => 18
([(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => 108
([(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 864
([(0,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 18
([(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 864
([(0,6),(1,5),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 18
([(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 864
([(0,6),(1,5),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
([(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 36
([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 30
([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 36
([(1,5),(1,6),(2,3),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => 1728
([(0,5),(1,3),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => 18
([(0,6),(1,5),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(5,6)],7) => 18
([(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 108
([(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => 864
([(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 864
([(0,6),(1,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 18
([(0,6),(1,5),(2,4),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => 18
([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 864
([(0,6),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 216
([(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 216
([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => 864
([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => 216
([(0,6),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => 6
([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 216
([(0,1),(2,5),(3,4),(4,6),(5,6)],7) => 60
([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => 6
([(0,1),(2,3),(3,6),(4,5),(4,6),(5,6)],7) => 60
([(0,5),(1,4),(2,3),(2,6),(3,6),(4,6),(5,6)],7) => 6
([(0,1),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => 60
([(0,5),(1,4),(1,6),(2,3),(2,6),(3,6),(4,6),(5,6)],7) => 6
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,6),(3,6),(4,6),(5,6)],7) => 6
([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => 6
([(0,6),(1,4),(2,3),(2,6),(3,5),(4,5),(5,6)],7) => 12
([(0,4),(1,3),(2,5),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 12
([(1,5),(1,6),(2,3),(2,4),(3,4),(5,6)],7) => 18
([(1,3),(2,5),(2,6),(3,4),(4,5),(4,6),(5,6)],7) => 72
([(0,1),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 60
([(1,2),(1,6),(2,6),(3,4),(3,5),(4,5),(5,6)],7) => 36
([(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 24
([(1,2),(1,6),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => 72
([(1,2),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 36
([(0,1),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 60
([(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 36
([(0,4),(1,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 18
([(1,5),(1,6),(2,3),(2,4),(3,4),(3,6),(4,5),(5,6)],7) => 4752
([(1,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,6),(4,6),(5,6)],7) => 5616
([(1,4),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 108
([(1,4),(1,6),(2,3),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 432
([(1,2),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 432
([(1,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 432
([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 432
([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 432
([(0,6),(1,5),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5)],7) => 90
([(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5)],7) => 864
([(1,2),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => 2376
([(1,4),(1,5),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => 864
([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => 108
([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,5)],7) => 2376
([(1,2),(1,4),(1,6),(2,3),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 864
([(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => 432
([(1,2),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 216
([(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 36
([(0,6),(1,5),(2,3),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 18
([(1,5),(1,6),(2,3),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 432
([(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => 864
([(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 432
([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 216
([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 30
([(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 36
([(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 432
([(1,2),(1,5),(1,6),(2,3),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 216
([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => 216
([(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => 432
([(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => 216
([(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 216
([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 72
([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 72
([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 72
([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 36
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Created: Aug 18, 2023 at 22:21 by Martin Rubey
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Last Updated: Aug 18, 2023 at 22:21 by Martin Rubey