***************************************************************************** * www.FindStat.org - The Combinatorial Statistic Finder * * * * Copyright (C) 2019 The FindStatCrew * * * * This information is distributed in the hope that it will be useful, * * but WITHOUT ANY WARRANTY; without even the implied warranty of * * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. * ***************************************************************************** ----------------------------------------------------------------------------- Statistic identifier: St001917 ----------------------------------------------------------------------------- Collection: Graphs ----------------------------------------------------------------------------- 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. ----------------------------------------------------------------------------- References: [1] Defant, C. Toric Promotion [[arXiv:2112.06843]] ----------------------------------------------------------------------------- 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 ----------------------------------------------------------------------------- Created: Aug 18, 2023 at 22:21 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Aug 18, 2023 at 22:21 by Martin Rubey