# This program computes all repeat-transitive 3-constellations of degree < = n. # The growth is huge: |T[n]| = (n-1)! (n+1)!/2 Compute3Constellations := proc(N) local T,i,j,n; T[1] := {[[[1]],[[1]]]}; # Write permutations in expanded form for n from 2 to N do T[n] := {seq(seq(seq([Insert(v[1],i,n), Insert(v[2],j,n)], i=1..`if`(j=n,n-1,n)), j=1..n), v = T[n-1])} od; [seq(T[i],i=1..N)] end: # This program inserts edge #n at the kth place of a permutation: Insert := proc(g, k, n) local d,k0; if k=n then [op(g),[n]] # expanded form, include the 1-cycle [n] else k0 := k; d := 1; while k0 > nops(g[d]) do k0 := k0 - nops(g[d]); d := d+1 od; subsop(d = [op(g[d][1..k0]), n, op(g[d][k0+1..-1])], g) fi end: # Compute3Constellations up to degree N=5: V := Compute3Constellations(5): lprint("Number of repeat-transitive 3-constellations of degrees 1..5:"): map(nops,V); lprint("Here we give repeat-transitive 3-constellations in the form [g0,g1], omitting g_infinity"): lprint("and with g0,g1 in expanded form:"): for n to 3 do lprint(cat("repeat-transitive 3-constellations of degree ",n,":")): for i in V[n] do lprint(i) od: od: