Given a positive integer $n$ and a list of disjoint intervals in the form $\{\{i_1,i_1+1,i_1+2,\ldots,i_1+n_1\},\{i_2,i_2+1,i_2+2,\ldots i_2+n_2\},\ldots\}$ all contained in $[1,n]$, I want to generate the permutations of $\{1\ldots n\}$ treating integers in the same given interval as they were equivalent, hence never changing their order. I should have $\frac{n!}{(n_1!n_2!...)}$ permutations.
This is my attempt:
myperm[n_, alike_] := Module[{perms, temp}, perms = Flatten@{Delete[Range@n, Partition[Flatten@#, 1]], ConstantArray[First@#, Length@#] & /@ #} &@alike // Permutations; Do[temp = ConstantArray[0, n]; Do[temp[[perms[[i, j]]]]++; perms[[i, j]] += temp[[perms[[i, j]]]] - 1, {j, n}], {i, Length@perms}]; perms ] Are those nested Do[] and that local variable unavoidable?
