RosettaCodeData/Task/Permutations/Mathematica/permutations-1.math

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(***Standard list functions:*)
fold[f_, x_, {}] := x
fold[f_, x_, {h_, t___}] := fold[f, f[x, h], {t}]
insert[L_, x_, n_] := Join[L[[;; n - 1]], {x}, L[[n ;;]]]
(***Generate all permutations of a list S:*)
permutations[S_] :=
fold[Join @@ (Function[{L},
Table[insert[L, #2, k + 1], {k, 0, Length[L]}]] /@ #1) &, {{}},
S]