Wolfram: List Combinatorics

Tuples

• Tuples[ list, n]
• and more

return all possible n-tuples.

Tuples

Tuples[ {1,2,3}, 2]

(* {{1, 1}, {1, 2}, {1, 3}, {2, 1}, {2, 2}, {2, 3}, {3, 1}, {3, 2}, {3, 3}} *)

Subsets

• Subsets[list] → all subsets.
• Subsets[list, n] → max subset length n.
• Subsets[list, {n}] → subset length exactly n.
• Subsets[list, {n, m}] → subset length n to m.
• Subsets[list, spec, s] → first s subsets.

return all possible subsets

Subsets

Subsets[{1,2,3}]
(* {{}, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}} *)

(* max length n in each subset. *)
Subsets[{1,2,3}, 2]
(* {{}, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}} *)

(* exact length n in each subset. *)
Subsets[{1,2,3}, {2}]
(* {{1, 2}, {1, 3}, {2, 3}} *)

(* length n to m in each subset. *)
Subsets[{1,2,3}, {2,3}]
(* {{1, 2}, {1, 3}, {2, 3}, {1, 2, 3}} *)

(* just first 4 subsets. *)
Subsets[{1,2,3}, 2, 5]

(* {{}, {1}, {2}, {3}, {1, 2}} *)

Permutations

Permutations

• Groupings
• Subsequences