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Tuples

Tuples[list, n]
generates a list of all possible n-tuples of elements from list.
Tuples[{list1, list2, ...}]
generates a list of all possible tuples whose i^(th) element is from listi.
  • The elements of list are treated as distinct, so that Tuples[list, n] for a list of length k gives output of length kn.
  • The order of elements in Tuples[list, n] is based on the order of elements in list, so that Tuples[{a1, ..., ak}, n] gives {{a_1,a_1,…,a_1},{a_1,a_1,…,a_2},…,{a_k,a_k,…,a_k}}.
  • Tuples[list, {n1, n2, ...}] generates a list of all possible n_1⨯n_2⨯… arrays of elements in list.
  • The object list need not have head List. The head at each level in the arrays generated by Tuples will be the same as the head of list.
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