NextKSubset[l, s] gives the k-subset of list l, following the k-subset s in lexicographic order.

NextSubset[l, s] constructs the subset of l following subset s in canonical order.

NextTableau[t] gives the tableau of shape t, following t in lexicographic order.

NthSubset[n, l] gives the n\[Null]^th subset of list l in canonical order.

NumberOfInvolutions[n] counts the number of involutions on n elements.

PermutationGroupQ[l] yields True if the list of permutations l forms a permutation group.

PermutationType[p] returns the type of permutation p.

RandomComposition[n, k] constructs a random composition of integer n into k parts.

RandomKSubset[l, k] gives a random subset of set l with exactly k elements.

RandomPartition[n] constructs a random partition of integer n.