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.

RandomPermutation[n] generates a random permutation of the first n natural numbers.

RandomTableau[p] constructs a random Young tableau of shape p.

RankGraph[g, l] partitions the vertices into classes based on the shortest geodesic distance to a member of list l.

RankPermutation[p] gives the rank of permutation p in lexicographic order.