Index[p] gives the index of permutation p, the sum of all subscripts j such that p[[j]] is greater than p[[j + 1]].

InsertIntoTableau[e, t] inserts integer e into Young tableau t using the bumping algorithm. InsertIntoTableau[e, t, All] inserts e into Young tableau t and returns the new ...

Involutions[l] gives the list of involutions of the elements in the list l. Involutions[l, Cycles] gives the involutions in their cycle representation. Involution[n] gives ...

KSubsetGroupIndex[g, s, x] returns the cycle index of the k-subset group on s expressed as a polynomial in x[1], x[2], .... This function also takes the optional argument ...

KSubsets[l, k] gives all subsets of set l containing exactly k elements, ordered lexicographically.

LexicographicSubsets[l] gives all subsets of set l in lexicographic order. LexicographicSubsets[n] returns all subsets of {1, 2, ..., n} in lexicographic order.

ListGraphs[n, m] returns all nonisomorphic undirected graphs with n vertices and m edges. ListGraphs[n, m, Directed] returns all nonisomorphic directed graphs with n vertices ...

MakeUndirected[g] gives the underlying undirected graph of the given directed graph g.

MaximumClique[g] finds a largest clique in graph g. MaximumClique[g, k] returns a k-clique, if such a thing exists in g; otherwise it returns {}.

MinimumVertexCover[g] finds a minimum vertex cover of graph g.