GridGraph[n, m] constructs an n*m grid graph, the product of paths on n and m vertices. GridGraph[p, q, r] constructs a p*q*r grid graph, the product of GridGraph[p, q] and a ...

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 ...

IsomorphicQ[g, h] yields True if graphs g and h are isomorphic.

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 ...

KSubsetGroup[pg, s] returns the group induced by a permutation group pg on the set s of k-subsets of [n], where n is the index of pg. The optional argument Type can be ...

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 ...

ListNecklaces[n, c, Cyclic] returns all distinct necklaces whose beads are colored by colors from c. Here c is a list of n, not necessarily distinct colors, and two colored ...

MakeDirected[g] constructs a directed graph from a given undirected graph g by replacing each undirected edge in g by two directed edges pointing in opposite directions.

NthPair[n] returns the n\[Null]^th unordered pair of distinct positive integers, when sequenced to minimize the size of the larger integer. Pairs that have the same larger ...