NumberOfPermutationsByCycles[n, m] gives the number of permutations of length n with exactly m cycles.

NumberOfPermutationsByTypes[l] gives the number of permutations of type l.

NumberOfSpanningTrees[g] gives the number of labeled spanning trees of graph g.

PermutationGraph[p] gives the permutation graph for the permutation p.

PermutationToTableaux[p] returns the tableaux pair that can be constructed from p using the Robinson\[Dash]Schensted\[Dash]Knuth correspondence.

PermutationType[p] returns the type of permutation p.

PlanarQ[g] yields True if graph g is planar, meaning it can be drawn in the plane so no two edges cross.

PseudographQ[g] yields True if graph g is a pseudograph, meaning it contains self-loops.

Radius[g] gives the radius of graph g, the minimum eccentricity of any vertex of g.

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