SetPartitionQ[sp, s] determines if sp is a set partition of set s. SetPartitionQ[sp] tests if sp is a set of disjoint sets.

SetPartitions[set] returns the list of set partitions of set. SetPartitions[n] returns the list of set partitions of {1, 2, ..., n}.

ShakeGraph[g, d] performs a random perturbation of the vertices of graph g, with each vertex moving, at most, a distance d from its original position.

ShowGraphArray[{g_1, g_2, ...}] displays a row of graphs. ShowGraphArray[{{g_1, ...}, {g_2, ...}, \ ...}] displays a two-dimensional table of graphs.

StableMarriage[mpref, fpref] finds the male optimal stable marriage defined by lists of permutations describing male and female preferences.

Strings[l, n] constructs all possible combinatorial strings of length n from the elements of list l.

SymmetricGroupIndex[n, x] returns the cycle index of the symmetric group on n symbols, expressed as a polynomial in x[1], x[2], ..., x[n].

SymmetricQ[r] tests if a given square matrix r represents a symmetric relation. SymmetricQ[g] tests if the edges of a given graph represent a symmetric relation.

TableauxToPermutation[t_1, t_2] constructs the unique permutation associated with Young tableaux t_1 and t_2, where both tableaux have the same shape.

ThomassenGraph returns a hypotraceable graph, a graph G that has no Hamiltonian path but whose subgraph G - v for every vertex v has a Hamiltonian path.