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The generation of all members of a combinatorial family, such as permutations, partitions of an integer or binary trees with n nodes, has long been of interest in the computer science community. The development of loopless algorithms for such generation has been of more recent concern. This paper is an introduction to the idea and development of loopless algorithms. It illustrates the creation of a number of such algorithms, including multiset permutations, Gray codes and binary trees, and a new one for the generation of Schroder trees.

A simple undirected graph is said to be semisymmetric if it is regular and edge-transitive but not vertex-transitive. This paper uses the groups PSL (2, p) and PGL (2, p), where p is a prime, to construct two new infinite families of trivalent semisymmetric graphs.

An algorithm is presented that generates multiset permutations taking constant time between each permutation.