Seymour Lipschutz

Generating Multiset Permutations in Constant Time

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

Shifts and loopless generation of k -ary trees

A new shift operation on nodes of k-ary trees which preserves preorder node numbers is introduced. The shift graph SGn, k has as vertices all n-node k-ary trees and edges corresponding to one shift. The graph is proven to have a Hamiltonian path and an algorithm is presented which generates all n-node k-ary trees successively with constant time between them.

Note on Infinite Families of Trivalent Semisymmetric Graphs

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.

On the Word Problem and T-Fourth-Groups

Publisher Summary This chapter discusses a word problem and T-fourth groups. The chapter also discusses one-fourth condition, triangle condition, and preliminary lemmas and presents main results. The chapter describes a theorem where K is the free product of T-fourth groups with an infinite cyclic group amalgamated. K has a solvable word problem.

Loopless Algorithms And SchrÖder Trees

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 Schröder trees.

Revisiting matrix representations of the braid group

The Burau matrix representation of the braid group Bn is faithful if certain n-square matrices M 1,M 2,…,Mn freely generate a free group G. The author obtains properties of the matrices Mi which indicate that G is indeed freely generated by the Mi .