International Journal of Mathematics and Mathematical Sciences
Volume 9 (1986), Issue 2, Pages 245-251

The general quasi-order algorithm in number theory

Peter Hilton1 and Jean Pedersen2

1Department of Mathematical Sciences, State University of New York, Binghamton 13901, New York, USA
2Department of Mathematics, Santa Clara University, Santa Clara 95051, California, USA

Received 27 November 1985

Copyright © 1986 Peter Hilton and Jean Pedersen. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper deals with a generalization of the Binary Quasi-Order Theorem. This generalization involves a more complicated algorithm than (0.2)t. Some remarks are made on relative merits of two dual algorithms called the ψ-algorithm and the ϕ-algorithm. Some illustrative examples are given.