International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 32, Pages 1671-1677
On birational monomial transformations of plane
Department of Mathematics and Statistics, Texas Tech University, Lubbock 79409-1042, TX, USA
Received 20 June 2003; Revised 7 October 2003
Copyright © 2004 Anatoly B. Korchagin. 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.
We study birational monomial transformations of the form , where . These transformations form a group. We describe this group in terms of generators and relations and, for every such transformation , we prove a formula, which represents the transformation as a product of generators of the group. To prove this formula, we use birationally equivalent polynomials and . If is the transformation which carries one polynomial onto another, then the integral powers of generators in the product, which represents the transformation , can be calculated by the expansion of in the continued fraction.