Diagram Groups over Union of Two Semigroup Presentations of Natural Numbers by Adding Relations

Abstract

For any given semigroup presentation P , we may obtain diagram groups with base point u, where u is a word in generating set. The purpose of this paper is to determine the graphs Τpn(n € N), which are obtained from diagram group for union of two semigroup presentations with two and three different initial generators. The general polynomial of vertices, edge in these graphs with three and two different initial generators by adding a relation will be computed. Keywords: Diagram groups; semigroup presentation; generators; relation; initial generators.