Abstract

In his dissertation, F.A. Garside provided a solution to the word and conjugacy problems in the braid group on n-strands, using a particular element that he called the fundamental word. Others have since defined fundamental words in the generalized setting of Artin groups, and even more recently in Garside groups. We consider the problem of finding the number of representations of a power of the fundamental word in these settings. In the process, we find a Pascal-like identity that is satisfied in a certain class of Garside groups.

Degree

MS

College and Department

Physical and Mathematical Sciences; Mathematics

Rights

http://lib.byu.edu/about/copyright/

Date Submitted

2006-07-06

Document Type

Thesis

Handle

http://hdl.lib.byu.edu/1877/etd1381

Keywords

mathematics, geometric group theory, braid groups, Garside groups, combinatorics

Included in

Mathematics Commons

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