On the Combinatorics of Certain Garside Semigroups

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.

Name thesis:degree_name

MS

Grantor dc:publisher

Brigham Young University - Provo

Author dc:creator

• Cornwell, Christopher R.

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

Language dc:language

English

Repository record dc:identifier

https://scholarsarchive.byu.edu/etd/457

OAI identifier oai:identifier

oai:scholarsarchive.byu.edu:etd-1456