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.
College and Department
Physical and Mathematical Sciences; Mathematics
BYU ScholarsArchive Citation
Cornwell, Christopher R., "On the Combinatorics of Certain Garside Semigroups" (2006). All Theses and Dissertations. 457.
mathematics, geometric group theory, braid groups, Garside groups, combinatorics