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...

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Main Author:	Cornwell, Christopher R.
Format:	Others
Published:	BYU ScholarsArchive 2006
Subjects:	mathematics geometric group theory braid groups Garside groups combinatorics Mathematics
Online Access:	https://scholarsarchive.byu.edu/etd/457 https://scholarsarchive.byu.edu/cgi/viewcontent.cgi?article=1456&context=etd

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spelling	ndltd-BGMYU2-oai-scholarsarchive.byu.edu-etd-14562019-05-16T03:06:23Z On the Combinatorics of Certain Garside Semigroups Cornwell, Christopher R. 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. 2006-07-06T07:00:00Z text application/pdf https://scholarsarchive.byu.edu/etd/457 https://scholarsarchive.byu.edu/cgi/viewcontent.cgi?article=1456&context=etd http://lib.byu.edu/about/copyright/ All Theses and Dissertations BYU ScholarsArchive mathematics geometric group theory braid groups Garside groups combinatorics Mathematics
collection	NDLTD
format	Others
sources	NDLTD
topic	mathematics geometric group theory braid groups Garside groups combinatorics Mathematics
spellingShingle	mathematics geometric group theory braid groups Garside groups combinatorics Mathematics Cornwell, Christopher R. On the Combinatorics of Certain Garside Semigroups
description	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.
author	Cornwell, Christopher R.
author_facet	Cornwell, Christopher R.
author_sort	Cornwell, Christopher R.
title	On the Combinatorics of Certain Garside Semigroups
title_short	On the Combinatorics of Certain Garside Semigroups
title_full	On the Combinatorics of Certain Garside Semigroups
title_fullStr	On the Combinatorics of Certain Garside Semigroups
title_full_unstemmed	On the Combinatorics of Certain Garside Semigroups
title_sort	on the combinatorics of certain garside semigroups
publisher	BYU ScholarsArchive
publishDate	2006
url	https://scholarsarchive.byu.edu/etd/457 https://scholarsarchive.byu.edu/cgi/viewcontent.cgi?article=1456&context=etd
work_keys_str_mv	AT cornwellchristopherr onthecombinatoricsofcertaingarsidesemigroups
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On the Combinatorics of Certain Garside Semigroups

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