Efficient algorithms in Coxeter groups of large type
Gies, Paul Josef
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Permalink
https://hdl.handle.net/2142/20907
Description
Title
Efficient algorithms in Coxeter groups of large type
Author(s)
Gies, Paul Josef
Issue Date
1995
Doctoral Committee Chair(s)
Rotman, Joseph J.
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Mathematics
Language
eng
Abstract
We establish a quadratic time algorithm for the word problem and a cubic time algorithm for the conjugacy problem for Coxeter groups of large type. We also give conditions on the relators of a large-type Coxeter group that are necessary and sufficient for the group to be hyperbolic, and we give a normal form for large-type Coxeter groups that is a regular bicombing, thus establishing that all such groups are biautomatic.
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