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On finite Thurston-type orderings of braid groups

On finite Thurston-type orderings of braid groups We prove that for any finite Thurston-type ordering < T on the braid group B n , the restriction to the positive braid monoid ( , < T ) is a well-ordered set of order type ω ω n –2 . The proof uses a combinatorial description of the ordering < T . Our combinatorial description is based on a new normal form for positive braids which we call the ( -normal form. It can be seen as a generalization of Burckel's normal form and Dehornoy's Φ-normal form (alternating normal form). http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Groups - Complexity - Cryptology de Gruyter

On finite Thurston-type orderings of braid groups

Groups - Complexity - Cryptology , Volume 2 (2) – Dec 1, 2010

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Publisher
de Gruyter
Copyright
© de Gruyter 2010
ISSN
1867-1144
eISSN
1869-6104
DOI
10.1515/GCC.2010.009
Publisher site
See Article on Publisher Site

Abstract

We prove that for any finite Thurston-type ordering < T on the braid group B n , the restriction to the positive braid monoid ( , < T ) is a well-ordered set of order type ω ω n –2 . The proof uses a combinatorial description of the ordering < T . Our combinatorial description is based on a new normal form for positive braids which we call the ( -normal form. It can be seen as a generalization of Burckel's normal form and Dehornoy's Φ-normal form (alternating normal form).

Journal

Groups - Complexity - Cryptologyde Gruyter

Published: Dec 1, 2010

Keywords: Thurston-type ordering; braid groups; ordinals; Garside monoid; Artin–Tits group

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