Still another approach to the braid ordering

dc.creatorDehornoy, Patrick
dc.date2005-06-24
dc.date.accessioned2026-07-07T05:21:07Z
dc.date.available2026-07-07T05:21:07Z
dc.descriptionWe develop a new approach to the linear ordering of the braid group $B\_n$, based on investigating its restriction to the set $\Div(Δ\_n^d)$ of all divisors of $Δ\_n^d$ in the monoid $B\_\infty^+$, i.e., to positive $n$-braids whose normal form has length at most $d$. In the general case, we compute several numerical parameters attached with the finite orders $(\Div(Δ\_n^d), <)$. In the case of 3 strands, we moreover give a complete description of the increasing enumeration of $(\Div(Δ\_3^d), <)$. We deduce a new and specially direct construction of the ordering on $B\_3$, and a new proof of the result that its restriction to $B\_3^+$ is a well-ordering of ordinal type $ω^ω$.
dc.identifierhttps://arxiv.org/abs/math/0506495
dc.identifierhttp://arxiv.org/abs/math/0506495
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/75576
dc.subjectGroup Theory
dc.subject20F36, 05A05, 20F60
dc.titleStill another approach to the braid ordering
dc.typetext

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