Still another approach to the braid ordering
| dc.creator | Dehornoy, Patrick | |
| dc.date | 2005-06-24 | |
| dc.date.accessioned | 2026-07-07T05:21:07Z | |
| dc.date.available | 2026-07-07T05:21:07Z | |
| dc.description | We 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.identifier | https://arxiv.org/abs/math/0506495 | |
| dc.identifier | http://arxiv.org/abs/math/0506495 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/75576 | |
| dc.subject | Group Theory | |
| dc.subject | 20F36, 05A05, 20F60 | |
| dc.title | Still another approach to the braid ordering | |
| dc.type | text |