Still another approach to the braid ordering
Still another approach to the braid ordering
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另一种编织顺序的方法
DOI：
10.2140/pjm.2007.232.139
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发表时间：
2005
影响因子：
0.6
通讯作者：
Patrick Dehornoy
中科院分区：
文献类型：
--
作者：
Patrick Dehornoy
本文在研究辫群$B_n$对幺半群$B_\infty^+$中$\Delta_n ^d$的所有因子的集合$\Div（\Delta_n^d）$的限制的基础上，给出了辫群$\Delta_n^d$的线性序的一种新方法，即，到正$n$-标准形长度不超过$d$的辫子。在一般情况下，我们计算几个数值参数附加有限阶$（\Div（\Delta_n^d），<）$。在$3$ strands的情况下，我们还给出了$（\Div（\Delta_3^d），<）$的递增枚举的完整描述。本文给出了$B_3$上的序的一个新的特殊的直接构造，并证明了它对$B_3^+$的限制是序型$\omega^\omega$的良序.
We develop a new approach to the linear ordering of the braid group $B_n$, based on investigating its restriction to the set $\Div(\Delta_n^d)$ of all divisors of $\Delta_n^d$ 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 $(\Div(\Delta_n^d), <)$. In the case of $3$ strands, we moreover give a complete description of the increasing enumeration of $(\Div(\Delta_3^d), <)$. 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 $\omega^\omega$.