Alternating normal forms for braids and locally Garside monoids monoids
Alternating normal forms for braids and locally Garside monoids monoids
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辫子和局部 Garside 幺半群的交替范式
DOI：
10.1016/j.jpaa.2008.03.027
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发表时间：
2007
期刊：
影响因子：
--
通讯作者：
Patrick Dehornoy
中科院分区：
文献类型：
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作者：
Patrick Dehornoy
我们描述了辫子幺半群、Artin-Tits幺半群的新型正规形式，更一般地，描述了所有可除性具有一些方便的晶格性质的幺半群（“局部Garside幺半群”）。我们表明，在辫子的情况下，这些规范形式之一符合伯克尔介绍的规范形式，并推断，后者可以很容易地计算。这种方法导致了Bnin的标准阶（“Dehornoy阶”）的一个新的、简单的描述，以及这个阶的复杂性的二次上界。
We describe new types of normal forms for braid monoids, Artin–Tits monoids, and, more generally, for all monoids in which divisibility has some convenient lattice properties (“locally Garside monoids”). We show that, in the case of braids, one of these normal forms coincides with the normal form introduced by Burckel and deduce that the latter can be computed easily. This approach leads to a new, simple description for the standard order (“Dehornoy order”) of Bnin terms of that of Bn−1, and to a quadratic upper bound for the complexity of this order.