On completeness of word reversing

Word reversing is a combinatorial operation on words that detects pairs of equivalent words in monoids that admit a presentation of a certain form. Here we give conditions for this method to be complete in the sense that every pair of equivalent words can be detected by word reversing. In addition, we obtain explicit upper bounds on the complexity of the process. As an application, we show that Artin groups of Coxeter type B embed into Artin groups of type A and are left orderable. Assume that S; R is a presentation of monoid, i.e., R is a family of equalities of the form u = v where u, v are words in the free monoid S . We say that this presentation is complemented (on the right) if R contains no equality u = v where either u or v is empty or u and v begin with the same letter, and, moreover, for every pair (x, y) in S, there exists at most one relation u = v in R such that u begins with x and v begins with y. Thus, for instance, a, b ; aba = bb or a, b, c ; a = bbc, a = ca, ba = c ar...

• Type: Journal
• Year: 2000
• Where: DM
• Authors: Patrick Dehornoy
• Keywords: DM 2000, Equivalent Words, Monoids, Presentation