论文信息 - On completeness of word reversing

On completeness of word reversing

Abstract 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.

Patrick Dehornoy | Patrick Dehornoy

[1] Matthieu Picantin. Petits groupes gaussiens , 2000 .

[2] An isoperimetric inequality for Artin groups of finite type , 1993 .

[3] Patrick Dehornoy,et al. Gaussian Groups and Garside Groups, Two Generalisations of Artin Groups , 1999 .

[4] Patrick Dehornoy,et al. A Fast Method for Comparing Braids , 1997 .

[5] Patrick Dehornoy,et al. Braid groups and left distributive operations , 1994 .

[6] Egbert Brieskorn,et al. Artin-Gruppen und Coxeter-Gruppen , 1972 .

[7] Patrick Dehornoy. Gaussian Groups are Torsion Free , 1998 .

[8] John H. Remmers. ON THE GEOMETRY OF SEMIGROUP PRESENTATIONS , 1980 .

[9] P. Dehornoy. Deux propriétés des groupes de tresses , 1992 .

[10] R. Tennant. Algebra , 1941, Nature.

[11] Patrick Dehornoy,et al. Groups with a complemented presentation , 1997 .

[12] Bolyai János Matematikai Társulat,et al. Algebraic theory of semigroups , 1979 .

[13] David B. A. Epstein,et al. Word processing in groups , 1992 .

[14] S. Adjan,et al. Defining Relations and Algorithmic Problems for Groups and Semigroups , 1967 .

[15] P. Deligne,et al. Les immeubles des groupes de tresses généralisés , 1972 .

[16] Ronald Regan. Basic Set Theory , 2000 .