Gröbner-Shirshov bases for Coxeter groups I

Yuqun Chen; Cihua Liu

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arXiv · 0910.0096

Gröbner-Shirshov bases for Coxeter groups I

Yuqun Chen·Cihua Liu

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Abstract

A conjecture of Gröbner-Shirshov basis of any Coxeter group has proposed by L.A. Bokut and L.-S. Shiao \cite{bs01}. In this paper, we give an example to show that the conjecture is not true in general. We list all possible nontrivial inclusion compositions when we deal with the general cases of the Coxeter groups. We give a Gröbner-Shirshov basis of a Coxeter group which is without nontrivial inclusion compositions mentioned the above.

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Yuqun Chen, Cihua Liu. 2009-10-01. Gröbner-Shirshov bases for Coxeter groups I. https://arxiv.org/abs/0910.0096

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