Hilbert series of mixed braid monoid $ MB_{2, 2} $

Abstract

Hilbert series is a simplest way to calculate the dimension and the degree of an algebraic variety by an explicit polynomial equation. The mixed braid group $ B_{m, n} $ is a subgroup of the Artin braid group $ B_{m+n} $. In this paper we find the ambiguity-free presentation and the Hilbert series of canonical words of mixed braid monoid $ M\!B_{2, 2} $.

Keywords

• braid group
• mixed braid monoid
• canonical words
• complete presentation
• hilbert series