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

Zaffar Iqbal; Xiujun Zhang; Mobeen Munir; Ghina Mubashar; Zaffar Iqbal; Xiujun Zhang; Mobeen Munir; Ghina Mubashar

doi:10.3934/math.2022939

AIMS Mathematics

2022, Volume 7, Issue 9: 17080-17090. doi: 10.3934/math.2022939

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Research article

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

1.
Department of Mathematics, University of Gujrat, Pakistan
2.
School of Computer Science, Chengdu University, Chengdu, China
3.
Department of Mathematics, University of the Punjab, Quaid-e-Azam Campus, Lahore, Pakistan

Received: 30 April 2022 Revised: 03 July 2022 Accepted: 12 July 2022 Published: 20 July 2022
MSC : 20F36, 20F05, 13D40

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} $.
- braid group,
- mixed braid monoid,
- canonical words,
- complete presentation,
- Hilbert series
Citation: Zaffar Iqbal, Xiujun Zhang, Mobeen Munir, Ghina Mubashar. Hilbert series of mixed braid monoid $ MB_{2, 2} $[J]. AIMS Mathematics, 2022, 7(9): 17080-17090. doi: 10.3934/math.2022939

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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} $.

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