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Research Article | Open Access

Hilbert series of mixed braid monoid M B 2 , 2

Zaffar Iqbal1, Xiujun Zhang2, Mobeen Munir3( ), Ghina Mubashar1
Department of Mathematics, University of Gujrat, Pakistan
School of Computer Science, Chengdu University, Chengdu, China
Department of Mathematics, University of the Punjab, Quaid-e-Azam Campus, Lahore, Pakistan
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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 .

Keywords

braid groupmixed braid monoidcanonical wordscomplete presentationHilbert series
CLC number: 20F36, 20F05, 13D40

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AIMS Mathematics
Volume 7 Issue 9,
September 2022
Pages 17080-17090
DOI: 10.3934/math.2022939

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Cite this article:
Iqbal Z, Zhang X, Munir M, et al. Hilbert series of mixed braid monoid M B 2 , 2 . AIMS Mathematics, 2022, 7(9): 17080-17090. https://doi.org/10.3934/math.2022939

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Received: 30 April 2022
Revised: 03 July 2022
Accepted: 12 July 2022
Published: 15 September 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)