Hilbert series of mixed braid monoid $ MB_{2, 2} $
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 o...
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| Format: | Article |
| Language: | English |
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AIMS Press
2022-07-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2022939?viewType=HTML |
| _version_ | 1818041748492910592 |
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| author | Zaffar Iqbal Xiujun Zhang Mobeen Munir Ghina Mubashar |
| author_facet | Zaffar Iqbal Xiujun Zhang Mobeen Munir Ghina Mubashar |
| author_sort | Zaffar Iqbal |
| collection | DOAJ |
| description | 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} $. |
| first_indexed | 2024-12-10T08:35:21Z |
| format | Article |
| id | doaj.art-db49b248842543c2af8de4647aa5066c |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-12-10T08:35:21Z |
| publishDate | 2022-07-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-db49b248842543c2af8de4647aa5066c2022-12-22T01:55:59ZengAIMS PressAIMS Mathematics2473-69882022-07-0179170801709010.3934/math.2022939Hilbert series of mixed braid monoid $ MB_{2, 2} $Zaffar Iqbal 0Xiujun Zhang 1Mobeen Munir2Ghina Mubashar31. Department of Mathematics, University of Gujrat, Pakistan2. School of Computer Science, Chengdu University, Chengdu, China3. Department of Mathematics, University of the Punjab, Quaid-e-Azam Campus, Lahore, Pakistan1. Department of Mathematics, University of Gujrat, PakistanHilbert 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} $.https://www.aimspress.com/article/doi/10.3934/math.2022939?viewType=HTMLbraid groupmixed braid monoidcanonical wordscomplete presentationhilbert series |
| spellingShingle | Zaffar Iqbal Xiujun Zhang Mobeen Munir Ghina Mubashar Hilbert series of mixed braid monoid $ MB_{2, 2} $ AIMS Mathematics braid group mixed braid monoid canonical words complete presentation hilbert series |
| title | Hilbert series of mixed braid monoid $ MB_{2, 2} $ |
| title_full | Hilbert series of mixed braid monoid $ MB_{2, 2} $ |
| title_fullStr | Hilbert series of mixed braid monoid $ MB_{2, 2} $ |
| title_full_unstemmed | Hilbert series of mixed braid monoid $ MB_{2, 2} $ |
| title_short | Hilbert series of mixed braid monoid $ MB_{2, 2} $ |
| title_sort | hilbert series of mixed braid monoid mb 2 2 |
| topic | braid group mixed braid monoid canonical words complete presentation hilbert series |
| url | https://www.aimspress.com/article/doi/10.3934/math.2022939?viewType=HTML |
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