A basis construction for free arrangements between Linial arrangements and Shi arrangements
A central arrangement $ \cal{A} $ was termed free if the module of $ \cal{A} $-derivations was a free module. The combinatorial structure of arrangements was heavily influenced by the freeness. Yet, there has been scarce exploration into the construction of their bases. In this paper, we constructed...
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| Language: | English |
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AIMS Press
2024-12-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20241658 |
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| author | Meihui Jiang Ruimei Gao |
| author_facet | Meihui Jiang Ruimei Gao |
| author_sort | Meihui Jiang |
| collection | DOAJ |
| description | A central arrangement $ \cal{A} $ was termed free if the module of $ \cal{A} $-derivations was a free module. The combinatorial structure of arrangements was heavily influenced by the freeness. Yet, there has been scarce exploration into the construction of their bases. In this paper, we constructed the explicit bases for a class of free arrangements that positioned between the cone of Linial arrangements and Shi arrangements. |
| format | Article |
| id | doaj-art-331edf1e3d4e47fca88825ef0e9c2cd2 |
| institution | Kabale University |
| issn | 2473-6988 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-331edf1e3d4e47fca88825ef0e9c2cd22025-01-23T07:53:25ZengAIMS PressAIMS Mathematics2473-69882024-12-01912348273483710.3934/math.20241658A basis construction for free arrangements between Linial arrangements and Shi arrangementsMeihui Jiang0Ruimei Gao1School of Mathematics and Statistics, Changchun University of Science and Technology, Changchun 130022, ChinaSchool of Mathematics and Statistics, Changchun University of Science and Technology, Changchun 130022, ChinaA central arrangement $ \cal{A} $ was termed free if the module of $ \cal{A} $-derivations was a free module. The combinatorial structure of arrangements was heavily influenced by the freeness. Yet, there has been scarce exploration into the construction of their bases. In this paper, we constructed the explicit bases for a class of free arrangements that positioned between the cone of Linial arrangements and Shi arrangements.https://www.aimspress.com/article/doi/10.3934/math.20241658hyperplane arrangementshi arrangementfree arrangementbernoulli polynomialsubarrangement |
| spellingShingle | Meihui Jiang Ruimei Gao A basis construction for free arrangements between Linial arrangements and Shi arrangements AIMS Mathematics hyperplane arrangement shi arrangement free arrangement bernoulli polynomial subarrangement |
| title | A basis construction for free arrangements between Linial arrangements and Shi arrangements |
| title_full | A basis construction for free arrangements between Linial arrangements and Shi arrangements |
| title_fullStr | A basis construction for free arrangements between Linial arrangements and Shi arrangements |
| title_full_unstemmed | A basis construction for free arrangements between Linial arrangements and Shi arrangements |
| title_short | A basis construction for free arrangements between Linial arrangements and Shi arrangements |
| title_sort | basis construction for free arrangements between linial arrangements and shi arrangements |
| topic | hyperplane arrangement shi arrangement free arrangement bernoulli polynomial subarrangement |
| url | https://www.aimspress.com/article/doi/10.3934/math.20241658 |
| work_keys_str_mv | AT meihuijiang abasisconstructionforfreearrangementsbetweenlinialarrangementsandshiarrangements AT ruimeigao abasisconstructionforfreearrangementsbetweenlinialarrangementsandshiarrangements AT meihuijiang basisconstructionforfreearrangementsbetweenlinialarrangementsandshiarrangements AT ruimeigao basisconstructionforfreearrangementsbetweenlinialarrangementsandshiarrangements |