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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Main Authors: Meihui Jiang, Ruimei Gao
Format: Article
Language:English
Published: AIMS Press 2024-12-01
Series:AIMS Mathematics
Subjects:
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.
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institution Kabale University
issn 2473-6988
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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
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AT ruimeigao abasisconstructionforfreearrangementsbetweenlinialarrangementsandshiarrangements
AT meihuijiang basisconstructionforfreearrangementsbetweenlinialarrangementsandshiarrangements
AT ruimeigao basisconstructionforfreearrangementsbetweenlinialarrangementsandshiarrangements