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Research Article | Open Access

A basis construction for free arrangements between Linial arrangements and Shi arrangements

Meihui Jiang, Ruimei Gao( )
School of Mathematics and Statistics, Changchun University of Science and Technology, Changchun 130022, China
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Abstract

A central arrangement A was termed free if the module of 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.

Keywords

hyperplane arrangementShi arrangementfree arrangementBernoulli polynomialsubarrangement
CLC number: 13C10, 32S22

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AIMS Mathematics
Volume 9 Issue 12,
December 2024
Pages 34827-34837
DOI: 10.3934/math.20241658

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Cite this article:
Jiang M, Gao R. A basis construction for free arrangements between Linial arrangements and Shi arrangements. AIMS Mathematics, 2024, 9(12): 34827-34837. https://doi.org/10.3934/math.20241658

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Received: 12 September 2024
Revised: 23 November 2024
Accepted: 02 December 2024
Published: 15 December 2024
©2024 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)