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.
Citation: Meihui Jiang, Ruimei Gao. A basis construction for free arrangements between Linial arrangements and Shi arrangements[J]. AIMS Mathematics, 2024, 9(12): 34827-34837. doi: 10.3934/math.20241658
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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Meihui Jiang, Ruimei Gao. A basis construction for free arrangements between Linial arrangements and Shi arrangements[J]. AIMS Mathematics, 2024, 9(12): 34827-34837. doi: 10.3934/math.20241658
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