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Freeness of Hyperplane Arrangements between Boolean Arrangements and Weyl Arrangements of Type $ B_{\ell} $

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arxiv 1807.02432 v2 pith:HKNYKR3F submitted 2018-07-06 math.CO

classification math.CO
keywords arrangementstypefreenessbooleanweylcharacterizedgraphssubarrangements
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abstract

Every subarrangement of Weyl arrangements of type $ B_{\ell} $ is represented by a signed graph. Edelman and Reiner characterized freeness of subarrangements between type $ A_{\ell-1} $ and type $ B_{\ell} $ in terms of graphs. Recently, Suyama and the authors characterized freeness for subarrangements containing Boolean arrangements satisfying a certain condition. This article is a sequel to the previous work. Namely, we give a complete characterization for freeness of arrangements between Boolean arrangements and Weyl arrangements of type $ B_{\ell} $ in terms of graphs.

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Cited by 1 Pith paper

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  1. Modular Construction of Free Hyperplane Arrangements

    math.CO 2019-08 accept novelty 7.0 of 10

    Every modularly extended matroid has a divisional flag, so any hyperplane arrangement whose dependence matroid is modularly extended is divisionally free.

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