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arXiv · 2504.19893

Separator-based derivations of graphic arrangements

Leonie Mühlherr
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Abstract

The class of subarrangements of the well-studied braid arrangement, so-called graphic hyperplane arrangements, is important for analysing new concepts and properties in hyperplane arrangement theory. While there is a nice characterization of free graphic arrangements, many interesting questions beyond the free case remain open. This paper introduces an explicit set of generators for the module of logarithmic derivations of a general graphic arrangement based on graph separators. We obtain new insights in the derivation degree sequence in the non-free case and give bounds on the highest degree in the sequence. Moreover, this can broadly be used for future research in this area.

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Leonie Mühlherr. 2025-04-28. Separator-based derivations of graphic arrangements. https://arxiv.org/abs/2504.19893

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