2025/04/28 by Leonie Mühlherr, Mühlherr, Leonie · 1 citation
Mathematics · Computer Science · #Advanced Combinatorial Mathematics #Computational Geometry and Mesh Generation #Geometric and Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2504.19893
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.