Flag-accurate arrangements
Paul M\"ucksch, Gerhard Roehrle, Tan Nhat Tran

TL;DR
This paper introduces the concept of flag-accurate arrangements, a subclass of free arrangements characterized by a flag of flats, and explores their properties, especially in reflection and graphic arrangements, linking them to divisional freeness.
Contribution
It defines and studies flag-accuracy in arrangements, connecting it to divisional freeness and providing evidence that MAT-freeness implies flag-accuracy.
Findings
Flag-accurate arrangements include Coxeter arrangements.
MAT-free arrangements are shown to be accurate.
Evidence suggests MAT-freeness may imply flag-accuracy.
Abstract
In [MR21], the first two authors introduced the notion of an accurate arrangement, a particular notion of freeness. In this paper, we consider a special subclass, where the property of accuracy stems from a flag of flats in the intersection lattice of the underlying arrangement. Members of this family are called flag-accurate. One relevance of this new notion is that it entails divisional freeness. There are a number of important natural classes which are flag-accurate, the most prominent one among them is the one consisting of Coxeter arrangements. This warrants a systematic study which is put forward in the present paper. More specifically, let be a free arrangement of rank . Suppose that for every , the first exponents of -- when listed in increasing order -- are realized as the exponents of a free restriction of to…
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Computational Geometry and Mesh Generation · Digital Image Processing Techniques
