Congruence Normality for Simplicial Hyperplane Arrangements

Abstract: Simplicial hyperplane arrangements still have much to reveal. In rank 3, it is not known whether the list of simplicial hyperplane arrangements is complete. We determine whether the associated posets of regions possess the combinatorial property of "congruence normality" for arrangements with up to 37 hyperplanes. We use methods from oriented matroids, which make the computations possible. This refines the structure of the list, breaking it into three separate combinatorial categories. In particular, we show that arrangements stemming from finite Weyl groupoids have congruence normal posets of regions. This is joint work with Jean-Philippe Labbé and Michael Cuntz.

combinatorics

Audience: researchers in the topic

York University Applied Algebra Seminar