Diagonal Form of the Varchenko Matrices
Combinatorics
2018-02-08 v3
Abstract
Varchenko defined the Varchenko matrix associated to any real hyperplane arrangement and computed its determinant. In this paper, we show that the Varchenko matrix of a hyperplane arrangement has a diagonal form if and only if it is semigeneral, i.e., without degeneracy. In the case of semigeneral arrangement, we present an explicit computation of the diagonal form via combinatorial arguments and matrix operations, thus giving a combinatorial interpretation of the diagonal entries.
Keywords
Cite
@article{arxiv.1511.02923,
title = {Diagonal Form of the Varchenko Matrices},
author = {Yibo Gao and YiYu Zhang},
journal= {arXiv preprint arXiv:1511.02923},
year = {2018}
}