An edge-signed generalization of chordal graphs, free multiplicities on braid arrangements, and their characterizations

Takuro Abe, Koji Nuida, Yasuhide Numata

Research output: Contribution to conferencePaperpeer-review

2 Citations (Scopus)

Abstract

In this article, we propose a generalization of the notion of chordal graphs to signed graphs, which is based on the existence of a perfect elimination ordering for a chordal graph. We give a special kind of filtrations of the generalized chordal graphs, and show a characterization of those graphs. Moreover, we also describe a relation between signed graphs and a certain class of multiarrangements of hyperplanes, and show a characterization of free multiarrangements in that class in terms of the generalized chordal graphs, which generalizes a well-known result by Stanley on free hyperplane arrangements. Finally, we give a remark on a relation of our results with a recent conjecture by Athanasiadis on freeness characterization for another class of hyperplane arrangements.

Original languageEnglish
Pages1-12
Number of pages12
Publication statusPublished - 2009
Externally publishedYes
Event21st International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'09 - Linz, Austria
Duration: Jul 20 2009Jul 24 2009

Other

Other21st International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'09
CountryAustria
CityLinz
Period7/20/097/24/09

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

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