Signed-eliminable graphs and free multiplicities on the braid arrangement

Takuro Abe, Koji Nuida, Yasuhide Numata

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)

Abstract

We define specific multiplicities on the braid arrangement by using signed graphs. To consider their freeness, we introduce the notion of signed-eliminable graphs as a generalization of Stanley's classification theory of free graphic arrangements by chordal graphs. This generalization gives us a complete classification of the free multiplicities defined above. As an application, we prove one direction of a conjecture of Athanasiadis on the characterization of the freeness of certain deformations of the braid arrangement in terms of directed graphs.

Original languageEnglish
Pages (from-to)131-134
Number of pages4
JournalJournal of the London Mathematical Society
Volume80
Issue number1
DOIs
Publication statusPublished - Aug 2009
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Fingerprint Dive into the research topics of 'Signed-eliminable graphs and free multiplicities on the braid arrangement'. Together they form a unique fingerprint.

Cite this