Signed-eliminable graphs and free multiplicities on the braid arrangement

Takuro Abe, Koji Nuida, Yasuhide Numata

Research output: Contribution to journalArticlepeer-review

13 Citations (Scopus)


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
Issue number1
Publication statusPublished - Aug 2009
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • General Mathematics


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