Signed-eliminable graphs and free multiplicities on the braid arrangement
- Autores: Takuro Abe, Koji Nuida, Yasuhide Numata
- Localización: Journal of the London Mathematical Society, ISSN 0024-6107, Vol. 80, Nº 1, 2009, págs. 121-134
- Idioma: inglés
- DOI: 10.1112/jlms/jdp019
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Resumen
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.
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