Resumen de Signed-eliminable graphs and free multiplicities on the braid arrangement

Takuro Abe, Koji Nuida, Yasuhide Numata

• 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.