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arXiv · 0712.4110

Signed-eliminable graphs and free multiplicities on the braid arrangement

Takuro Abe·Koji Nuida·Yasuhide Numata
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Abstract

We define specific multiplicities on the braid arrangement by using edge-bicolored graphs. To consider their freeness, we introduce the notion of bicolor-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 the deformation of the braid arrangement in terms of directed graphs.

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Takuro Abe, Koji Nuida, Yasuhide Numata. 2017-07-31. Signed-eliminable graphs and free multiplicities on the braid arrangement. https://doi.org/10.1112/jlms%2Fjdp019

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