Geodesic
Broken circuit complexes and hyperplane arrangements
Journal of Algebraic Combinatorics, Tome 38 (2013) no. 4, pp. 989-1016.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

We study Stanley-Reisner ideals of broken circuit complexes and characterize those ones admitting linear resolutions or being complete intersections. These results will then be used to characterize hyperplane arrangements whose Orlik-Terao ideal has the same properties. As an application, we improve a result of Wilf on upper bounds for the coefficients of the chromatic polynomial of a maximal planar graph. We also show that for a matroid with a complete intersection broken circuit complex, the supersolvability of the matroid is equivalent to the Koszulness of its Orlik-Solomon algebra.
Classification : 52C35, 13C40, 05B35
Keywords: broken circuit complex, complete intersection, hyperplane arrangement, matroid, Orlik-Terao algebra, resolution 
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Van Le, Dinh; Römer, Tim. Broken circuit complexes and hyperplane arrangements. Journal of Algebraic Combinatorics, Tome 38 (2013) no. 4, pp. 989-1016. http://geodesic.mathdoc.fr/item/JAC_2013__38_4_a0/