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arXiv · 1211.5318

Broken circuit complexes and hyperplane arrangements

Le Van Dinh·Tim Roemer
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Abstract

We study Stanley-Reisner ideals of broken circuits complexes and characterize those ones admitting a linear resolution or being complete intersections. These results will then be used to characterize 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 an ordered matroid with disjoint minimal broken circuits, the supersolvability of the matroid is equivalent to the Koszulness of its Orlik-Solomon algebra.

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Le Van Dinh, Tim Roemer. 2012-11-22. Broken circuit complexes and hyperplane arrangements. https://doi.org/10.1007/s10801-013-0435-z

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