Broken circuit complexes and hyperplane arrangements
Autor(en): | Dinh Van Le Roemer, Tim |
Stichwörter: | ALGEBRAS; Broken circuit complex; COHOMOLOGY; Complete intersection; FREE RESOLUTIONS; Hyperplane arrangement; Mathematics; Matroid; MONOMIAL IDEALS; Orlik-Terao algebra; Resolution | Erscheinungsdatum: | 2013 | Herausgeber: | SPRINGER | Journal: | JOURNAL OF ALGEBRAIC COMBINATORICS | Volumen: | 38 | Ausgabe: | 4 | Startseite: | 989 | Seitenende: | 1016 | Zusammenfassung: | 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. |
ISSN: | 09259899 | DOI: | 10.1007/s10801-013-0435-z |
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geprüft am 20.05.2024