Duke Mathematical Journal

Syzygies of oriented matroids

Isabella Novik, Alexander Postnikov, and Bernd Sturmfels

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Abstract

We construct minimal cellular resolutions of squarefree monomial ideals arising from hyperplane arrangements, matroids, and oriented matroids. These are Stanley-Reisner ideals of complexes of independent sets and of triangulations of Lawrence matroid polytopes. Our resolution provides a cellular realization of R. Stanley's formula for their Betti numbers. For unimodular matroids our resolutions are related to hyperplane arrangements on tori, and we recover the resolutions constructed by D. Bayer, S. Popescu, and B. Sturmfels [3]. We resolve the combinatorial problems posed in [3] by computing Möbius invariants of graphic and cographic arrangements in terms of Hermite polynomials.

Article information

Source
Duke Math. J., Volume 111, Number 2 (2002), 287-317.

Dates
First available in Project Euclid: 18 June 2004

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1087575042

Digital Object Identifier
doi:10.1215/S0012-7094-02-11124-7

Mathematical Reviews number (MathSciNet)
MR1882136

Zentralblatt MATH identifier
1022.13002

Subjects
Primary: 13D02: Syzygies, resolutions, complexes
Secondary: 05B35: Matroids, geometric lattices [See also 52B40, 90C27] 52C40: Oriented matroids

Citation

Novik, Isabella; Postnikov, Alexander; Sturmfels, Bernd. Syzygies of oriented matroids. Duke Math. J. 111 (2002), no. 2, 287--317. doi:10.1215/S0012-7094-02-11124-7. https://projecteuclid.org/euclid.dmj/1087575042


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