Duke Mathematical Journal

Syzygies of oriented matroids

Isabella Novik, Alexander Postnikov, and Bernd Sturmfels

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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

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

First available in Project Euclid: 18 June 2004

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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


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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