Duke Mathematical Journal
- Duke Math. J.
- Volume 111, Number 2 (2002), 287-317.
Syzygies of oriented matroids
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 . We resolve the combinatorial problems posed in  by computing Möbius invariants of graphic and cographic arrangements in terms of Hermite polynomials.
Duke Math. J., Volume 111, Number 2 (2002), 287-317.
First available in Project Euclid: 18 June 2004
Permanent link to this document
Digital Object Identifier
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