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1 February 2002 Syzygies of oriented matroids
Isabella Novik, Alexander Postnikov, Bernd Sturmfels
Duke Math. J. 111(2): 287-317 (1 February 2002). DOI: 10.1215/S0012-7094-02-11124-7

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.

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Isabella Novik. Alexander Postnikov. Bernd Sturmfels. "Syzygies of oriented matroids." Duke Math. J. 111 (2) 287 - 317, 1 February 2002. https://doi.org/10.1215/S0012-7094-02-11124-7

Information

Published: 1 February 2002
First available in Project Euclid: 18 June 2004

zbMATH: 1022.13002
MathSciNet: MR1882136
Digital Object Identifier: 10.1215/S0012-7094-02-11124-7

Subjects:
Primary: 13D02
Secondary: 05B35 , 52C40

Rights: Copyright © 2002 Duke University Press

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Vol.111 • No. 2 • 1 February 2002
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