Syzygies of Oriented Matroids

@inproceedings{Novik2000SyzygiesOO,
  title={Syzygies of Oriented Matroids},
  author={Isabella Novik and Alexander Postnikov and Bernd Sturmfels},
  year={2000}
}
We construct minimal cellular resolutions of squarefree monomial ideals arising from hyperplane arrangements, matroids, and oriented matroids. These are StanleyReisner 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… CONTINUE READING

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