Syzygies of oriented matroids
Novik, Isabella ; Postnikov, Alexander ; Sturmfels, Bernd
Duke Math. J., Tome 115 (2002) no. 1, p. 287-317 / Harvested from Project Euclid
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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.
Publié le : 2002-02-01
Classification:  13D02,  05B35,  52C40 
@article{1087575042,
     author = {Novik, Isabella and Postnikov, Alexander and Sturmfels, Bernd},
     title = {Syzygies of oriented matroids},
     journal = {Duke Math. J.},
     volume = {115},
     number = {1},
     year = {2002},
     pages = { 287-317},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1087575042}
}

Novik, Isabella; Postnikov, Alexander; Sturmfels, Bernd. Syzygies of oriented matroids. Duke Math. J., Tome 115 (2002) no. 1, pp.  287-317. http://gdmltest.u-ga.fr/item/1087575042/