SYZYGIES OF ORIENTED MATROIDS

By Isabella Novik, Alexander Postnikov, Bernd Sturmfels. 2000

72 citations recorded by the source corpus.

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, S. Popescu, and B. Sturmfels []. We resolve the combinatorial problems posed in [3] by computing Mobius invariants of graphic and cographic arrangements in terms of Hermite polynomials.

Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Discrete Mathematics and Combinatorics

View Paper: https://www.semanticscholar.org/paper/5e410336b21780f2fcafbb78258165a1f89604ec

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In Algebra and Number Theory

1. Jürgen Herzog
2. Takayuki Hibi
3. Aldo Conca
4. Asia Rauf
5. Huy Tài Hà
6. Ngô Viêt Trung
7. Adam Van Tuyl
8. Steven Dale Cutkosky

In Computational Theory and Mathematics

1. Jürgen Herzog
2. Asia Rauf
3. Takayuki Hibi
4. Aldo Conca
5. Huy Tài Hà
6. Ngô Viêt Trung
7. Adam Van Tuyl
8. Susan Morey

In Discrete Mathematics and Combinatorics

1. Jürgen Herzog

Citations in the corpus

• Resolutions by mapping cones (2001, background): “These include then of course also matroidal ideals for which explicite resolutions in different terms are already known by Reiner and Welker [14], and Novik, Postnikov and Sturmfels [13].”