The lattice of convex sets of an oriented matroid

@article{Edelman1982TheLO,
  title={The lattice of convex sets of an oriented matroid},
  author={Paul H. Edelman},
  journal={J. Comb. Theory, Ser. B},
  year={1982},
  volume={33},
  pages={239-244}
}
In this paper we further investigate the structure of the convex sets of an acyclic oriented matroid. This subject was first explored by Las Vergnas [6]. The main tool of our study is the theory of the anti-exchange closure [2]. We show that the convex closure of Las Vergnas satisfies the anti-exchange law in the case where the matroid is a geometry. From this we are able to detail the structure of the lattice of convex sets. This is done in Section II. In Section III this analysis is used to… CONTINUE READING
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