A d-polytope P is neighborly if every subset of b d 2 c vertices is a face of P. In 1982, Shemer introduced a sewing construction that allows to add a vertex to a neighborly polytope in such a way as to obtain a new neighborly polytope. With this, he constructed superexponentially many different neighborly polytopes. The concept
of neighborliness extends naturally to oriented matroids. Duals of neighborly oriented matroids also have a nice
characterization: balanced oriented matroids. In this paper, we generalize Shemer’s sewing construction to oriented
matroids, providing a simpler proof. Moreover we provide a new technique that allows to construct balanced oriented
matroids. In the dual setting, it constructs a neighborly oriented matroid whose contraction at a particular vertex is a prescribed neighborly oriented matroid. We compare the families of polytopes that can be constructed with both methods, and show that the new construction allows to construct many new polytopes.
CitationPadrol, A. Constructing neighborly polytopes and oriented matroids. A: International Conference on Formal Power Series and Algebraic Combinatorics. "24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012)". Nagoya: 2012, p. 203-214.
All rights reserved. This work is protected by the corresponding intellectual and industrial property rights. Without prejudice to any existing legal exemptions, reproduction, distribution, public communication or transformation of this work are prohibited without permission of the copyright holder. If you wish to make any use of the work not provided for in the law, please contact: email@example.com