A generalization of a theorem of Mandel

Randriamaro, Hery

doi:10.28919/eml/8236

Eng. Math. Lett. 2023 (2023), Article ID 1

A generalization of a theorem of Mandel

Hery Randriamaro

PDF (161.9 KB) https://doi.org/10.28919/eml/8236

Abstract

A theorem of Mandel allows to determine the covector set of an oriented matroid from its set of topes by using the composition condition. We provide a generalization of that result, stating that the covector set of a conditional oriented matroid can also be determined by its set of topes, but by using the face symmetry condition. It permits to represent geometrical configurations in terms of conditional oriented matroids, more suitable for computer calculations. We treat apartments of hyperplane arrangements as example.

Published: 30 October 2023
Volume: 2023 (2023)
License: CC BY 3.0

Copyright © 2023 Hery Randriamaro. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Cite this article

H. Randriamaro, A generalization of a theorem of Mandel, Eng. Math. Lett. 2023 (2023), 1. https://doi.org/10.28919/eml/8236

BibTeX

@article{Randriamaro2023,
  author  = {Randriamaro, Hery},
  title   = {A generalization of a theorem of Mandel},
  journal = {Eng. Math. Lett.},
  volume  = {2023},
  year    = {2023},
  pages   = {1},
  doi     = {10.28919/eml/8236}
}