A Generalization of a Theorem of Mandel

Authors: Hery Randriamaro

8 pages, 1 figure
License: CC BY 4.0

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.

Submitted to arXiv on 19 Sep. 2023

Explore the paper tree

Click on the tree nodes to be redirected to a given paper and access their summaries and virtual assistant

Also access our AI generated Summaries, or ask questions about this paper to our AI assistant.

Look for similar papers (in beta version)

By clicking on the button above, our algorithm will scan all papers in our database to find the closest based on the contents of the full papers and not just on metadata. Please note that it only works for papers that we have generated summaries for and you can rerun it from time to time to get a more accurate result while our database grows.