Pattern Recognition on Oriented Matroids: Decompositions of Topes, and Dehn-Sommerville Type Relations
Combinatorics
2017-03-14 v1
Abstract
If V(R) is the vertex set of a symmetric cycle R in the tope graph of a simple oriented matroid M, then for any tope T of M there exists a unique inclusion-minimal subset Q(T;R) of V(R) such that T is the sum of the topes of Q(T;R). If |Q(T;R)|>3, then the decomposition Q(T;R) of the tope T with respect to the symmetric cycle R satisfies certain Dehn-Sommerville type relations.
Keywords
Cite
@article{arxiv.1703.04508,
title = {Pattern Recognition on Oriented Matroids: Decompositions of Topes, and Dehn-Sommerville Type Relations},
author = {Andrey O. Matveev},
journal= {arXiv preprint arXiv:1703.04508},
year = {2017}
}
Comments
5 pages