Pattern Recognition on Oriented Matroids: Topes and Critical Committees
Combinatorics
2013-04-01 v6
Abstract
Let the sign components of the maximal covectors of a simple oriented matroid M be represented by the real numbers -1 and 1. Consider the vertex set V(R) of a symmetric cycle R of adjacent topes in the tope graph of M as a subposet of the tope poset of M. If B is the bottom element of the tope poset then B is equal to the unweighted sum of the members of the set min V(R) of minimal elements of the subposet V(R); if B is the positive tope then the set min V(R) is a critical tope committee for the acyclic oriented matroid M.
Keywords
Cite
@article{arxiv.1011.6082,
title = {Pattern Recognition on Oriented Matroids: Topes and Critical Committees},
author = {Andrey O. Matveev},
journal= {arXiv preprint arXiv:1011.6082},
year = {2013}
}
Comments
7 pages, 3 figures. v2,3 - misprints corrected, Corollary 2.2 and Example 2.3 modified; v.4,5,6 - minor improvements