Pattern Recognition on Oriented Matroids: Layers of Tope Committees
Abstract
Description
A tope committee K* for a simple oriented matroid M is a subset of its maximal covectors such that every positive halfspace of M contains more than half of the covectors from K*. The structures of the family of all committees for M, and of the family of its committees that contain no pairs of opposites, are described. A Farey subsequence associated with the elements of the m-th layer of the Boolean lattice of rank 2m is explored.
15 pages; v.2,3 - introductory section and misprints in section 5 corrected; v.4,5 - minor improvements; v.6 - connection of Section 3 with INTEGERS 7 (2007) #20 described; v.7 - Proposition 4.1 and Theorem 5.1 reformulated, other minor changes in text and references
15 pages; v.2,3 - introductory section and misprints in section 5 corrected; v.4,5 - minor improvements; v.6 - connection of Section 3 with INTEGERS 7 (2007) #20 described; v.7 - Proposition 4.1 and Theorem 5.1 reformulated, other minor changes in text and references