Andrey O. Matveev
Published 2006-12-13, updated 2008-11-30Version 7
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.
Comments: 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
Pattern Recognition on Oriented Matroids: The Existence of a Tope Committee
Pattern Recognition on Oriented Matroids: Subtopes and Decompositions of (Sub)topes
Pattern Recognition on Oriented Matroids: Three-Tope Committees
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