2006/12/13 by Andrey O. Matveev, Matveev, Andrey O.
Mathematics · #05E30 #11B57 #52C35 #52C40 #68T10 #90C27 #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05E30 #msc:11B57 #msc:52C35 #msc:52C40 #msc:68T10 #msc:90C27
paper · pdf · doi:10.48550/arxiv.math/0612369
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
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.