Pattern Recognition on Oriented Matroids: Layers of Tope Committees

Details Pattern Recognition on Oriented Matroids: Layers of Tope Committees Pattern Recognition on Oriented Matroids: Layers of Tope Committees

2006-12-13

arxiv.org/abs/math/0612369v7

Mathematics

Combinatorics

15 pages; v.2,3 - introductory section and misprints in section 5 corrected; v.4,5 - minor improvements; v.6 - connection of S

Scientific paper

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.

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