Pattern Recognition on Oriented Matroids: Three-Tope Committees

Details Pattern Recognition on Oriented Matroids: Three-Tope Committees Pattern Recognition on Oriented Matroids: Three-Tope Committees

2008-11-30

arxiv.org/abs/0812.0156v2

Mathematics

Combinatorics

7 pages; v.2 - minor improvements

Scientific paper

A three-tope committee K* for a simple oriented matroid M is a 3-subset of
its maximal covectors such that every positive halfspace of M contains at least
two topes from K*. We consider three-tope committees as the vertex sets of
triangles in graphs associated with the topes and enumerate them making use of
the properties of the poset of convex subsets of the ground set of M.

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