Pattern Recognition on Oriented Matroids: Topes and Critical Committees

Details Pattern Recognition on Oriented Matroids: Topes and Critical Committees Pattern Recognition on Oriented Matroids: Topes and Critical Committees

2010-11-28

arxiv.org/abs/1011.6082v5

Mathematics

Combinatorics

7 pages, 3 figures. v2,3 - misprints corrected, Corollary 2.2 and Example 2.3 modified; v4 - minor improvements; v.5 - a typo

Scientific paper

Let the sign components of the maximal covectors of a simple oriented matroid M be represented by the real numbers -1 and 1. Consider the vertex set V(R) of a symmetric cycle R of adjacent topes in the tope graph of M as a subposet of the tope poset of M. If B is the bottom element of the tope poset then B is equal to the unweighted sum of the members of the set min V(R) of minimal elements of the subposet V(R); if B is the positive tope then the set min V(R) is a critical tope committee for the acyclic oriented matroid M.

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