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arXiv · 1011.6082

Pattern Recognition on Oriented Matroids: Topes and Critical Committees

Andrey O. Matveev
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Abstract

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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Andrey O. Matveev. 2013-03-29. Pattern Recognition on Oriented Matroids: Topes and Critical Committees. https://arxiv.org/abs/1011.6082

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