Oriented matroids and Ky Fan's theorem

Details Oriented matroids and Ky Fan's theorem Oriented matroids and Ky Fan's theorem

2007-10-10

arxiv.org/abs/0710.1981v1

Mathematics

Combinatorics

Scientific paper

L. Lovasz has shown that Sperner's combinatorial lemma admits a generalization involving a matroid defined on the set of vertices of the associated triangulation. Inspired by this result we prove that classical Ky Fan's theorem admits an oriented matroid generalization of similar nature. Ky Fan's theorem is obtained as a corollary if the underlying oriented matroid is chosen to be the alternating matroid C^{m,r} .

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