The intersection of a matroid and an oriented matroid

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We prove the following "matroid intersection" theorem: Let M be a matroid with rank function rho and let O be an oriented matroid of rank r, both defined on the same ground set V and satisfying rho(V) > r. If every subset S subset of V with rho(V \ S) < r contains a positive circuit of O, then there is a positive circuit of O which is independent in M. This contains Imre Barany's colorful Caratheodory theorem as a special case. The proof uses topological methods and combines the Folkman-Lawrence representation theorem with a generalization of Kalai and Meshulam's topological colorful Helly theorem. (C) 2015 Elsevier Inc. All rights reserved.
Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
Issue Date
2016-02
Language
English
Article Type
Article
Keywords

THEOREM; NUMBERS

Citation

ADVANCES IN MATHEMATICS, v.290, pp.1 - 14

ISSN
0001-8708
DOI
10.1016/j.aim.2015.11.040
URI
http://hdl.handle.net/10203/207985
Appears in Collection
MA-Journal Papers(저널논문)
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