<P>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 wit...
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https://www.riss.kr/link?id=A107643088
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2016
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SCI,SCIE,SCOPUS
학술저널
1-14(14쪽)
0
상세조회0
다운로드다국어 초록 (Multilingual Abstract)
<P>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 wit...
<P>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.</P>
Weakly holomorphic Hecke eigenforms and Hecke eigenpolynomials