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THE INTERSECTION OF TWO INFINITE MATROIDS

Published online by Cambridge University Press:  01 December 1998

RON AHARONI  and
RAN ZIV
RON AHARONI
Affiliation:
Department of Mathematics, Technion, Haifa, Israel
RAN ZIV
Affiliation:
School of Science and Technology, Tel Hai College, Upper Galilee, Israel
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Abstract

Conjecture: Let [Mscr ] and [Nscr ] be two matroids (possibly of infinite ranks) on the same set S. Then there exists a set I independent in both [Mscr ] and [Nscr ], which can be partitioned as I=H∪K, where sp[Mscr ](H)∪sp[Nscr ](K)=S. This conjecture is an extension of Edmonds' matroid intersection theorem to the infinite case. We prove the conjecture when one of the matroids (say [Mscr ]) is the sum of countably many matroids of finite rank (the other matroid being general). For the proof we have also to answer the following question: when does there exist a subset of S which is spanning for [Mscr ] and independent in [Nscr ]?

Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 58 , Issue 3 , December 1998 , pp. 513 - 525
Copyright
The London Mathematical Society 1998

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