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Journal of the London Mathematical Society 1998 58(3):513-525; doi:10.1112/S0024610798006723
© 1998 by London Mathematical Society
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© The London Mathematical Society

The Intersection of Two Infinite Matroids

Ron Aharoni and Ran Ziv

Department of Mathematics, Technion Haifa, Israel
School of Science and Technology, Tel Hai College Upper Galilee, Israel

Received 16 June 1996. Revision received 16 January 1997.

Conjecture: Let M and N be two matroids (possibly of infinite ranks) on the same set S. Then there exists a set I independent in both M and N, which can be partitioned as I=H{cup}K, where spM(H){cup}spN(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 M) 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 M and independent in N?


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