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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Another exchange property for bases


Author: Curtis Greene
Journal: Proc. Amer. Math. Soc. 46 (1974), 155-156
MSC: Primary 05B35
DOI: https://doi.org/10.1090/S0002-9939-1974-0345850-X
MathSciNet review: 0345850
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Abstract: Let $ X$ and $ Y$ be bases of a combinatorial geometry of rank $ n$. If $ A \subseteq X$ and $ B \subseteq Y$, with $ \vert A\vert + \vert B\vert \geq n + 1$, then there exist subsets $ {A_0} \subseteq A$ and $ {B_0} \subseteq B$ such that $ (X - {A_0}) \cup {B_0}$ and $ (Y - {B_0}) \cup {A_0}$ are both bases.


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DOI: https://doi.org/10.1090/S0002-9939-1974-0345850-X
Keywords: Combinatorial geometry, matroid
Article copyright: © Copyright 1974 American Mathematical Society