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A multiple exchange property for bases

Author: Curtis Greene
Journal: Proc. Amer. Math. Soc. 39 (1973), 45-50
MSC: Primary 05B35
MathSciNet review: 0311494
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Abstract: Let $ X$ and $ Y$ be bases of a combinatorial geometry $ G$, and let $ A$ be any subset of $ X$. Then there exists a subset $ B$ of $ Y$ with the property that $ (X - A) \cup B$ and $ (Y - B) \cup A$ are both bases of $ G$.

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Keywords: Combinatorial geometries, bases, exchange property, Laplace expansion
Article copyright: © Copyright 1973 American Mathematical Society