Another exchange property for bases

Greene, Curtis

doi:10.1090/S0002-9939-1974-0345850-X

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

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Another exchange property for bases
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by Curtis Greene PDF

Proc. Amer. Math. Soc. 46 (1974), 155-156 Request permission

Abstract:

Let $X$ and $Y$ be bases of a combinatorial geometry of rank $n$. If $A \subseteq X$ and $B \subseteq Y$, with $|A| + |B| \geq n + 1$, 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.

References

Curtis Greene, A multiple exchange property for bases, Proc. Amer. Math. Soc. 39 (1973), 45–50. MR 311494, DOI 10.1090/S0002-9939-1973-0311494-8