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Proceedings of the American Mathematical Society

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

 

 

An exchange theorem for independence structures


Author: C. J. H. McDiarmid
Journal: Proc. Amer. Math. Soc. 47 (1975), 513-514
MSC: Primary 05B35
DOI: https://doi.org/10.1090/S0002-9939-1975-0363960-9
MathSciNet review: 0363960
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Abstract: I give a simple proof of the following result, which extends a result of C. Greene [1]. Let $ X$ and $ Y$ be sets in an independence structure $ \mathcal{E}$ and let $ X = {X_1} \cup {X_2}$ be a partition of $ X$. Then there exists a partition $ Y = {Y_1} \cup {Y_2}$ of $ Y$ such that for $ i = 1,2,{X_i} \cap {Y_i} = \phi $ and $ {X_i} \cup {Y_i}$ is in $ \mathcal{E}$.


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DOI: https://doi.org/10.1090/S0002-9939-1975-0363960-9
Article copyright: © Copyright 1975 American Mathematical Society