A proof of Rado's Theorem via principal extension

We give a new proof of Rado's Theorem that, given a partition (X1,…,Xn) of the ground set of a matroid M, there is an independent set of M containing exactly one element from each of the sets (X1,…,Xn) if and only if for each subset J of {1,…,n} we have r(∪j∈JXj)≥|J|.

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Bibliographic Details
Published in:Advances in applied mathematics 2021-05, Vol.126, p.102013, Article 102013
Main Authors: Geelen, Jim, Sun, Hao
Format: Article
Language:English
Subjects:
Matroids
Rado's Theorem
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Description
Summary:We give a new proof of Rado's Theorem that, given a partition (X1,…,Xn) of the ground set of a matroid M, there is an independent set of M containing exactly one element from each of the sets (X1,…,Xn) if and only if for each subset J of {1,…,n} we have r(∪j∈JXj)≥|J|.
ISSN:0196-8858
1090-2074
DOI:10.1016/j.aam.2020.102013