Abstract
Let \(\mathcal{M} = ({M_i}:i \in K)\) be a finite or infinite family consisting of matroids on a common ground set E each of which may be finitary or cofinitary. We prove the following Cantor-Bernstein-type result: If there is a collection of bases, one for each Mi, which covers the set E, and also a collection of bases which are pairwise disjoint, then there is a collection of bases which partition E. We also show that the failure of this Cantor-Bernstein-type statement for arbitrary matroid families is consistent relative to the axioms of set theory ZFC.
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The second author was supported by the Institute for Basic Science (IBS-R029-C1).
The third author would like to thank the generous support of the Alexander von Humboldt Foundation and NKFIH OTKA-129211.
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Erde, J., Gollin, J.P., Joó, A. et al. Base Partition for Mixed Families of Finitary and Cofinitary Matroids. Combinatorica 41, 31–52 (2021). https://doi.org/10.1007/s00493-020-4422-4
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DOI: https://doi.org/10.1007/s00493-020-4422-4