Abstract
Let M = (Mi: i ∈ 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.
Original language | English |
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Number of pages | 22 |
Journal | Combinatorica |
Early online date | 30 Nov 2020 |
DOIs | |
Publication status | E-pub ahead of print - 30 Nov 2020 |
Keywords
- Infinite matroid
- Base packing
- Base covering
ASJC Scopus subject areas
- Computational Mathematics
- Discrete Mathematics and Combinatorics