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Base Partition for Mixed Families of Finitary and Cofinitary Matroids

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Title
Base Partition for Mixed Families of Finitary and Cofinitary Matroids
Author(s)
Erde, Joshua; J. PASCAL GOLLIN; Joó, Attila; Knappe, Paul; Pitz, Max
Publication Date
2021-02
Journal
Combinatorica, v.41, no.1, pp.31 - 52
Publisher
Springer Verlag
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.
URI
https://pr.ibs.re.kr/handle/8788114/9981
DOI
10.1007/s00493-020-4422-4
ISSN
0209-9683
Appears in Collections:
Pioneer Research Center for Mathematical and Computational Sciences(수리 및 계산과학 연구단) > Discrete Mathematics Group(이산 수학 그룹) > 1. Journal Papers (저널논문)
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