Base Partition for Mixed Families of Finitary and Cofinitary Matroids

Joshua Erde, Max Pitz, Paul Knappe, Attila Joó, J Pascal Gollin

Research output: Contribution to journalArticle

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 languageEnglish
Number of pages22
JournalCombinatorica
Early online date30 Nov 2020
DOIs
Publication statusE-pub ahead of print - 30 Nov 2020

Keywords

  • Infinite matroid
  • Base packing
  • Base covering

ASJC Scopus subject areas

  • Computational Mathematics
  • Discrete Mathematics and Combinatorics

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