Base Partition for Mixed Families of Finitary and Cofinitary Matroids

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

*Korrespondierende/r Autor/-in für diese Arbeit

Publikation: Beitrag in einer FachzeitschriftArtikelBegutachtung

Abstract

Let M = (M i:i ϵ 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 M i, 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.

Originalspracheenglisch
Seiten (von - bis)31-52
Seitenumfang22
FachzeitschriftCombinatorica
Jahrgang41
Ausgabenummer1
DOIs
PublikationsstatusVeröffentlicht - Feb. 2021

ASJC Scopus subject areas

  • Computational Mathematics
  • Diskrete Mathematik und Kombinatorik

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