Base Partition for Mixed Families of Finitary and Cofinitary Matroids

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

Publikation: Beitrag in einer FachzeitschriftArtikel

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
Frühes Online-Datum30 Nov 2020
DOIs
PublikationsstatusVeröffentlicht - Feb 2021

ASJC Scopus subject areas

  • !!Computational Mathematics
  • !!Discrete Mathematics and Combinatorics

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