Proof of Nash-Williams' Intersection Conjecture for countable matroids

Attila Joó

paper

Proof of Nash-Williams' Intersection Conjecture for countable matroids

arXiv:1912.13253

Abstract

We prove that if $M$ and $N$ are finitary matroids on a common countable edge set $E$ then they admit a common independent set $I$ such that there is a bipartition $E = E_{M} \cup E_{N}$ for which $I \cap E_{M}$ spans $E_{M}$ in $M$ and $I \cap E_{N}$ spans $E_{N}$ in $N$ . It answers positively the Matroid Intersection Conjecture of Nash-Williams in the countable case.