Intersection of a partitional and a general infinite matroid

Abstract

Let E be a possibly infinite set and let M and N be matroids defined on E. We say that the pair {M, N } has the Intersection property if M and N share an independent set I admitting a bipartitionThe Matroid Intersection Conjecture of Nash-Williams says that every matroid pair has the Intersection property.It was shown by N. Bowler and J. Carmesin that the conjecture can be reduced to the special case where one of the matroids is a partitional matroid. We prove that if M is an arbitrary matroid and N is a partitional matroid of finitely many components, then {M, N } has the Intersection property.