Splicing matroids

In memory of Tom Brylawski
https://doi.org/10.1016/j.ejc.2011.01.018Get rights and content
Under an Elsevier user license
open archive

Abstract

We introduce and study a natural variant of matroid amalgams. For matroids M(A) and N(B) with M.(AB)=N|(AB), we define a splice of M and N to be a matroid L on AB with L|A=M and L.B=N. We show that splices exist for each such pair of matroids M and N; furthermore, there is a freest splice of M and N, which we call the free splice. We characterize when a matroid L(AB) is the free splice of L|A and L.B. We study minors of free splices and the interaction between free splice and several other matroid operations. Although free splice is not an associative operation, we prove a weakened counterpart of associativity that holds in general and we characterize the triples for which associativity holds. We also study free splice as it relates to various classes of matroids.

Cited by (0)