Matchings in matroids over abelian groups
Abstract
We formulate and prove matroid analogues of results concerning matchings in groups. A matching in an abelian group is a bijection between two finite subsets of satisfying for all . A group has the matching property if for every two finite subsets of the same size with , there exists a matching from to . In [19] it was proved that an abelian group has the matching property if and only if it is torsion-free or cyclic of prime order. Here we consider a similar question in a matroid setting. We introduce an analogous notion of matching between matroids whose ground sets are subsets of an abelian group , and we obtain criteria for the existence of such matchings. Our tools are classical theorems in matroid theory, group theory and additive number theory.
Cite
@article{arxiv.2202.07719,
title = {Matchings in matroids over abelian groups},
author = {Mohsen Aliabadi and Shira Zerbib},
journal= {arXiv preprint arXiv:2202.07719},
year = {2024}
}
Comments
To appear in Journal of Algebraic Combinatorics