Matchings in matroids over abelian groups, II

The concept of matchings originated in group theory to address a linear algebra problem related to canonical forms for symmetric tensors. In an abelian group [Formula: see text], a matching is a bijection [Formula: see text] between two finite subsets [Formula: see text] and [Formula: see text] of [Formula: see text] such that [Formula: see text] for all [Formula: see text]. A group [Formula: see text] has the matching property if, for every two finite subsets [Formula: see text] of the same size with [Formula: see text], there exists a matching from [Formula: see text] to [Formula: see text]. In prior work [M. Aliabadi and S. Zerbib, Matchings in matroids over abelian groups, J. Algebr. Comb. 59(4) (2024) 761–785], matroid analog of results concerning matchings in groups were introduced and established. This paper serves as a sequel, extending that line of inquiry by investigating sparse paving, panhandle, and Schubert matroids through the lens of matchability. While some proofs draw upon earlier findings on the matchability of sparse paving matroids, the paper is designed to be self-contained and accessible without reference to the preceding sequel. Our approach combines tools from both matroid theory and additive number theory.