Conditions for matchability in groups and field extensions
Combinatorics
2022-03-09 v3
Abstract
The origins of the notion of matchings in groups spawn from a linear algebra problem proposed by E. K. Wakeford [24] which was tackled in 1996 [10]. In this paper, we first discuss unmatchable subsets in abelian groups. Then we formulate and prove linear analogues of results concerning matchings, along with a conjecture that, if true, would extend the primitive subspace theorem. We discuss the dimension -intersection property for vector spaces and its connection to matching subspaces in a field extension, and we prove the linear version of an intersection property result of certain subsets of a given set.
Cite
@article{arxiv.2107.09029,
title = {Conditions for matchability in groups and field extensions},
author = {Mohsen Aliabadi and Jack Kinseth and Christopher Kunz and Haris Serdarevic and Cole Wills},
journal= {arXiv preprint arXiv:2107.09029},
year = {2022}
}
Comments
Fixed minor typos & The paper is shortened. To appear in Linear and Multilinear Algebra