On local matchability in groups and vector spaces

TL;DR

This paper introduces the concept of local matchability in groups and vector spaces, providing new proofs and extending the idea to linear algebra using tools from additive number theory, combinatorics, and algebra.

Contribution

It defines locally matchable subsets in groups and their linear analogues, offering alternative proofs and expanding the theory with interdisciplinary mathematical tools.

Findings

Introduction of local matchability in groups and vector spaces

Linear analogue of local matchability in field extensions

New proofs for existing matching theory results

Abstract

In this paper, we define locally matchable subsets of a group which is extracted from the concept of matchings in groups and used as a tool to give alternative proofs for existing results in matching theory. We also give the linear analogue of locally matchability for subspaces in a field extension. Our tools mix additive number theory, combinatorics and algebra