A note on matchings in abelian groups

TL;DR

This paper explores acyclic matchings in cyclic abelian groups, introducing weakly matched subsets and providing a constructive approach to understanding these matchings in the context of algebraic combinatorics.

Contribution

It offers a new constructive method for studying acyclic matchings in cyclic groups and introduces the concept of weakly matched subsets, expanding the theoretical framework.

Findings

Developed a constructive approach to acyclic matchings in cyclic groups

Introduced the notion of weakly matched subsets and analyzed their properties

Established relationships between weakly matched subsets and matchings in abelian groups

Abstract

The question of finding sets of monomials which are removable from a generic homogeneous polynomial through a linear change in its variables was raised by E. K. Wakeford in 1916. This linear algebra question motivated J. Losonczy to define the concept of acyclic matchings in Z n, and later in abelian groups. In this paper, we give a constructive approach to study the acyclic matchings in cyclic groups. We also introduce the notion of weakly matched subsets and investigate its relation with matchings in abelian groups.