2024/04/01 by Mohsen Aliabadi, Peter J. Taylor, Aliabadi, Mohsen +1 · 1 citation
Mathematics · #Finite Group Theory Research #advanced mathematical theories #Geometric and Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2404.02178
A matching from a finite subset A⊂ℤn to another subset B⊂ℤn is a bijection f : A → B with the property that a+f(a) never lies in A. A matching is called acyclic if it is uniquely determined by its multiplicity function. Alon et al. established the acyclic matching property for ℤn, which was later extended to all abelian torsion-free groups. In a prior work, the authors of this paper settled the acyclic matching property for all abelian groups. The objective of this note is to explore a related concept, known as the weak acyclic matching property, within the context of abelian groups.