Séminaire Lotharingien de Combinatoire, B91b (2025), 6 pp.
The Weak Acyclic Matching Property in Abelian Groups
Mohsen Aliabadi and Peter Taylor
Abstract.
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.
Received: May 7, 2024.
Accepted: August 4, 2025.
Final Version: August 6, 2025.
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