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math.CO2025
Decomposition theorems for unmatchable pairs in groups and field extensions
Mohsen Aliabadi, Jozsef Losonczy
A theory of matchings for finite subsets of an abelian group, introduced in connection with a conjecture of Wakeford on canonical forms for homogeneous polynomials, has since been…
math.CO2025
Matchings in Matroids over Abelian Groups, III
Mohsen Aliabadi, Elliot Krop
This paper develops matroidal analogues of classical results on matchings in abelian groups. By embedding matroid ground sets in an abelian group, we introduce base matchings betwe…
math.CO2025
Characterization of matchable sets and subspaces via Dyson transforms
Mohsen Aliabadi, Jozsef Losonczy
A \emph{matching} from a finite subset \( A \) of an abelian group \( G \) to another subset \( B \) is a bijection \( f : A \to B \) such that \( af(a) \notin A \) for all \( a \i…