5 papers
Matchings and product growth in modular abelian independence groups
Mohsen Aliabadi, Jozsef Losonczy
We unify two matching theories, one for finite subsets of groups and the other for finite-dimensional subspaces in a field extension. To achieve this, we study groups equipped with…
On partially matchable subspaces in a field extension
Mohsen Aliabadi, Jozsef Losonczy
We develop a theory of partial matchings between finite-dimensional subspaces in a field extension , providing structural, quantitative, and extremal results…
Structure and Decomposition of Deltoids in Abelian Groups
Mohsen Aliabadi, Jozsef Losonczy
Deltoids provide a natural framework for studying defective (partial) matchings in abelian groups, and we develop both structure and existence results in this setting. Given finite…
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…
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…