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…
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…
On partially matchable subspaces in a field extension
Mohsen Aliabadi, Jozsef Losonczy
We formulate and prove linear counterparts of results on partial matchings between finite subsets in abelian groups. The chosen setting is a field extension , where…
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…
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…