17 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…
Extremal Chowla sets and their linear analogues: A human-AI mathematical investigation using Co-Scientist
Mohsen Aliabadi, Keith Driscoll, Elliot Krop +3
We introduce an extremal invariant associated with Chowla-type order conditions in finite groups. A nonempty subset of a finite group is called a Chowla set if every elemen…
Odd-cycle defects in the Alon-Friedland bound
Mohsen Aliabadi, Elliot Krop
Let \(G\) be a finite simple graph. We study perfect matchings through two complementary viewpoints: reductions to bipartite permanent terms and the directed cycle covers counted b…
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…
An improved constant for Vizing's conjecture
Mohsen Aliabadi, Elliot Krop
For any graph , a subset dominates if . The minimum cardinality over all such is called the domination number, written . The c…
A nonabelian twist on differences of bijections
Mohsen Aliabadi
Hall's theorem on differences of bijections characterizes the multisets in a finite abelian group that can be written in the form $$ a_i=b_i-c_i, $…