11 citations · 19 across the 27 of their papers we have counts for
33 papers
Extremal subspace covers in finite vector spaces
Mohsen Aliabadi
Let be an -dimensional vector space over the finite field , where . It is classical that proper subspaces are necessary and sufficient to cover $V…
A counterexample to the Chung-Graham-Spiro gap-set conjecture
Mohsen Aliabadi
Chung, Graham, and Spiro introduced slow Fibonacci walks and used them to partition the integers into two sequences, the down-integers and the up-integers. They studied the…
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…
Higher-power inverse functional identities and Frobenius collision obstructions
Mohsen Aliabadi
Let be a division ring, let , and let be additive maps satisfying for every nonzero . We establish general vanishing…
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…
A Bound for Vizing's Conjecture
Mohsen Aliabadi, Elliot Krop
Vizing's conjecture, dating back to 1963, asserts that \[ γ(G\mathbin{\square}H) \geq γ(G)γ(H) \] for all finite graphs and , where denotes the domination number and $\s…
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, $…
A counterexample to a basis conjecture of Brualdi, Friedland, and Pothen
Mohsen Aliabadi
Brualdi, Friedland, and Pothen studied sparse bases of row spaces and proposed a rank-intersection criterion for elementary row-space vectors of sparse generic matrices. We give a…
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…
Diagonal parity and loop toggling for symmetric matrices over
Mohsen Aliabadi
Let be a symmetric matrix over , and let be its diagonal vector. It is known that . Thus t…
Paving matroids that are not sparse paving
Mohsen Aliabadi
The Mayhew--Newman--Welsh--Whittle conjecture predicts that asymptotically almost all matroids are sparse paving. We study the gap between paving and sparse paving matroids at the…
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…
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…
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…
Matchings in matroids over abelian groups, II
Mohsen Aliabadi, Yujia Wu, Sophia Yermolenko
The concept of matchings originated in group theory to address a linear algebra problem related to canonical forms for symmetric tensors. In an abelian group , a matching is…
The weak acyclic matching property in abelian groups
Mohsen Aliabadi, Peter Taylor
A matching from a finite subset to another subset is a bijection with the property that never lies in $…
Classifying abelian groups through acyclic matchings
Mohsen Aliabadi, Peter Taylor
The inquiry into identifying sets of monomials that can be eliminated from a generic homogeneous polynomial via a linear change of coordinates was initiated by E. K. Wakeford. This…
Conditions for matchability in groups and field extensions II
Mohsen Aliabadi
We present sufficient conditions for the existence of matchings in abelian groups and their linear counterparts. These conditions lead to extensions of existing results in matching…
Matchings in matroids over abelian groups
Mohsen Aliabadi, Shira Zerbib
We formulate and prove matroid analogues of results concerning matchings in groups. A matching in an abelian group is a bijection between two finite subsets $A,B…
Conditions for matchability in groups and field extensions
Mohsen Aliabadi, Jack Kinseth, Christopher Kunz +2
The origins of the notion of matchings in groups spawn from a linear algebra problem proposed by E. K. Wakeford [24] which was tackled in 1996 [10]. In this paper, we first discuss…
Results and questions on matchings in groups and vector subspaces of fields
Mohsen Aliabadi, Khashayar Filom
A matching from a finite subset of an abelian group to another subset is a bijection with the property that never lies in . A matching is cal…
On the complexity of finding tensor ranks
Mohsen Aliabadi, Shmuel Friedland
The purpose of this note is to give a linear algebra algorithm to find out if a rank of a given tensor over a field $\F$ is at most over the algebraic closure of $\F$, where $k…