11 citations · 19 across the 27 of their papers we have counts for
13 papers · 1 filter
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…