18 papers · 1 filter
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…
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 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 $\diag(M)$ be its diagonal vector. It is known that \[ \diag(M)\in \Img(M). \] Thus the affine system $Mx=\diag(M)$ is alw…