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math.CO2025
A Study of the Binary and Boolean Rank of Matrices with Small Constant Real Rank
Michal Parnas, Adi Shraibman
We initiate the study of the binary and Boolean rank of matrices that have a small rank over the reals. The relationship between these three rank functions is an important op…
math.CO2024
The Rank-Ramsey Problem and the Log-Rank Conjecture
Gal Beniamini, Nati Linial, Adi Shraibman
A graph is called Rank-Ramsey if (i) Its clique number is small, and (ii) The adjacency matrix of its complement has small rank. We initiate a systematic study of such graphs. Our…