Michal Parnas

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20172026

most citedOn maximal isolation sets in the uniform intersection matrix

1 citations · 1 across the 7 of their papers we have counts for

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math.CO2026

On the Binary Rank of Matrices with Constant Real Rank

Michal Parnas

We study the problem of determining upper bounds on the maximal binary rank, $b_{d}$ , of a $0, 1$ matrix with real rank $d$ , for small constant $d$ . We prove a general upper bound of…

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 $0, 1$ matrices that have a small rank over the reals. The relationship between these three rank functions is an important op…

math.CO2022

The Binary Rank of Circulant Block Matrices

Ishay Haviv, Michal Parnas

The binary rank of a $0, 1$ matrix is the smallest size of a partition of its ones into monochromatic combinatorial rectangles. A matrix $M$ is called $(k_1, \ldots, k_m ; n_1, \ldo…

math.CO2022

On the Binary and Boolean Rank of Regular Matrices

Ishay Haviv, Michal Parnas

A $0, 1$ matrix is said to be regular if all of its rows and columns have the same number of ones. We prove that for infinitely many integers $k$ , there exists a square regular $0,1…

math.CO2021

Upper Bounds on the Boolean Rank of Kronecker Products

Ishay Haviv, Michal Parnas

The Boolean rank of a $0, 1$ -matrix $A$ , denoted $R_{B} (A)$ , is the smallest number of monochromatic combinatorial rectangles needed to cover the $1$ -entries of $A$ . In 1988,…

math.CO2020

Circulant almost cross intersecting families

Michal Parnas

Let $F$ and $G$ be two $t$ -uniform families of subsets over $[k] = {1, 2, ..., k}$ , where $∣ F ∣ = ∣ G ∣$ , and let $C$ be the adjacency matrix of…

math.CO2019★ 1 cited

On maximal isolation sets in the uniform intersection matrix

Michal Parnas, Adi Shraibman

Let $A_{k, t}$ be the matrix that represents the adjacency matrix of the intersection bipartite graph of all subsets of size $t$ of ${1, 2, ..., k}$ . We give constructions of large i…