R. Berkowitz

activity

20162020

collaborators

Showing math.COShow all

5 papers · 1 filter

math.CO2019

Number of arithmetic progressions in dense random subsets of $Z / n Z$

Ross Berkowitz, Ashwin Sah, Mehtaab Sawhney

We examine the behavior of the number of $k$ -term arithmetic progressions in a random subset of $Z / n Z$ . We prove that if a set is chosen by including each element…

math.CO2019

Connected-Intersecting Families of Graphs

Aaron Berger, Ross Berkowitz, Pat Devlin +4

For a graph property $P$ and a common vertex set $V = {1, 2, \dots, n}$ , a family of graphs on $V$ is \emph{ $P$ -intersecting} iff $G \cap H$ satisfies $\math…

math.CO2018

A Local Limit Theorem for Cliques in G(n,p)

Ross Berkowitz

We prove a local limit theorem the number of $r$ -cliques in $G (n, p)$ for $p \in (0, 1)$ and $r \geq 3$ fixed constants. Our bounds hold in both the $ℓ^{\infty}$ and $ℓ^{1}$ metric. Th…

math.CO2018

Expected Chromatic Number of Random Subgraphs

Ross Berkowitz, Pat Devlin, Catherine Lee +2

Given a graph $G$ and $p \in [0, 1]$ , let $G_{p}$ denote the random subgraph of $G$ obtained by keeping each edge independently with probability $p$ . Alon, Krivelevich, and Sudokov pr…

math.CO2016

A stability result using the matrix norm to bound the permanent

Ross Berkowitz, Pat Devlin

We prove a stability version of a general result that bounds the permanent of a matrix in terms of its operator norm. More specifically, suppose $A$ is an $n \times n$ matrix over…