Ernie Croot

activity

19992026

most citedProgression-free sets in Z_4^n are exponentially small

94 citations · 124 across the 48 of their papers we have counts for

collaborators

Showing 2023Show all

3 papers · 1 filter

math.CO2023

On the image of convolutions along an arithmetic progression

Ernie Croot, Chi-Nuo Lee

We consider the question of determining the structure of the set of all $d$ -dimensional vectors of the form $N^{- 1} (1_{A} * 1_{- A} (x_{1}), ..., 1_{A} * 1_{- A} (x_{d}))$ for $A \subseteq \{1,...…

math.NT2023

Prime sum graphs and the induced trees they contain

Ernie Croot, Patrick Jin

In this paper we show that prime sum graphs on $n$ vertices -- which are graphs on vertex set ${1, 2, ..., n}$ where $ij$ is an edge when $i + j$ is prime -- contain all trees with at…

math.NT2023

Prime Graph and Its Structures

Ernest Croot, Patrick Jin

We study the basic properties of a prime sum graph, which is a simple graph defined on $N$ where two vertices are adjacent if and only if their sum is a prime number. Furth…