O. Roche-Newton

activity

20112023

most citedA short proof of a near-optimal cardinality estimate for the product of a sum set

11 citations · 15 across the 7 of their papers we have counts for

collaborators

19 papers

math.MG2023★ 1 cited

Convexity, Elementary Methods, and Distances

Oliver Roche-Newton, Dmitrii Zhelezov

This paper considers an extremal version of the Erdős distinct distances problem. For a point set $P \subset R^{d}$ , let $Δ (P)$ denote the set of all Euclidean distances dete…

math.CO2022

Counting arcs in $F_{q}^{2}$

Krishnendu Bhowmick, Oliver Roche-Newton

An arc in $F_{q}^{2}$ is a set $P \subset F_{q}^{2}$ such that no three points of $P$ are collinear. We use the method of hypergraph containers to prove several counting re…

math.CO2021★ 1 cited

Convexity, Superquadratic Growth, and Dot Products

Brandon Hanson, Oliver Roche-Newton, Steven Senger

Let $P \subset R^{2}$ be a point set with cardinality $N$ . We give an improved bound for the number of dot products determined by $P$ , proving that, \[ |\{ p \cdot q :p,q \in…

math.CO2021

Additive and multiplicative Sidon sets

Oliver Roche-Newton, Audie Warren

We give a construction of a set $A \subset N$ such that any subset $A^{'} \subset A$ with $∣ A^{'} ∣ ≫ ∣ A ∣^{2/3}$ is neither an additive nor multiplicative Sidon set. In doing so…

math.CO2020

The Elekes-Szabó Problem and the Uniformity Conjecture

Mehdi Makhul, Oliver Roche-Newton, Sophie Stevens +1

In this paper we give a conditional improvement to the Elekes-Szabó problem over the rationals, assuming the Uniformity Conjecture. Our main result states that for $F\in \mathbb{Q}…

math.CO2020

Sums, products and dilates on sparse graphs

Oliver Roche-Newton

Let $A \subset R$ and $G \subset A \times A$ . We prove that, for any $λ \in R ∖ {- 1, 0, 1}$ , \[ \max \{|A+_G A|, |A+_G λA|, |A\cdot_G A|\} \gg |G|^{6/11}. \]