James Aaronson

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20182020

most citedA counterexample to a strong variant of the Polynomial Freiman-Ruzsa conjecture

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

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math.CO2020

A note on transitive union-closed families

James Aaronson, David Ellis, Imre Leader

We show that the Union-Closed Conjecture holds for the union-closed family generated by the cyclic translates of any fixed set.

math.CO2020

Exact hyperplane covers for subsets of the hypercube

James Aaronson, Carla Groenland, Andrzej Grzesik +2

Alon and Füredi (1993) showed that the number of hyperplanes required to cover ${0, 1}^{n} ∖ {0}$ without covering $0$ is $n$ . We initiate the study of such exact hyperplan…

math.CO2019

Cyclically covering subspaces in $F_{2}^{n}$

James Aaronson, Carla Groenland, Tom Johnston

A subspace of $F_{2}^{n}$ is called cyclically covering if every vector in $F_{2}^{n}$ has a cyclic shift which is inside the subspace. Let $h_{2} (n)$ denote the largest po…

math.CO2019★ 1 cited

A counterexample to a strong variant of the Polynomial Freiman-Ruzsa conjecture

James Aaronson

Let $p$ be a prime. One formulation of the Polynomial Freiman-Ruzsa conjecture over $F_{p}$ can be stated as follows. If $ϕ : F_{p}^{n} \to F_{p}^{N}$ is a…

math.CO2018

Functions with large additive energy supported on a Hamming Sphere

James Aaronson

In this note, we prove that, among functions $f$ supported on a Hamming Sphere in $F_{2}^{n}$ with fixed $ℓ^{2}$ norm, the additive energy is maximised when $f$ is constant.…

A note on transitive union-closed families

Exact hyperplane covers for subsets of the hypercube

Cyclically covering subspaces in F2n​

A counterexample to a strong variant of the Polynomial Freiman-Ruzsa conjecture

Functions with large additive energy supported on a Hamming Sphere

Cyclically covering subspaces in $F_{2}^{n}$