James Aaronson

activity

20162020

most citedExact hyperplane covers for subsets of the hypercube

5 citations · 16 across the 6 of their papers we have counts for

collaborators

7 papers

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★ 5 cited

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★ 1 cited

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★ 2 cited

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.…

math.CO2018★ 4 cited

Maximising the number of solutions to a linear equation in a set of integers

James Aaronson

Given a linear equation of the form $a_{1} x_{1} + a_{2} x_{2} + a_{3} x_{3} = 0$ with integer coefficients $a_{i}$ , we are interested in maximising the number of solutions to this equation in a se…

math.CO2016★ 3 cited

A connection between matchings and removal in abelian groups

James Aaronson

In a finite abelian group $G$ , define an additive matching to be a collection of triples $(x_{i}, y_{i}, z_{i})$ such that $x_{i} + y_{j} + z_{k} = 0$ if and only if $i = j = k$ . In the case t…

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

Maximising the number of solutions to a linear equation in a set of integers

A connection between matchings and removal in abelian groups

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