Thomas Karam

collaborators

4 papers

math.CO2024

The structure of sets with cube-avoiding sumsets

Thomas Karam, Peter Keevash

We prove that if $d \geq 2$ is an integer, $G$ is a finite abelian group, $Z_{0}$ is a subset of $G$ not contained in any strict coset in $G$ , and $E_{1}, \dots, E_{d}$ are dense subsets of…

cs.IT2024

On entropy Marton-type inequalities and small symmetric differences with cosets of abelian groups

Thomas Karam

We recognise that an entropy inequality akin to the main intermediate goal of recent works (Gowers, Green, Manners, Tao [3],[2]) regarding a conjecture of Marton provides a black b…

math.NT2024

On small densities defined without pseudorandomness

Thomas Karam

We identify an assumption on linear forms $ϕ_{1}, \dots, ϕ_{k} : F_{p}^{n} \to F_{p}$ that is much weaker than approximate joint equidistribution on the Boolean cube $\{0,1\…

math.CO2023

On the expressive power of mod- $p$ linear forms on the Boolean cube

Thomas Karam

Let $(A_{i})_{i \in [s]}$ be a sequence of dense subsets of the Boolean cube ${0, 1}^{n}$ and let $p$ be a prime. We show that if $s$ is assumed to be superpolynomial in $n$ …

The structure of sets with cube-avoiding sumsets

On entropy Marton-type inequalities and small symmetric differences with cosets of abelian groups

On small densities defined without pseudorandomness

On the expressive power of mod-p linear forms on the Boolean cube

On the expressive power of mod- $p$ linear forms on the Boolean cube