Thomas Karam

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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…

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 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