Tomasz Kosciuszko

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20232025

most citedCounting solutions to invariant equations in dense sets

2 citations · 2 across the 4 of their papers we have counts for

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math.CO2025

Schur-like numbers and a lemma of Shearer

Tomasz Kosciuszko

Suppose that each number $1, 2, ..., N$ has one of n colours assigned. We show that if there are no monochromatic solutions to the equation $x_{1} + x_{2} + x_{3} = y_{1} + y_{2}$ , then $N=O((n!)^{1/2}…

math.CO2023

New bounds in the Bogolyubov-Ruzsa lemma

Tomasz Kosciuszko, Tomasz Schoen

We establish new bounds in the Bogolyubov-Ruzsa lemma, demonstrating that if A is a subset of a finite abelian group with density alpha, then 3A-3A contains a Bohr set of rank O(lo…