activity
20232025
most citedCounting solutions to invariant equations in dense sets

2 citations · 2 across the 3 of their papers we have counts for

collaborators

3 papers

math.CO2025

Schur-like numbers and a lemma of Shearer

Tomasz Kosciuszko

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

math.NT2024

Sets with no solutions to some symmetric linear equations

Tomasz Kosciuszko

We expand the class of linear symmetric equations for which large sets with no non-trivial solutions are known. Our idea is based on first finding a small set with no solutions and…

math.NT2023★ 2 cited

Counting solutions to invariant equations in dense sets

Tomasz Kosciuszko

We prove a lower bound of exp(-C (log(2/alpha))^7)N^{k-1} to the number of solutions of an invariant equation in k variables, contained in a set of density alpha. Moreover, we give…