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