B. Kuca

activity

20172021

most citedThe Unreasonable Rigidity of Ulam Sets

1 citations · 1 across the 1 of their papers we have counts for

collaborators

Showing math.NTShow all

4 papers · 1 filter

math.NT2021

Multidimensional polynomial Szemerédi theorem in finite fields for polynomials of distinct degrees

Borys Kuca

We obtain a polynomial upper bound in the finite-field version of the multidimensional polynomial Szemerédi theorem for distinct-degree polynomials. That is, if $P_{1}, ..., P_{t}$ are…

math.NT2019

Further bounds in the polynomial Szemerédi theorem over finite fields

Borys Kuca

We provide upper bounds for the size of subsets of finite fields lacking the polynomial progression $x, x + y, ..., x + (m - 1) y, x + y^{m}, ..., x + y^{m + k - 1} .$ These are the first known u…

math.NT2018

Structures in Additive Sequences

Borys Kuca

Consider the sequence $V (2, n)$ constructed in a greedy fashion by setting $a_{1} = 2$ , $a_{2} = n$ and defining $a_{m + 1}$ as the smallest integer larger than $a_{m}$ that can b…

math.NT2017★ 1 cited

The Unreasonable Rigidity of Ulam Sets

Joshua Hinman, Borys Kuca, Alexander Schlesinger +1

We give a number of results about families of Ulam sets. Generalizing behavior of Ulam sets U(1,n), we prove using an novel model theoretic approach that there is a rigidity phenom…