3 citations · 15 across the 35 of their papers we have counts for
10 papers · 1 filter
Generalized Arithmetic Kakeya
Cosmin Pohoata, Dmitrii Zakharov
Around the early 2000-s, Bourgain, Katz and Tao introduced an arithmetic approach to study Kakeya-type problems. They showed that the Euclidean Kakeya conjecture follows from a nat…
Color avoidance for monotone paths
Eion Mulrenin, Cosmin Pohoata, Dmitrii Zakharov
In 2014, Moshkovitz and Shapira determined the tower height for hypergraph Ramsey numbers of tight monotone paths. We address the color-avoiding version of this problem in which on…
Sharp bound for the Erdős-Straus non-averaging set problem
Huy Tuan Pham, Dmitrii Zakharov
A set of integers is non-averaging if there is no element in which can be written as an average of a subset of not containing . We show that the largest non-aver…
Ruzsa's problem on Bi-Sidon sets
János Pach, Dmitrii Zakharov
A subset of real numbers is called bi-Sidon if it is a Sidon set with respect to both addition and multiplication, i.e., if all pairwise sums and all pairwise products of eleme…
Lower bounds for incidences
Alex Cohen, Cosmin Pohoata, Dmitrii Zakharov
Let be a set of points in the unit square and let be a set of -tubes such that passes through . We prove a lower bound for the numbe…
On the minimal period of integer tilings
Izabella Łaba, Dmitrii Zakharov
If a finite set tiles the integers by translations, it also admits a tiling whose period has the same prime factors as . We prove that the minimal period of such a til…
An explicit economical additive basis
Vishesh Jain, Huy Tuan Pham, Mehtaab Sawhney +1
We present an explicit subset such that and for all , \[\lim_{N\to \infty}\frac{\big|\big\{(n_1,n_2):…
On sets of orthogonal exponentials on the disk
Dmitrii Zakharov
We show that if is a set of mutually orthogonal exponentials with respect to the unit disk then holds. This improv…
Most integers are not a sum of two palindromes
Dmitrii Zakharov
For , we show that the number of positive integers at most which can be written as sum of two base palindromes is at most . This answers a ques…
On skew corner-free sets
Cosmin Pohoata, Dmitrii Zakharov
We construct skew corner-free sets in of size , thereby disproving a conjecture of Kevin Pratt. We also show that any skew corner-free set in $\mathbb{F}_{q}^{n} \…