2 citations · 3 across the 6 of their papers we have counts for
6 papers
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…
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…
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} \…
A new upper bound for the Heilbronn triangle problem
Alex Cohen, Cosmin Pohoata, Dmitrii Zakharov
For sufficiently large , we show that in every configuration of points chosen inside the unit square there exists a triangle of area less than . This improv…
On the Erdős--Ginzburg--Ziv Problem in large dimension
Lisa Sauermann, Dmitrii Zakharov
The Erdős--Ginzburg--Ziv Problem is a classical extremal problem in discrete geometry. Given and , the problem asks about the smallest number such that among any poi…
Convex polytopes from fewer points
Cosmin Pohoata, Dmitrii Zakharov
Let be the smallest integer such that any set of points in in general position contains points in convex position. In 1960, Erdős and S…