V. Lev

collaborators

3 papers

math.NT2025

On the density of Kravitz sets

Vsevolod Lev, MÃ¡tÃ© Matolcsi, PÃ©ter PÃ¡l Pach +1

We show that for a subset $A$ of the cyclic group of prime order $p > 3$ , if the sumset $A + A - 2 A$ is not the whole group, then $∣ A ∣ \leq \frac{2}{7} p$ . Besides combinatorial arguments, we…

math.CO2024

Past and future of the cap set problem

Ernie Croot, Vsevolod F. Lev, PÃ©ter PÃ¡l Pach

We survey the history of the capset problem in the context of related results on progression-free sets, discuss recent progress, and mention further directions to explore.

math.GR2024

Quotient sets in nonabelian groups

Vsevolod F. Lev

We show that for a finite, nonempty subset $A$ of a group, the quotient set $A^{- 1} A := {a_{1}^{- 1} a_{2} : a_{1}, a_{2} \in A}$ has size $∣ A^{- 1} A ∣ \geq \frac{5}{3} ∣ A ∣$ , unless $A$ is densely…