V. Lev

activity

20052025

most citedProgression-free sets in Z_4^n are exponentially small

94 citations · 124 across the 35 of their papers we have counts for

collaborators

42 papers

math.NT2025

On the density of Kravitz sets

Vsevolod Lev, Máté Matolcsi, Péter Pál 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, Péter Pál 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…

math.NT2023

Sum-free sets in $Z_{5}^{n}$

Vsevolod F. Lev

It is well-known that for a prime $p \equiv 2 (mod 3)$ and integer $n \geq 1$ , the maximum possible size of a sum-free subset of the elementary abelian group $Z_{p}^{n}$ is $\frac1…

math.NT2023

Towards $3 n - 4$ in groups of prime order

Vsevolod F. Lev, Oriol Serra

We show that if $A$ is a subset of a group of prime order $p$ such that $∣2 A ∣ < 2.7652∣ A ∣$ and $∣ A ∣ < 1.25 \cdot 1 0^{- 6} p$ , then $A$ is contained in an arithmetic progression with at mos…

math.NT2022

A nonlinear bound for the number of subsequence sums

Vsevolod F. Lev

We show that a finite zero-sum-free sequence $α$ over an abelian group has at least $c ∣ α ∣^{4/3}$ distinct subsequence sums, unless $α$ is "controlled" by a small number of its term…

On the density of Kravitz sets

Past and future of the cap set problem

Quotient sets in nonabelian groups

Sum-free sets in Z5n​

Towards 3n−4 in groups of prime order

A nonlinear bound for the number of subsequence sums

Sum-free sets in $Z_{5}^{n}$

Towards $3 n - 4$ in groups of prime order