Alexandr Grebennikov

activity

20222026

most citedA note on the concurrent normal conjecture

3 citations · 5 across the 9 of their papers we have counts for

collaborators

10 papers

math.CO2026

Optimal bound for the polynomial Littlewood-Offord problem

Alexandr Grebennikov

We present an exposition of an argument, discovered by GPT-6 Pro, that gives an optimal bound for the polynomial Littlewood-Offord problem. Namely, let $F$ be a degree- $d$ multilin…

math.CO2026

No- $(k + 1)$ -in-line problem for $k ⩾ 3$

Anubhab Ghosal, Ritesh Goenka, Alexandr Grebennikov +3

What is the maximum number of points one can place in an $n \times n$ grid such that every Euclidean line contains at most $k$ points? For $k = 2$ , this is the notorious no-three-i…

math.CO2025

Edge-statistics beyond $1/ e$

Alexandr Grebennikov, Matthew Kwan

For integers $k$ and $ℓ$ , let $ind (k, ℓ)$ be the maximum proportion of $k$ -vertex subsets of a large graph that induce exactly $ℓ$ edges. The edge-statistic…

math.CO2025

No- $(k + 1)$ -in-line problem for large constant $k$

Alexandr Grebennikov, Matthew Kwan

How many points can be placed in an $n \times n$ grid so that every (affine) line contains at most $k$ points? We prove that for $n ⩾ k ⩾ 1 0^{37}$ the maximum number…

math.CO2025

Geometric Littlewood-Offord problems via lattice point counting

Alexandr Grebennikov, Matthew Kwan

Consider nonzero vectors $a_{1}, \dots, a_{n} \in C^{k}$ , independent Rademacher random variables $ξ_{1}, \dots, ξ_{n}$ , and a set $S \subseteq C^{k}$ . What upper bounds…

math.CO2025

On almost Gallai colourings in complete graphs

Alexandr Grebennikov, Letícia Mattos, Tibor Szabó

For $t \in N$ , we say that a colouring of $E (K_{n})$ is $almost$ $t$ - $Gallai$ if no two rainbow $t$ -cliques share an edge. Motivated by a lemma of Berkowit…

math.CO2024★ 1 cited

$C_{10}$ has positive Turán density in the hypercube

Alexandr Grebennikov, João Pedro Marciano

The $n$ -dimensional hypercube $Q_{n}$ is a graph with vertex set ${0, 1}^{n}$ such that there is an edge between two vertices if and only if they differ in exactly one coordinate. For…

math.GT2023

Multiplicities in the length spectrum and growth rate of Salem numbers

Alexandr Grebennikov

We prove that mean multiplicities in the length spectrum of a non-compact arithmetic hyperbolic orbifold of dimension $n ⩾ 4$ have exponential growth rate $$ \langle g(L) \…

math.NT2022★ 1 cited

On the sequence $n! mod p$

A. Grebennikov, A. Sagdeev, A. Semchankau +1

We prove, that the sequence $1!, 2!, 3!, \dots$ produces at least $(2 + o (1)) p$ distinct residues modulo prime $p$ . Moreover, factorials on an interval $\mathcal{I} \…

math.MG2022★ 3 cited

A note on the concurrent normal conjecture

A. Grebennikov, G. Panina

It is conjectured since long that for any convex body $K \in R^{n}$ there exists a point in the interior of $K$ which belongs to at least $2 n$ normals from different points…

Optimal bound for the polynomial Littlewood-Offord problem

No-(k+1)-in-line problem for k⩾3

Edge-statistics beyond 1/e

No-(k+1)-in-line problem for large constant k

Geometric Littlewood-Offord problems via lattice point counting

On almost Gallai colourings in complete graphs

C10​ has positive Turán density in the hypercube

Multiplicities in the length spectrum and growth rate of Salem numbers

On the sequence n!modp

A note on the concurrent normal conjecture

No- $(k + 1)$ -in-line problem for $k ⩾ 3$

Edge-statistics beyond $1/ e$

No- $(k + 1)$ -in-line problem for large constant $k$

$C_{10}$ has positive Turán density in the hypercube

On the sequence $n! mod p$