Alexandr Grebennikov

activity

20242026

collaborators

7 papers

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 $n \geq k \geq 1 0^{37}$ the maximum number of points i…

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 $I^¾_{1}, \dots, I^¾_{n}$ , and a set $S \subseteq C^{k}$ . What upper bound…

math.CO2025

On almost Gallai colourings in complete graphs

Alexandr Grebennikov, LetÃcia Mattos, Tibor SzabÃ³

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.CO2025

$C_{10}$ has positive TurÃ¡n density in the hypercube

Alexandr Grebennikov, JoÃ£o 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…

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 TurÃ¡n density in the hypercube

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 TurÃ¡n density in the hypercube