Alexandr Grebennikov

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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.CO2021

On the palindromic Hosoya polynomial of trees

Dmitry Badulin, Alexandr Grebennikov, Konstantin Vorob'ev

A graph $G$ on $n$ vertices of diameter $D$ is called $H$ -palindromic if $α (G, k) = α (G, D - k)$ for all $k = 0, 1, \dots, ⌊ \frac{D}{2} ⌋$ , where $α (G, k)$ is th…