Dmitry Krachun

collaborators

3 papers

math.CO2024

Discrete Brunn-Minkowski Inequality for subsets of the cube

Lars Becker, Paata Ivanisvili, Dmitry Krachun +1

We show that for all $A, B \subseteq {0, 1, 2}^{d}$ we have $∣ A + B ∣ \geq (∣ A ∣∣ B ∣)^{l o g (5) / (2 l o g (3))} .$ We also show that for all finite $A, B \subset Z^{d}$ , and any $V…

math.CO2023

Tight lower bound on $∣ A + λ A ∣$ for algebraic integer $λ$

D. Krachun, F. Petrov

We prove an asymptotically tight lower bound on $∣ A + λ A ∣$ for $A \subset C$ and algebraic integer $λ$ . The proof combines strong version of Freiman's theorem, structural the…

math.CO2023

Strong greedoid structure of $r$ -removed $P$ -orderings

Dmitrii Krachun, Rozalina Mirgalimova

Inspired by the notion of \emph{ $r$ -removed $P$ -orderings} introduced in the setting of Dedekind domains by Bhargava \cite{Bha09-1} we study its generalization in the framework of…

Discrete Brunn-Minkowski Inequality for subsets of the cube

Tight lower bound on ∣A+λA∣ for algebraic integer λ

Strong greedoid structure of r-removed P-orderings

Tight lower bound on $∣ A + λ A ∣$ for algebraic integer $λ$

Strong greedoid structure of $r$ -removed $P$ -orderings