D. Krachun

activity

20162026

most citedRotational invariance in critical planar lattice models

10 citations · 13 across the 14 of their papers we have counts for

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4 papers · 1 filter

math.CO2026

Square-Difference-Free Sets beyond the Three-Quarter Barrier

Dmitry Krachun

Let $D (N)$ denote the largest cardinality of a subset of ${1, \dots, N}$ containing no nonzero square difference. While a construction certifying $D (N) \geq (1 - o (1)) N^{1/2}$ is alm…

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.CO2020

On the size of $A + λ A$ for algebraic $λ$

Dmitry Krachun, Fedor Petrov

For a finite set $A \subset R$ and real $λ$ , let $A + λ A := {a + λb : a, b \in A}$ . Combining a structural theorem of Freiman on sets with small doubling constants together wit…

Square-Difference-Free Sets beyond the Three-Quarter Barrier

Discrete Brunn-Minkowski Inequality for subsets of the cube

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

On the size of A+λA for algebraic λ

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

On the size of $A + λ A$ for algebraic $λ$