B. Bukh

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20242026

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6 papers · 1 filter

math.CO2025

Covering large-dimensional Euclidean spaces by random translates of a given convex body

Boris Bukh, Jun Gao, Xizhi Liu +2

Determining the minimum density of a covering of $R^{n}$ by Euclidean unit balls as $n \to \infty$ is a major open problem, with the best known results being the lower bound…

math.CO2025

Most frequent subsequences in a word

Boris Bukh, Aleksandre Saatashvili

We prove that every $n$ -letter word over $k$ -letter alphabet contains some word as a subsequence in at least $k^{n /4 k (1 + o (1))}$ many ways, and that this is sharp as $k \to \infty$ . F…

math.CO2025

The Oddtown problem modulo a composite number

Boris Bukh, Ting-Wei Chao, Zeyu Zheng

A family of subsets $A$ of an $n$ -element set is called an $ℓ$ -Oddtown if the sizes of all sets are not divisible by $ℓ$ , but the sizes of pairwise intersections ar…

math.CO2025

Maximal sets of a given diameter in Hamming cubes

Boris Bukh, Aleksandre Saatashvili

A subset of the Hamming cube over $n$ -letter alphabet is said to be $d$ -maximal if its diameter is $d$ , and adding any point increases the diameter. Our main result shows that each…

math.CO2025

Convex polytopes in restricted point sets in $R^{d}$

Boris Bukh, Zichao Dong

For a finite point set $P \subset R^{d}$ , denote by $diam (P)$ the ratio of the largest to the smallest distances between pairs of points in $P$ . Let $c_{d, I^\pm} (n)$ be…

math.CO2025

Colouring random subgraphs

Boris Bukh, Michael Krivelevich, Bhargav Narayanan

We study several basic problems about colouring the $p$ -random subgraph $G_{p}$ of an arbitrary graph $G$ , focusing primarily on the chromatic number and colouring number of $G_{p}$ . I…

Covering large-dimensional Euclidean spaces by random translates of a given convex body

Most frequent subsequences in a word

The Oddtown problem modulo a composite number

Maximal sets of a given diameter in Hamming cubes

Convex polytopes in restricted point sets in Rd

Colouring random subgraphs

Convex polytopes in restricted point sets in $R^{d}$