A. Kupavskii

activity

20132026

most citedDistance graphs with large chromatic number and arbitrary girth

15 citations · 149 across the 60 of their papers we have counts for

collaborators

Showing 2019Show all

6 papers · 1 filter

math.CO2019

Almost sharp bounds on the number of discrete chains in the plane

Nora Frankl, Andrey Kupavskii

The following generalisation of the Erdős unit distance problem was recently suggested by Palsson, Senger and Sheffer. Given $k$ positive real numbers $δ_{1}, \dots, δ_{k}$ , a $(k + 1)$ -tu…

math.MG2019

The right acute angles problem?

Andrey Kupavskii, Dmitriy Zakharov

The Danzer--Grünbaum acute angles problem asks for the largest size of a set of points in $R^{d}$ that determines only acute angles. Recently, the problem was essentially s…

math.CO2019

Nearly $k$ -distance sets

Nóra Frankl, Andrey Kupavskii

We say that a set of points $S \subset R^{d}$ is an $ε$ -nearly $k$ -distance set if there exist $1 \leq t_{1} \leq \dots \leq t_{k},$ such that the distance between any two d…

math.CO2019

Sharp results concerning disjoint cross-intersecting families

Peter Frankl, Andrey Kupavskii

For an $n$ -element set $X$ let $(k X)$ be the collection of all its $k$ -subsets. Two families of sets $A$ and $B$ are called cross-intersecting if $A\cap B…

math.CO2019

Beyond the Erdős Matching Conjecture

Peter Frankl, Andrey Kupavskii

A family $F \subset (k [ n ])$ is $U (s, q)$ of for any $F_{1}, \dots, F_{s} \in F$ we have $∣ F_{1} \cup \dots \cup F_{s} ∣ \leq q$ . This notion generalizes the property of a…

math.CO2019★ 12 cited

Simple juntas for shifted families

Peter Frankl, Andrey Kupavskii

We say that a family $F$ of $k$ -element sets is a {\it $j$ -junta} if there is a set $J$ of size $j$ such that, for any $F$ , its presence in $F$ depends on its int…

Almost sharp bounds on the number of discrete chains in the plane

The right acute angles problem?

Nearly k-distance sets

Sharp results concerning disjoint cross-intersecting families

Beyond the Erdős Matching Conjecture

Simple juntas for shifted families

Nearly $k$ -distance sets