A. Kupavskii

activity

20242026

collaborators

11 papers

cs.CC2026

Hyperplanes Avoiding Problem and Integer Points Counting in Polyhedra

Grigorii Dakhno, Dmitry Gribanov, Nikita Kasianov +4

In our work, we consider the problem of computing a vector $x \in Z^{n}$ of minimum $∥ \cdot ∥_{p}$ -norm such that $a^{⊤} x \neq = a_{0}$ , for any vector $(a, a_{0})$ from a given subset of…

math.CO2026

Cutting corners

Andrey Kupavskii, Arsenii Sagdeev, Dmitrii Zakharov

We say that a subset $M$ of $R^{n}$ is exponentially Ramsey if there are $I^µ > 0$ and $n_{0}$ such that $I ¨ (R^{n}, M) \geq (1 + I^µ)^{n}$ for any $n > n_{0}$ , where $I ¨ (R^{n}, M)$ …

math.CO2025

Non-dissective coverings by planks

Andrey Kupavskii, Janos Pach

A plank is the part of space between two parallel planes. The following open problem, posed 45 years ago, can be viwed as the converse of Tarski's plank problem (Bang's theorem): I…

math.CO2025

The ErdÅs-Rado Sunflower Problem for Vector Spaces

Ferdinand Ihringer, Andrey Kupavskii

The famous ErdÅs-Rado sunflower conjecture suggests that an $s$ -sun\-flower-free family of $k$ -element sets has size at most $(C s)^{k}$ for some absolute constant $C$ . In this note,…

cs.CG2025

Tree covers of size $2$ for the Euclidean plane

Artur Bikeev, Andrey Kupavskii, Maxim Turevskii

For a given metric space $(P, I ¨ )$ , a tree cover of stretch $t$ is a collection of trees on $P$ such that edges $(x, y)$ of trees receive length $I ¨ (x, y)$ , and such that for any pair…

math.CO2025

Intersecting Families of Spanning Trees

Peter Frankl, Glenn Hurlbert, Ferdinand Ihringer +4

A family $F$ of spanning trees of the complete graph on $n$ vertices $K_{n}$ is \emph{ $t$ -intersecting} if any two members have a forest on $t$ edges in common. We prove an…

Hyperplanes Avoiding Problem and Integer Points Counting in Polyhedra

Cutting corners

Non-dissective coverings by planks

The ErdÅs-Rado Sunflower Problem for Vector Spaces

Tree covers of size 2 for the Euclidean plane

Intersecting Families of Spanning Trees

The ErdÅs-Rado Sunflower Problem for Vector Spaces

Tree covers of size $2$ for the Euclidean plane