A. Kupavskii

activity

20172025

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35 papers · 1 filter

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

A complete $t$ -intersection theorem for families of spanning trees

Elizaveta Iarovikova, Andrey Kupavskii

Let $T_{n}$ denote the set of all labelled spanning trees of $K_{n}$ . A family $F \subset T_{n}$ is $t$ -intersecting if for all $A, B \in F$ the trees…

math.CO2025

The Erdős-Rado Sunflower Problem for Vector Spaces

Ferdinand Ihringer, Andrey Kupavskii

The famous Erdős-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,…

math.CO2025

The Hajnal--Rothschild problem

Peter Frankl, Andrey Kupavskii

For a family $F$ define $ν (F, t)$ as the largest $s$ for which there exist $A_{1}, \dots, A_{s} \in F$ such that for $i \neq = j$ we have $∣ A_{i} \cap A_{j} ∣ < t$ . Wha…

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…

math.CO2024

Linear dependencies, polynomial factors in the Duke--Erd\H os forbidden sunflower problem

Andrey Kupavskii, Fedor Noskov

We call a family of $s$ sets ${F_{1}, \dots, F_{s}}$ a \textit{sunflower with $s$ petals} if, for any distinct $i, j \in [s]$ , one has $F_{i} \cap F_{j} = \cap_{u = 1}^{s} F_{u}$ . The set $…

Non-dissective coverings by planks

A complete t-intersection theorem for families of spanning trees

The Erdős-Rado Sunflower Problem for Vector Spaces

The Hajnal--Rothschild problem

Intersecting Families of Spanning Trees

Linear dependencies, polynomial factors in the Duke--Erd\H os forbidden sunflower problem

A complete $t$ -intersection theorem for families of spanning trees