Andrey Kupavskii

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20242026

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10 papers · 1 filter

math.CO2026

A Complete Intersection Theorem for Large Permutation Groups

Nathan Keller, Andrey Kupavskii, Noam Lifshitz +1

A family of permutations is called $t$ -intersecting if any two permutations in the family agree on at least $t$ elements. We prove that there exists $n_{0} \in N$ such that…

math.CO2026

Structure and properties of large cross-intersecting families

Yang Huang, Andrey Kupavskii

The study of intersecting families, initiated by Erdős, Ko, and Rado, is a central topic in extremal combinatorics. A classical stability result of Hilton and Milner determines the…

math.CO2026

Matchings in permutations

Eduard Inozemtsev, Dmitrii Kolupaev, Andrey Kupavskii

We say that two permutations $[n] \to [n]$ intersect if they map some element $x$ to the same element $y$ . A matching in a family of permutations is a collection of pairwise disjoin…

math.CO2026

More on the Erd\H os--Kleitman problem on matchings in set families

Andrey Kupavskii, Georgy Sokolov

Let $e (n, s)$ denote the maximum size of a family $F$ of subsets of an $n$ -element set that contains no $s$ pairwise disjoint members. In 1968, answering a question of Erd…

math.CO2026

Structure of $t$ -Intersecting Families of Vector Spaces

Ferdinand Ihringer, Andrey Kupavskii

We study $t$ -intersecting and $t$ -cross-intersecting families of $k$ -dimensional subspaces in finite vector spaces of dimension $n$ . We show that all large $t$ -intersecting familie…

math.CO2026

Families without $s$ -matchings: the other end

Andrey Kupavskii, Georgy Sokolov

In this paper, we determine the largest family $F \subset 2^{[n]}$ without $s$ pairwise disjoint sets, provided $n = m s + c$ for positive integers $m, c$ , and $s \geq s_0(m, c)…

math.CO2026

Frankl's diversity theorem for permutations

Eduard Inozemtsev, Andrey Kupavskii

In 1987, Frankl proved an influential stability result for the Erd\H os--Ko--Rado theorem, which bounds the size of an intersecting family in terms of its distance from the nearest…

math.CO2024

Structure of non-trivial intersecting families

Andrey Kupavskii

We say that a family of $k$ -subsets of an $n$ -element set is {\it intersecting}, if any two of its sets intersect. In this paper, we study the structure of large intersecting famil…

math.CO2024

An almost complete $t$ -intersection theorem for permutations

Andrey Kupavskii

For any $ε > 0$ and $n > (1 + ε) t$ , $n > n_{0} (ε)$ we determine the size of the largest $t$ -intersecting family of permutations, as well as give a sharp stability result. This resolves a con…

math.CO2024

Intersecting families with covering number $3$

Andrey Kupavskii

A covering number of a family is the size of the smallest set that intersects all sets from the family. In 1978 Frankl determined for $n \geq n_{0} (k)$ the largest intersecting family…

A Complete Intersection Theorem for Large Permutation Groups

Structure and properties of large cross-intersecting families

Matchings in permutations

More on the Erd\H os--Kleitman problem on matchings in set families

Structure of t-Intersecting Families of Vector Spaces

Families without s-matchings: the other end

Frankl's diversity theorem for permutations

Structure of non-trivial intersecting families

An almost complete t-intersection theorem for permutations

Intersecting families with covering number 3

Structure of $t$ -Intersecting Families of Vector Spaces

Families without $s$ -matchings: the other end

An almost complete $t$ -intersection theorem for permutations

Intersecting families with covering number $3$