11 papers
A Complete Intersection Theorem for Large Permutation Groups
Nathan Keller, Andrey Kupavskii, Noam Lifshitz +1
A family of permutations is called -intersecting if any two permutations in the family agree on at least elements. We prove that there exists such that…
Structure and properties of large cross-intersecting families
Yang Huang, Andrey Kupavskii
The study of intersecting families, initiated by ErdÅs, Ko, and Rado, is a central topic in extremal combinatorics. A classical stability result of Hilton and Milner determines th…
Near-optimal edge partitioning via intersecting families
Alexander Yakunin, Andrey Kupavskii, Alexander Sushin +1
We study the problem of edge partitioning, where the goal is to partition the edge set of a graph into parts. The replication factor of a vertex is the number of parts that…
Matchings in permutations
Eduard Inozemtsev, Dmitrii Kolupaev, Andrey Kupavskii
We say that two permutations intersect if they map some element to the same element . A matching in a family of permutations is a collection of pairwise disjoin…
More on the Erd\H os--Kleitman problem on matchings in set families
Andrey Kupavskii, Georgy Sokolov
Let denote the maximum size of a family of subsets of an -element set that contains no pairwise disjoint members. In 1968, answering a question of Erd…
Structure of -Intersecting Families of Vector Spaces
Ferdinand Ihringer, Andrey Kupavskii
We study -intersecting and -cross-intersecting families of -dimensional subspaces in finite vector spaces of dimension . We show that all large -intersecting familie…