Extremal Set Theory

Eötvös Loránd Tudományegyetem

Matematika Doktori Iskola

Katona Gyula

matematika- és számítástudományok

The typical problem in the theory is to find the largest family of subsets of an n-element set under certain conditions. The Erdős-Ko-Rado theorem determines this maximum if the family consists of k-element sets and any two sets intersect. Sperner''s theorem claims that if the family contains no pair in inclusion then we cannot have more sets than the family consisting of all n/2-element sets. But it is still unknown, even asymptotically, what the maximal size of a family is if it contains no 4 (distinct) sets A, B, C, D such that C is the intersection of A and B, D is their union. These types of problems, jointly determined with the student, will be studied and solved.

2 fő

Eötvös Loránd University Department of Computer science and Rényi Institute

2026-05-31

English

General knowledge in combinatorics.