Research-The structure of large non-t rivial t-intersecting families for finite sets and vector spaces

Research

Algebra & Combinatorics Seminar

The structure of large non-t rivial t-intersecting families for finite sets and vector spaces

Speaker: Benjian Lv (Beijing Normal University)
Time: Nov 5, 2020, 16:00-17:00
Location: Tencent Meeting ID 379 344 430

Abstract

Let ℱ be a family of k -subsets of an n-set. The family ℱ is said to be t -intersecting if the size of the intersection of any two subsets in ℱ is not less than t. A t-intersecting family ℱ is said to be trivial if ℱ consists of subsets which contain a fixed t-subset of the n-set. The Erdős-Ko-Rado theorem describes the size and structure of a maximum t-intersecting family, and the Hilton-Milner theorem describes the size and structure of a maximum non-trivial 1-intersecting family. In this talk, we show some results about the structure of maximal non-trivial t-intersecting families with large size for finite sets and vector spaces.