Subscribe by RSS

Graduate Seminar Series

Mon., Feb. 13, 2023 3:30 p.m.

Location: CK 185 and Live Stream

Speaker: Rachel Evans

Title: Maximal intersecting families in block graphs of 2-( n, k, 1) designs are typically trivial (99 kB)

Abstract:

The famous theorem by Erdös, Ko and Rado proves that the largest intersecting family for any system of k-sets from a base set of size n is n−1 choose k−1. The only way to construct such a family is trivially, meaning that every k-set in the clique contains a common element.

The goal of my research is to show that almost all maximal intersecting families in a design are trivial. This seminar will cover a proposed proof outline in the following way: discuss a potential bound on the size of a minimal generating set for a maximal intersecting family in a design, provide a bound for the total number of maximal intersecting families, and use a counting argument to conclude that almost all maximal intersecting families in a design are trivially constructed.

Live Stream: