main-content

## Swipe to navigate through the articles of this issue

01-06-2015 | Issue 3/2015

# The largest Erdős–Ko–Rado sets in $$2-(v,k,1)$$ designs

Journal:
Designs, Codes and Cryptography > Issue 3/2015
Author:
Maarten De Boeck
Important notes
Communicated by L. Teirlinck.

## Abstract

An Erdős–Ko–Rado set in a block design is a set of pairwise intersecting blocks. In this article we study Erdős–Ko–Rado sets in $$2\,-\,(v,k,1)$$ designs, Steiner systems. The Steiner triple systems and other special classes are treated separately. For $$k\ge 4$$, we prove that the largest Erdős–Ko–Rado sets cannot be larger than a point-pencil if $$r\ge k^{2}-3k+\frac{3}{4}\sqrt{k}+2$$ and that the largest Erdős–Ko–Rado sets are point-pencils if also $$r\ne k^{2}-k+1$$ and $$(r,k)\ne (8,4)$$. For unitals we also determine an upper bound on the size of the second-largest maximal Erdős–Ko–Rado sets.