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01.06.2015 | Ausgabe 3/2015

Designs, Codes and Cryptography 3/2015

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

Zeitschrift:
Designs, Codes and Cryptography > Ausgabe 3/2015
Autor:
Maarten De Boeck
Wichtige Hinweise
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.

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