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Designs, Codes and Cryptography

, Volume 87, Issue 4, pp 717–744 | Cite as

An Erdős-Ko-Rado theorem for the group \(\hbox {PSU}(3, q)\)

  • Karen MeagherEmail author
Article
  • 56 Downloads
Part of the following topical collections:
  1. Special Issue: Finite Geometries

Abstract

In this paper we consider the derangement graph for the group \(\mathop {\text {PSU}}(3,q)\), where q is a prime power. We calculate all eigenvalues for this derangement graph and use the eigenvalues to prove that \(\mathop {\text {PSU}}(3,q)\), under its two-transitive action on a set of size \(q^3+1\), has the Erdős-Ko-Rado property and, provided that \(q\ne 2, 5\), another property that we call the Erdős-Ko-Rado module property.

Keywords

Derangement graph Independent sets Erdős-Ko-Rado theorem PSU(3, q) 

Mathematics Subject Classification

Primary 05C35 Secondary 05C69 20B05 

Notes

Acknowledgements

The author would like to thank the anonymous referees who checked this paper in detail and offered excellent suggests to improve it.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of ReginaReginaCanada

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