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On KM-arcs in non-Desarguesian projective planes

  • Peter VandendriesscheEmail author
Article
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Abstract

In this paper we investigate KM-arcs in non-Desarguesian projective planes. We provide a construction of a KM-arc in every Hall plane of even order, and we classify all KM-arcs in the known projective planes of order 16. In particular, we find several examples of KM-arcs with non-concurrent t-secants, showing that the famous result on their concurrency does not holds in non-Desarguesian planes.

Keywords

Non-Desarguesian projective plane KM-arcs \((q+t, t)\)-arcs of type \((0, 2, t)\) 

Mathematics Subject Classification

51E20 51E21 

Notes

Acknowledgements

The author would like to thank Aart Blokhuis and Francesco Pavese for their suggestion to look at substructures in the Hall plane specifically.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Ghent UniversityGentBelgium

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