Latin Squares, Homologies and Eulerӳ Conjecture

Authors

  • Christoph Hering
  • Andreas Krebs

DOI:

https://doi.org/10.1285/i15900932v29n1supplp115

Keywords:

Latin Squares, Orthomorphisms, Projective Planes

Abstract

We construct pairs of orthogonal Latin Squares of order $n$ by means of suitable orthomorphisms of the cyclic group of order $n-1$. These pairs always have $n-3$ confluent common transversals. They lead to partial planes of order $n$ with $5n-2$ lines and $5$ complete points. Also, we provide an easy construction of counter examples to Euler's conjecture.

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Published

20-10-2010

Issue

Volume 29, suppl. 1 (2009)

Section

Articoli

License

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http://creativecommons.org/licenses/by-nc-nd/3.0/it/legalcode