Latin Squares, Homologies and Eulerӳ Conjecture


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.

DOI Code: 10.1285/i15900932v29n1supplp115

Latin Squares; Orthomorphisms; Projective Planes

Full Text: PDF

Creative Commons License
This work is licensed under a Creative Commons Attribuzione - Non commerciale - Non opere derivate 3.0 Italia License.