An LP-based proof for the non-existence of a pair of orthogonal Latin squares of order 6

An LP-based proof for the non-existence of a pair of orthogonal Latin squares of order 6

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Article ID: iaor20051117
Country: Netherlands
Volume: 32
Issue: 4
Start Page Number: 336
End Page Number: 344
Publication Date: Jul 2004
Journal: Operations Research Letters
Authors: , ,
Keywords: Latin squares
Abstract:

This paper presents an alternative proof for the non-existence of orthogonal Latin squares of order 6. Our method is algebraic, rather than enumerative, and applies linear programming in order to obtain appropriate dual vectors. The proof is achieveable only after extending previously known results for symmetry elimination.

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