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

Authors:
G. Appa;D. Magos;I. Mourtos
Affiliations:
Operational Research Department, London School of Economics, Houghton Street, London WC2A 2AE, UK;Department of Informatics, Technological Educational Institute of Athens, Ag. Spyridonos Str., 122 10 Egaleo, Greece;Operational Research Department, London School of Economics, Houghton Street, London WC2A 2AE, UK
Venue:
Operations Research Letters
Year:
2004

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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 achievable only after extending previously known results for symmetry elimination.