Abstract
An intercalate in a Latin square is a subsquare of order 2; I(n) denotes the maximum number of intercalates in any Latin square of order n.
Upper bounds for I(n) are found, and it is shown that they are attained if and only if n=2α or 2α-1. A number of lower bounds are found for I(n).
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References
P. Dembowski, Finite Geometries (Springer-Verlag, New York, 1968).
J. Dénes and A.D. Keedwell, Latin Squares and Their Applications (Akadémiai Kiadó, Budapest, 1974).
H.W. Norton, The 7×7 squares. Ann. Eugenics 9 (1939), 269–307.
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© 1981 Springer-Verlag
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Heinrich, K., Wallis, W.D. (1981). The maximum number of intercalates in a latin square. In: McAvaney, K.L. (eds) Combinatorial Mathematics VIII. Lecture Notes in Mathematics, vol 884. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0091822
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DOI: https://doi.org/10.1007/BFb0091822
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