Abstract
Some of the oldest combinatorial objects, whose study apparently goes back to ancient times, are the Latin squares. To obtain a Latin square, one has to fill the n 2 cells of an (n × n)-square array with the numbers 1, 2, ... , n so that that every number appears exactly once in every row and in every column. In other words, the rows and columns each represent permutations of the set {1, ... , n}. Let us call n the order of the Latin square.
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References
T. Evans: Embedding incomplete Latin squares, Amer. Math. Monthly 67 (1960), 958–961.
C. C. Lindner: On completing Latin rectangles, Canadian Math. Bull. 13 (1970), 65–68.
H. J. Ryser: A combinatorial theorem with an application to Latin rectangles, Proc. Amer. Math. Soc. 2 (1951), 550–552.
B. Smetaniuk: A new construction on Latin squares 1: A proof of the Evans conjecture, Ars Combinatoria 11 (1981), 155–172.
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© 1998 Springer-Verlag Berlin Heidelberg
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Aigner, M., Ziegler, G.M. (1998). Completing Latin squares. In: Proofs from THE BOOK. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-22343-7_23
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DOI: https://doi.org/10.1007/978-3-662-22343-7_23
Publisher Name: Springer, Berlin, Heidelberg
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