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Some comments on Latin squares and on Graeco-Latin squares, illustrated with postage stamps and old playing cards. (English) Zbl 1247.05004

Summary: We present some comments on Latin squares and on Graeco-Latin squares, with special emphasis on their use in statistics and in a historical context. We also comment on the Knut Vik square, the knight’s move design and the knight’s tour, as well as the Magic Card Puzzle. We consider the well-known 36 officers problem studied by L. Euler [“Recherches sur une nouvelle espéce de quarrés magiques,” Verh. Zeeuwsch Genoot. Wet. Vlissing. 9, 85–239 (1782)], and give two examples of diagonal Latin squares of order 6 due, respectively, to Abbé François-Guillaume Poignard ([F.-G. Poignard, “Traité des quarrés sublimes contenant des méthodes générales, toutes nouvelles et faciles, pour faire les sept quarrés planétaires et tous autres á l’infini par des nombres, en toutes sortes de progressions,” Fricx, Bruxelles (1704)] and J. Dénes (from a lecture at the University of Surrey in 1970, see [J. Dénes and A. D. Keedwell, Latin squares and their applications. (Budapest: Akademiai Kiado) (1974; Zbl 0283.05014)]). We illustrate our comments with images of postage stamps and old playing cards. An extensive annotated bibliography ends the paper.

MSC:

05-03 History of combinatorics
05B10 Combinatorial aspects of difference sets (number-theoretic, group-theoretic, etc.)
01A45 History of mathematics in the 17th century
01A50 History of mathematics in the 18th century
05B15 Orthogonal arrays, Latin squares, Room squares
62K05 Optimal statistical designs
62K10 Statistical block designs
62K15 Factorial statistical designs

Citations:

Zbl 0283.05014
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Full Text: DOI

References:

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