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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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On the construction of sets of mutually orthogonal Latin squares and the falsity of a conjecture of Euler
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by R. C. Bose and S. S. Shrikhande PDF
Trans. Amer. Math. Soc. 95 (1960), 191-209 Request permission
References
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  • R. C. Bose and S. S. Shrikhande, On the falsity of Euler’s conjecture about the non-existence of two orthogonal Latin squares of order $4t+2$, Proc. Nat. Acad. Sci. U.S.A. 45 (1959), 734–737. MR 104590, DOI 10.1073/pnas.45.5.734
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    • O. Eckenstein, Bibliography of Kirkman’s school girl problem, Messenger of Math. vol. 41 (1911-1912) pp. 33-36. L. Euler, Recherches sur une nouvelle espéce des quarres magiques, Verh. zeeuwsch Genoot. Wetenschappen vol. 9 (1782) pp. 85-239.
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    • H. F. MacNeish, Das problem der $36$ offiziere, Jber. Deutsch. Math. Verein. vol. 30 (1921) pp. 151-153.
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  • Henry B. Mann, The construction of orthogonal Latin squares, Ann. Math. Statistics 13 (1942), 418–423. MR 7736, DOI 10.1214/aoms/1177731539
    • E. T. Parker, Construction of some sets of pairwise orthogonal Latin squares, Abstract 553-67, Notices Amer. Math. Soc. vol. 5 (1958) p. 815. J. Peterson, Les $36$ officers, Ann. of Math. (1901-1902) pp. 413-427. P. Wernicke, Das problem der $36$ offiziere, Jber. Deutsch. Math. Verein. vol. 19 (1910) pp. 264-267. F. Yates, Incomplete randomized blocks, Ann. of Eugen. London vol. 7 (1936) pp. 121-140.
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Additional Information
  • © Copyright 1960 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 95 (1960), 191-209
  • MSC: Primary 05.00
  • DOI: https://doi.org/10.1090/S0002-9947-1960-0111695-3
  • MathSciNet review: 0111695