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
- Trans. Amer. Math. Soc. 95 (1960), 191-209
- DOI: https://doi.org/10.1090/S0002-9947-1960-0111695-3
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References
- W. W. Rouse Ball, Mathematical Recreations and Essays, The Macmillan Company, New York, 1947. Revised by H. S. M. Coxeter. MR 0019629
- R. C. Bose, On the construction of balanced incomplete block designs, Ann. Eugenics 9 (1939), 353–399. MR 1221
- R. C. Bose, A note on the resolvability of balanced incomplete designs, Sankhyā 6 (1942), 105–110. MR 8064
- R. C. Bose, Mathematical theory of the symmetrical factorial design, Sankhyā 8 (1947), 107–166. MR 26781 —, A note on orthogonal arrays, Ann. Math. Statist. vol. 21 (1950) pp. 304-305 (abstract). —, On the application of finite projective geometry for deriving a certain series of balanced Kirkman arrangements, Bull. Calcutta Math. Soc. Silver Jubilee vol. 51 (1959).
- R. C. Bose and W. S. Connor, Combinatorial properties of group divisible incomplete block designs, Ann. Math. Statistics 23 (1952), 367–383. MR 49144, DOI 10.1214/aoms/1177729382
- R. C. Bose, S. S. Shrikhande, and K. N. Bhattacharya, On the construction of group divisible incomplete block designs, Ann. Math. Statistics 24 (1953), 167–195. MR 55964, DOI 10.1214/aoms/1177729027
- 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
- K. A. Bush, A generalization of a theorem due to MacNeish, Ann. Math. Statistics 23 (1952), 293–295. MR 49145, DOI 10.1214/aoms/1177729449
- K. A. Bush, Orthogonal arrays of index unity, Ann. Math. Statistics 23 (1952), 426–434. MR 49146, DOI 10.1214/aoms/1177729387 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.
- F. W. Levi, Finite Geometrical Systems, University of Calcutta, Calcutta, 1942. MR 0006834 H. F. MacNeish, Das problem der $36$ offiziere, Jber. Deutsch. Math. Verein. vol. 30 (1921) pp. 151-153.
- Harris F. MacNeish, Euler squares, Ann. of Math. (2) 23 (1922), no. 3, 221–227. MR 1502613, DOI 10.2307/1967920
- 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.
Bibliographic 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