On the construction of sets of mutually orthogonal Latin squares and the falsity of a conjecture of Euler
Authors:
R. C. Bose and S. S. Shrikhande
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
Full-text PDF
References | Similar Articles | Additional Information
- [1] W. W. R. Ball, Mathematical recreations and essays, revised by H. S. M. Coxeter, London Macmillan and Co. Ltd., 1942. MR 0019629 (8:440b)
- [2] R. C. Bose, On the construction of balanced incomplete block designs, Ann. of Eugen. London vol. 9 (1939) pp. 353-399. MR 0001221 (1:199b)
- [3] -, A note on the resolvability of balanced incomplete block designs, Sankhyā vol. 6 (1942) pp. 105-110. MR 0008064 (4:237a)
- [4] -, Mathematical theory of the symmetrical factorial design, Sankhyā vol. 8 (1947) pp. 107-166. MR 0026781 (10:201g)
- [5] -, A note on orthogonal arrays, Ann. Math. Statist. vol. 21 (1950) pp. 304-305 (abstract).
- [6] -, 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).
- [7] R. C. Bose and W. S. Connor, Combinatorial properties of group divisible incomplete block designs, Ann. Math. Statist. vol. 23 (1952) pp. 367-383. MR 0049144 (14:124e)
- [8] R. C. Bose, S. S. Shrikhande and K. N. Bhattacharya, On the construction of group divisible incomplete block designs, Ann. Math. Statist. vol. 24 (1953) pp. 167-195. MR 0055964 (15:3c)
- [9]
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
, Proc. Nat. Acad. Sci. U.S.A. vol. 45 (1959) pp. 734-737. MR 0104590 (21:3343)
- [10] K. A. Bush, A generalization of a theorem due to MacNeish, Ann. Math. Statist. vol. 23 (1952) pp. 293-295. MR 0049145 (14:125a)
- [11] -, Orthogonal arrays of index unity, Ann. Math. Statist. vol. 23 (1952) pp. 426-434. MR 0049146 (14:125b)
- [12] O. Eckenstein, Bibliography of Kirkman's school girl problem, Messenger of Math. vol. 41 (1911-1912) pp. 33-36.
- [13] L. Euler, Recherches sur une nouvelle espéce des quarres magiques, Verh. zeeuwsch Genoot. Wetenschappen vol. 9 (1782) pp. 85-239.
- [14] F. W. Levi, Finite geometrical systems, University of Calcutta, 1942. MR 0006834 (4:49f)
- [15]
H. F. MacNeish, Das problem der
offiziere, Jber. Deutsch. Math. Verein. vol. 30 (1921) pp. 151-153.
- [16] -, Euler's squares, Ann. of Math. vol. 23 (1922) pp. 221-227. MR 1502613
- [17] H. B. Mann, The construction of orthogonal Latin squares, Ann. Math. Statist. vol. 13 (1942) pp. 418-423. MR 0007736 (4:184b)
- [18] E. T. Parker, Construction of some sets of pairwise orthogonal Latin squares, Abstract 553-67, Notices Amer. Math. Soc. vol. 5 (1958) p. 815.
- [19]
J. Peterson, Les
officers, Ann. of Math. (1901-1902) pp. 413-427.
- [20]
P. Wernicke, Das problem der
offiziere, Jber. Deutsch. Math. Verein. vol. 19 (1910) pp. 264-267.
- [21] F. Yates, Incomplete randomized blocks, Ann. of Eugen. London vol. 7 (1936) pp. 121-140.
Retrieve articles in Transactions of the American Mathematical Society with MSC: 05.00
Retrieve articles in all journals with MSC: 05.00
Additional Information
DOI:
https://doi.org/10.1090/S0002-9947-1960-0111695-3
Article copyright:
© Copyright 1960
American Mathematical Society