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Brayton, R. K.; Coppersmith, Donald; Hoffman, A. J.

Self-orthogonal latin squares of all orders \(n \neq 2,3,6\). (English) Zbl 0277.05011

Bull. Am. Math. Soc. 80, 116-118 (1974).
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Cited in 2 Reviews
Cited in 30 Documents

MSC:

05B15 Orthogonal arrays, Latin squares, Room squares
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References:

[1] R. C. Bose, S. S. Shrikhande, and E. T. Parker, Further results on the construction of mutually orthogonal Latin squares and the falsity of Euler’s conjecture, Canad. J. Math. 12 (1960), 189 – 203. · Zbl 0093.31905 · doi:10.4153/CJM-1960-016-5
[2] R. C. Bose and S. S. Shrikhande, On the construction of sets of mutually orthogonal Latin squares and the falsity of a conjecture of Euler, Trans. Amer. Math. Soc. 95 (1960), 191 – 209. · Zbl 0093.31904
[3] D. J. Crampin and A. J. W. Hilton, The spectrum of latin squares orthogonal to their transposes (manuscript). · Zbl 0325.05011
[4] Diane M. Johnson, A. L. Dulmage, and N. S. Mendelsohn, Orthomorphisms of groups and orthogonal latin squares. I, Canad. J. Math. 13 (1961), 356 – 372. · Zbl 0097.25102 · doi:10.4153/CJM-1961-031-7
[5] Haim Hanani, The existence and construction of balanced incomplete block designs, Ann. Math. Statist. 32 (1961), 361 – 386. · Zbl 0107.36102 · doi:10.1214/aoms/1177705047
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[7] J. D. Horton, Variations on a theme by Moore, Proceedings of the Louisiana Conference on Combinatorics, Graph Theory and Computing (Louisiana State Univ., Baton Rouge, La., 1970) Louisiana State Univ., Baton Rouge, La., 1970, pp. 146 – 166. · Zbl 0248.05018
[8] Charles C. Lindner, The generalized singular direct product for quasigroups, Canad. Math. Bull. 14 (1971), 61 – 63. · Zbl 0215.11501 · doi:10.4153/CMB-1971-011-0
[9] Charles C. Lindner, Construction of quasigroups satisfying the identity \?(\?\?)=\?\?, Canad. Math. Bull. 14 (1971), 57 – 59. · Zbl 0215.11502 · doi:10.4153/CMB-1971-010-3
[10] C. C. Lindner, Application of the singular direct product to constructing various types of orthogonal latin squares, Memphis State University Combinatorial Conference, 1972.
[11] John Melian (oral communications).
[12] N. S. Mendelsohn, Combinatorial designs as models of universal algebras, Recent Progress in Combinatorics (Proc. Third Waterloo Conf. on Combinatorics, 1968) Academic Press, New York, 1969, pp. 123 – 132.
[13] N. S. Mendelsohn, Latin squares orthogonal to their transposes, J. Combinatorial Theory Ser. A 11 (1971), 187 – 189. · Zbl 0218.20056
[14] R. C. Mullin and E. Nemeth, A construction for self orthogonal Latin squares from certain Room squares, Proc. Louisiana Conf. on Combinatorics, Graph Theory and Computing (Louisiana State Univ., Baton Rouge, La., 1970) Louisiana State Univ., Baton Rouge, La., 1970, pp. 213 – 226. · Zbl 0235.05006
[15] E. Nemeth, Study of Room squares, Ph.D. Thesis, University of Waterloo, Ontario · Zbl 0186.01902
[16] E. T. Parker, Construction of some sets of mutually orthogonal latin squares, Proc. Amer. Math. Soc. 10 (1959), 946 – 949. · Zbl 0093.02002
[17] A. Sade, Produit direct-singulier de quasigroupes orthogonaux et anti-abéliens, Ann. Soc. Sci. Bruxelles Sér. I 74 (1960), 91 – 99 (French). · Zbl 0100.02204
[18] A. Sade, Une nouvelle construction des quasigroupes orthogonaux à leur conjoint, Notices Amer. Math. Soc. 19 (1972), 434. Abstract # 72T-A105.
[19] Sherman K. Stein, On the foundations of quasigroups, Trans. Amer. Math. Soc. 85 (1957), 228 – 256. · Zbl 0079.02402
[20] Richard M. Wilson, An existence theory for pairwise balanced designs. I. Composition theorems and morphisms, J. Combinatorial Theory Ser. A 13 (1972), 220 – 245. · Zbl 0263.05014
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