Conjugate orthogonal quasigroups. (English) Zbl 0398.20086
Keywords:
Conjugate Orthogonal Quasigroups; Finite Quasigroup; Latin Square; Alpha- Self-Orthogonal QuasigroupReferences:
| [1] | Bose, R. C.; Parker, E. T.; Shrikhande, S., Further results on the construction of mutually orthogonal latin squares and the falsity of Euler’s conjecture, Canad. J. Math., 12, 189-203 (1960) · Zbl 0093.31905 |
| [2] | Brayton, R. K.; Coppersmith, D.; Hoffman, A. J., Self-orthogonal latin squares of all orders \(n\) ≠ 2, 3 or 6, Bull. Amer. Math. Soc., 80, 116-118 (1974) · Zbl 0277.05011 |
| [3] | Brayton, R. K.; Coppersmith, D.; Hoffman, A. J., Self-orthogonal latin squares, (Colloquio Internationale sulle Teorie Combinatorie. Colloquio Internationale sulle Teorie Combinatorie, Atti dei Convegni Lincei (1976), Accad. Naz. Lincei: Accad. Naz. Lincei Rome), No. 17 · Zbl 0363.05018 |
| [4] | Denes, J.; Keedwell, A. D., Latin Squares and Their Applications (1974), Academic Press: Academic Press New York/London · Zbl 0283.05014 |
| [5] | Evans, T., Algebraic structures associated with latin squares and orthogonal arrays, (Proceedings of the Conference on Algebraic Aspects of Combinatorics, (University of Toronto, 1974) (Jan. 1975), Utilitas Mathematica) · Zbl 0318.05011 |
| [6] | Hall, M., Combinatorial Theory (1967), Blaisdell: Blaisdell Waltham, Mass · Zbl 0196.02401 |
| [7] | Lindner, C. C., The generalized singular direct product for quasigroups, Canad. Math. Bull., 14, 61-63 (1971) · Zbl 0215.11501 |
| [8] | C. C. Lindnerin; C. C. Lindnerin |
| [9] | Lindner, C. C.; Mendelsohn, E., On the conjugates of an \(n^2\) × 4 orthogonal array, Discrete Math., 20, No. 2, 123-132 (1977/1978) · Zbl 0369.05010 |
| [10] | Van Lint, J. H., (Combinatorial Theory Seminar Eindhoven. Combinatorial Theory Seminar Eindhoven, Lecture Notes in Mathematics, Vol. 382 (1974), Springer-Verlag: Springer-Verlag Berlin/Heidelberg/New York) · Zbl 0315.05001 |
| [11] | MacNeish, H. F., Euler squares, Ann. of Math., 23, 221-227 (1922) · JFM 48.0071.02 |
| [12] | Mills, W. H., Three mutually orthogonal latin squares, J. Combinatorial Theory, 13, 79-82 (1972) · Zbl 0243.05016 |
| [13] | Sade, A., Produit direct-singulier de quasigroups orthogonaux et anti-abelians, Ann. Soc. Sci. Bruxelles, Sér. I, 74, 91-99 (1960) · Zbl 0100.02204 |
| [14] | Steedly, D., Separable Quasigroups, (Ph. D. Thesis (1973), Aubrun University) |
| [15] | Stein, S. K., On the foundations of quasigroups, Trans. Amer. Math. Soc., 85, 228-256 (1957) · Zbl 0079.02402 |
| [16] | Wilson, R. M., An existence theory for pairwise balanced designs, Parts I and II, J. Combinatorial Theory Ser. A, 13, 220-273 (1972) · Zbl 0263.05015 |
| [17] | Wilson, R. M., Concerning the number of mutually orthogonal latin squares, Discrete Math., 9, 181-198 (1974) · Zbl 0283.05009 |
| [18] | Wilson, R. M., A few more squares, (Proceedings of the Fifth Southeastern Conference on Combinatorics, Graph Theory and Computing (1974), Florida Atlantic University: Florida Atlantic University Boca Raton, Florida), 661-673, Congressus Numeratum, No. X, Utilitas, Math. 1974 |
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