Diagonally cyclic latin squares

European Journal of Combinatorics

Volumn 25, Issue 3, 2004, Pages 393-413

  Wanless, Ian M ^a,b  

^a AUSTRALIAN NATIONAL UNIVERSITY   (Australia)

^b CHRIST CHURCH   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0842325241     PISSN: 01956698     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ejc.2003.09.014     Document Type: Article

References (35)

1. Afsarinejad K. On the optimality of Knut Vik designs Util. Math. 41 1992 91-96
2. Bedford D. Construction of orthogonal latin squares using left neofields Discrete Math. 115 1993 17-38
3. Bedford D. Orthomorphisms and near orthomorphisms of groups and orthogonal latin squares: a survey Bull. Inst. Combin. Appl. 15 1995 13-33
4. Beresina L.J. Berezina M.T. On a certain construction of mutually orthogonal latin squares Ars Combin. 29A 1990 199-200
5. Bruck R.H. Some results in the theory of quasigroups Trans. Amer. Math. Soc. 55 1944 19-52
6. D. Bryant, M. Buchanan, I.M. Wanless, The spectrum for quasigroups with cyclic automorphisms and additional symmetries (in preparation)
7. Colbourn C.J. Dinitz J.H. (Eds.), The CRC Handbook of Combinatorial Designs 1996 CRC Press Boca Raton, FL
8. Dénes J. Keedwell A.D. Latin Squares and their Applications 1974 Akadémiai Kiadó Budapest
9. Dénes J. Keedwell A.D. Latin Squares: New Developments in the Theory and Applications Annals of Discrete Math. vol. 46 1991 North-Holland Amsterdam
10. Evans A.B. Maximal sets of mutually orthogonal latin squares II European J. Combin. 13 1992 345-350
11. Evans A.B. Orthomorphism Graphs of Groups Lecture Notes in Mathematics vol. 1535 1992 Springer
12. Evans A.B. On orthogonal orthomorphisms of cyclic and non-abelian groups Discrete Math. 243 2002 229-233
13. Franklin M.F. Cyclic generation of orthogonal latin squares Ars Combin. 17 1984 129-139
14. Franklin M.F. Cyclic generation of self-orthogonal latin squares Util. Math. 25 1984 135-146
15. M. Grüttmüller, Completing partial latin squares with two prescribed diagonals, Preprints aus dem Fachbereich Mathematik, Universität Rostock
16. M. Grüttmüller, Completing partial latin squares with prescribed diagonals, Preprints aus dem Fachbereich Mathematik, Universität Rostock
17. Hedayat A. A complete solution to the existence and nonexistence of Knut Vik designs and orthogonal Knut Vik designs J. Combin. Theory Ser. A 22 1977 331-337
18. Hedayat A. Seiden E. On the theory and application of sum composition of latin squares and orthogonal latin squares Pacific J. Math. 54 1974 85-113
19. Keedwell A.D. Uniform P-circuit designs, quasigroups and Room squares Util. Math. 14 1978 141-159
20. B.M. Maenhaut, I.M. Wanless, Atomic latin squares of order eleven, J. Combin. Des. (in press)
21. Owens P.J. Complete sets of pairwise orthogonal latin squares and the corresponding projective planes J. Combin. Theory Ser. A 59 1992 240-252
22. Owens P.J. Preece D.A. Complete sets of pairwise orthogonal latin squares of order 9 J. Combin. Math. Combin. Comput. 18 1995 83-96
23. Owens P.J. Preece D.A. Aspects of complete sets of 9×9 pairwise orthogonal latin squares Discrete Math. 167/168 1997 519-525
24. Parker E.T. Construction of some sets of mutually orthogonal latin squares Proc. Amer. Math. Soc. 10 1959 946-949
25. Parker E.T. Orthogonal latin squares Proc. Natl. Acad. Sci. USA 45 1959 859-862
26. van Rees G.H.J. Subsquares and transversals in latin squares Ars Combin. 29 B 1990 193-204
27. Shieh Y.-P. Hsiang J. Hsu D.F. On the enumeration of abelian K-complete mappings Congr. Numer. 144 2000 67-88
28. Steedley D. Separable quasigroups Aequationes Math. 11 1974 189-195
29. Todorov D.T. Three mutually orthogonal latin squares of order 14 Ars Combin. 20 1985 45-47
30. Todorov D.T. Four mutually orthogonal latin squares of order 20 Ars Combin. 27 1989 63-65
31. Wallis W.D. Zhu L. The existence of orthogonal latin squares with small subsquares J. Combin. Inform. System Sci. 9 1984 1-13
32. Wanless I.M. Latin squares with one subsquare J. Combin. Des. 9 2001 128-146
33. I.M. Wanless, Cycle switching in latin squares, Graphs Combin. (in press)
34. I.M. Wanless, A partial Latin squares problem posed by Blackburn, Bull. Inst. Comb. Appl. (in press)
35. K. Yamamoto, Generation principles of latin squares, Bull. Inst. Internat. Statist. 38 (1961) 73-76.