Latin squares with one subsquare

Journal of Combinatorial Designs

Volumn 9, Issue 2, 2001, Pages 128-146

  Wanless, I M ^a  

^a CHRIST CHURCH   (United Kingdom)

Author keywords

Intercalate; Latin squares; Prolongation; Subsquare; Subsquare free

Indexed keywords

EID: 0242720090     PISSN: 10638539     EISSN: None     Source Type: Journal    
DOI: 10.1002/1520-6610(2001)9:2<128::AID-JCD1003>3.0.CO;2-C     Document Type: Article

References (16)

1. L. D. Andersen and E. Mendelsohn, A direct construction for Latin squares without proper subsquares, Ann Discrete Math 15 (1982), 27-53.
2. J. Dénes and A. D. Keedwell, "Latin squares and their applications," Akadémiai Kiadó, Budapest, 1974.
3. R. H. F. Denniston, Remarks on Latin squares with no subsquares of order two, Utilitas Math 13 (1978), 299-302.
4. J. R. Elliott and P. B. Gibbons, The construction of subsquare free Latin squares by simulated annealing, Australas J Combin 5 (1992), 209-228.
5. P. B. Gibbons and E. Mendelsohn, The existence of a subsquare free Latin square of side 12, SIAM J Algebraic Discrete Methods 8 (1987), 93-99.
6. K. Heinrich, Latin squares with no proper subsquares, J Comb Th Ser A 29 (1980), 346-353.
7. K. Heinrich, Latin squares with and without subsquares of prescribed type, in "Latin squares: New developments in the theory and applications," Ann Discrete Math 46 (1991), 101-147.
8. A. Kotzig and J. Turgeon, On certain constructions for Latin squares with no Latin subsquares of order two, Discrete Math. 16 (1976), 263-270.
9. B. D. McKay and I. M. Wanless, Most Latin squares have many subsquares, J Comb Th Ser A 86 (1999), 323-347.
10. M. McLeish, A direct construction of Latin squares with no subsquares of order two, Ars Combin 10 (1980), 179-186.
11. H. W. Norton, The 7 × 7 squares, Ann Eugenics 9 (1939), 269-307.
12. A. Sade, An omission in Norton's list of 7 × 7 squares, Ann Math Statist 22 (1951), 306-307.
13. I. M. Wanless, Permanents, matchings and Latin rectangles, Ph.D. thesis, Australian National University, 1997.
14. I. M. Wanless, On McLeish's construction for Latin squares without intercalates, Ars Combin 58 (2001), to appear.
15. I. M. Wanless, The existence spectrum of Latin squares without proper subsquares, in preparation.
16. I. M. Wanless, Perfect factorisations of bipartite graphs and Latin squares without proper subrectangles, Elect J Combin 6 (1999), R9.