Symmetries that latin squares inherit from 1-factorizations

Journal of Combinatorial Designs

Volumn 13, Issue 3, 2005, Pages 157-172

  Wanless, Ian M ^a   Ihrig, Edwin C ^b  

^a AUSTRALIAN NATIONAL UNIVERSITY   (Australia)

^b ARIZONA STATE UNIVERSITY   (United States)

Author keywords

1 Factorization; Atomic latin square; Autotopy, paratopy; Idempotent; Latin square; Main class; Perfect 1 factorization; Totally symmetric

Indexed keywords

EID: 18744374878     PISSN: 10638539     EISSN: 15206610     Source Type: Journal    
DOI: 10.1002/jcd.20045     Document Type: Article

References (22)

1. D. Bryant, B. M. Maenhaut, and I. M. Wanless, A family of perfect factorisations of complete bipartite graphs, J Combin Theory Ser A 98(2002), 328-342.
2. D. Bryant, B. M. Maenhaut, and I. M. Wanless, New families of atomic Latin squares and perfect one-factorisations, submitted for publication.
3. P. J. Cameron and G. Korchmáros, One-factorizations of complete graphs with a doubly transitive automorphism group, Bull London Math Soc 25(1993), 1-6.
4. C. J. Colbourn and A. Rosa, Triple systems, Clarendon, Oxford, 1999.
5. J. Dénes and A. D. Keedwell, Latin squares and 1-factorizations of complete graphs, I, Connections between the enumeration of latin squares and rectangles and r-factorizations of labelled graphs, Ars Combin 25 A (1988), 109-126.
6. J. Dénes and A. D. Keedwell, Latin squares and their applications, Akadémiai Kiadó, Budapest, 1974.
7. J. Dénes and A. D. Keedwell, Latin squares: New developments in the theory and applications, Annals Discrete Math, Vol. 46, North-Holland, Amsterdam, 1991.
8. D. Duncan and E. Ihrig, The structure of symmetry groups of GK (2n; Gq), J Combin Des 2(1994), 341-349.
9. E. Ihrig, Conditions ensuring starter induced 1-factorizations are not isomorphic, J Combin Des 11(2003), 124-143.
10. A. D. Keedwell, Uniform P-circuit designs, quasigroups, and Room squares, Utilitas Math 14(1978), 141-159.
11. A. Kotzig, Groupoids and partitions of complete graphs, Combinatorial Structures and their Applications, Gordon and Breach, New York, 1970, pp. 215-221.
12. P. J. Laufer, On strongly Hamiltonian complete bipartite graphs, Ars Combin 9(1980), 43-46.
13. B. M. Maenhaut and I. M. Wanless, Atomic latin squares of order eleven, J Combin Des 12(2004), 12-34.
14. P. J. Owens and D. A. Preece, Some new non-cyclic latin squares that have cyclic and Youden properties, Ars Combin 44(1996), 137-148.
15. L. Petrenyuk and A. Petrenyuk, Intersection of perfect one-factorizations of complete graphs, Cybernetics 16(1980), 6-9.
16. A. Sade, Quasigroupes parastrophiques: Expressions et identités, Math Nachr 20(1959), 73-106.
17. A. Sade, Critères d'isotopie d'un quasigroupe avec un quasigroupe demi-symétrique, Univ Lisboa Revista Fac Ci A 11(2) (1964/1965), 121-136.
18. M. Suzuki, Group theory II, Grundlehren der Mathematischen Wissenschaften, 248, Springer-Verlag, New York, 1986.
19. I. M. Wanless, Perfect factorisations of bipartite graphs and latin squares without proper subrectangles, Electron J Combin 6(1999), R9, 16 pp.
20. I. M. Wanless, Atomic latin squares based on cyclotomic orthomorphisms, (submitted for publication).
21. W. D. Wallis, One-factorizations, Math Appl, Vol. 390, Kluwer Academic, Dordrecht, 1997.
22. L. Xu, V. Bohossian, J. Bruck, and D. G. Wagner, Low-density MDS codes and factors of complete graphs, IEEE Trans Inform Theory 45(1999), 1817-1826. (Pubitemid 32077611)