Bulletin of the Korean Mathematical Society (대한수학회보)

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MENDELSOHN TRIPLE SYSTEMS EXCLUDING CONTIGUOUS UNITS WITH λ = 1

  • Cho, Chung-Je (Department of Mathematics and Statistics College of Sciences Sookmyung Women's University)
  • Published : 2008.05.31
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Abstract

We obtain a necessary and sufficient condition for the existence of Mendelsohn triple systems excluding contiguous units with ${\lambda}$ = 1. Also, we obtain the spectrum for cyclic such systems.

Keywords

References

  1. I. Anderson, Combinatorial Designs : Construction Methods, Ellis Horwood, New York, Halsted Press, 1990
  2. F. E. Bennett, Direct constructions for perfect 3-cyclic designs, Algebraic and geometric combinatorics, 63-68, North-Holland Math. Stud., 65, North-Holland, Amsterdam, 1982
  3. C. J. Colbourn, Automorphisms of directed triple systems, Bull. Austral. Math. Soc. 43 (1991), no. 2, 257-264 https://doi.org/10.1017/S0004972700029026
  4. C. J. Colbourn and M. J. Colbourn, Every twofold triple system can be directed, J. Combin. Theory Ser. A 34 (1983), no. 3, 375-378 https://doi.org/10.1016/0097-3165(83)90070-5
  5. C. J. Colbourn and J. J. Harms, Directing triple systems, Ars Combin. 15 (1983), 261-266
  6. C. J. Colbourn and A. C. H. Ling, A class of partial triple systems with applications in survey sampling, Comm. Statist. Theory Methods 27 (1998), no. 4, 1009-1018 https://doi.org/10.1080/03610929808832141
  7. C. J. Colbourn and A. Rosa, Quadratic leaves of maximal partial triple systems, Graphs Combin. 2 (1986), no. 4, 317-337 https://doi.org/10.1007/BF01788106
  8. H. Hanani, The existence and construction of balanced incomplete block designs, Ann. Math. Statist. 32 (1961), 361-386 https://doi.org/10.1214/aoms/1177705047
  9. J. J. Harms and C. J. Colbourn, An optimal algorithm for directing triple systems using Eulerian circuits, Cycles in graphs (Burnaby, B.C., 1982), 433-438, North-Holland Math. Stud., 115, North-Holland, Amsterdam, 1985
  10. S. H. Y. Hung and N. S. Mendelsohn, Directed triple systems, J. Combinatorial Theory Ser. A 14 (1973), 310-318 https://doi.org/10.1016/0097-3165(73)90007-1
  11. N. S. Mendelsohn, A natural generalization of Steiner triple systems, Computers in number theory (Proc. Sci. Res. Council Atlas Sympos. No. 2, Oxford, 1969), pp. 323-338. Academic Press, London, 1971
  12. J. Seberry and D. Skillicorn, All directed BIBDs with k = 3 exist, J. Combin. Theory Ser. A 29 (1980), no. 2, 244-248 https://doi.org/10.1016/0097-3165(80)90014-X
  13. D. T. Todorov, Three mutually orthogonal Latin squares of order 14, Ars Combin. 20 (1985), 45-47
  14. W. D. Wallis, Three orthogonal Latin squares, Adv. in Math. (Beijing) 15 (1986), no. 3, 269-281 https://doi.org/10.1016/0001-8708(75)90139-5
  15. R. Wei, Cyclic BSEC of block size 3, Discrete Math. 250 (2002), no. 1-3, 291-298 https://doi.org/10.1016/S0012-365X(01)00429-0

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