Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

 
 

 

Enumeration of small nonisomorphic $ 1$-rotational twofold triple systems


Authors: Yeow Meng Chee and Gordon F. Royle
Journal: Math. Comp. 59 (1992), 609-612
MSC: Primary 05B07
DOI: https://doi.org/10.1090/S0025-5718-1992-1140647-4
MathSciNet review: 1140647
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper, twofold triple systems of order v are enumerated for all $ \upsilon \leq 19$.


References [Enhancements On Off] (What's this?)

  • [1] C. J. Colbourn, M. J. Colbourn, J. J. Harms, and A. Rosa, A complete census of (10, 3, 2) block designs and of Mendelsohn triple systems of order ten, iii. (10, 3, 2) block designs without repeated blocks, Congr. Numer. 39 (1983), 211-234. MR 703586 (84j:05018)
  • [2] M. J. Colbourn, Cyclic block designs: computational aspects of their construction and analysis, Ph.D. Thesis, Department of Computer Science, University of Toronto, Toronto, Ontario, 1980. MR 567776 (81a:05016)
  • [3] B. Ganter, A. Gulzow, R. Mathon, and A. Rosa, A complete census of (10, 3, 2)-block designs and of Mendelsohn triple systems of order ten, iv. (10, 3, 2)-block designs with repeated blocks, Math. Schriften Kassel 5/78.
  • [4] H. Hanani, The existence and construction of balanced incomplete block designs, Ann. Math. Statist. 32 (1961), 361-386. MR 0166888 (29:4161)
  • [5] M. Hall, Jr., Combinatorial theory, Blaisdell, Waltham, MA, 1967. MR 0224481 (37:80)
  • [6] E. S. Kramer and D. M. Mesner, t-designs on hypergraphs, Discrete Math. 15 (1976), 263-296. MR 0460143 (57:139)
  • [7] S. Kuriki and M. Jimbo, On 1-rotational $ {S_\lambda }(2,3,\upsilon )$ designs, Discrete Math. 46 (1983), 33-40. MR 708159 (85b:05033)
  • [8] R. Mathon and A. Rosa, A census of Mendelsohn triple systems of order nine, Ars Combin. 4 (1977), 309-315. MR 0462968 (57:2933)
  • [9] -, On the $ (15,5,\lambda )$-family of BIBDs, Discrete Math. 77 (1989), 205-216. MR 1022461 (90k:05029)
  • [10] B. D. McKay, Practical graph isomorphism, Congr. Numer. 30 (1981), 45-87. MR 635936 (83e:05061)
  • [11] -, Nauty user's guide, Computer Science Technical Report TR-CS-84-05, Australian National University, 1984.
  • [12] E. J. Morgan, Some small quasi-multiple designs, Ars Combin. 3 (1977), 233-250. MR 0457248 (56:15456)
  • [13] H. K. Nandi, Enumeration of nonisomorphic solutions of balanced incomplete block designs, Sankhyā 7 (1946), 305-312. MR 0017247 (8:127c)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 05B07

Retrieve articles in all journals with MSC: 05B07


Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1992-1140647-4
Article copyright: © Copyright 1992 American Mathematical Society

American Mathematical Society