Hostname: page-component-5c6d5d7d68-thh2z Total loading time: 0 Render date: 2024-08-16T00:42:01.492Z Has data issue: false hasContentIssue false
  • English
  • Français

Semiregular group divisible designs with dual properties

Published online by Cambridge University Press:  17 April 2009

Alan Rahilly
Alan Rahilly
Affiliation:
Department of Mathematics, The University of Queensland, Queensland 4072, Australia
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A construction method for group divisible designs is employed to construct (i) infinitely many non-symmetric semiregular group divisible designs whose duals are semiregular group divisible designs, and (ii) infinitely many transversal designs whose duals are group divisible 3-associate designs. A construction method for affine α−resolvable balanced incomplete block designs is also given and illustrated.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 45 , Issue 1 , February 1992 , pp. 61 - 69
Copyright
Copyright © Australian Mathematical Society 1992

References

[1]Beker, H., ‘Strongly divisible 1-designs’, Geom. Dedicata 8 (1979), 299–316.Google Scholar
[2]Bose, R.C. and Connor, W.S., ‘Combinatorial properties of group divisible incomplete block designs’, Ann. Math. Statist. 23 (1952), 367–383.Google Scholar
[3]Dembowski, P., Finite geometries (Springer-Verlag, Berlin, Heidelberg, New York, 1968).Google Scholar
[4]Jungnickel, D., ‘On automorphism groups of divisible designs’, Canad. J. Math. 34 (1982), 257–297.Google Scholar
[5]Mavron, V.C., ‘Constructions for resolvable and related designs’, Aequationes Math. 23 (1981), 131–145.CrossRefGoogle Scholar
[6]Mitchell, C., ‘Group divisible designs with dual properties’, Mitt. Math. Sem. Giessen 165 (1984), 105–117.Google Scholar
[7]Raghavarao, D., ‘A generalization of group divisible designs’, Ann. Math. Statist. 31 (1960), 756–771.Google Scholar
[8]Rahilly, Alan, ‘Semiregular group divisible designs whose duals are semiregular group divisible’, Australas. J. Combin. 2 (1990), 157–179.Google Scholar
[9]Shrikhande, S.S. and Raghavarao, D., ‘A method of construction of incomplete block designs’, Sankhyā Ser. A 25 (1963), 399–402.Google Scholar