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Graphs and Combinatorics

, Volume 14, Issue 1, pp 11–24 | Cite as

A Construction for Resolvable Designs and Its Generalizations

  • Sanpei Kageyama
  • Ying Miao

Abstract.

 In [14], D.K. Ray-Chaudhuri and R.M. Wilson developed a construction for resolvable designs, making use of free difference families in finite fields, to prove the asymptotic existence of resolvable designs with index unity. In this paper, generalizations of this construction are discussed. First, these generalizations, some of which require free difference families over rings in which there are some units such that their differences are still units, are used to construct frames, resolvable designs and resolvable (modified) group divisible designs with index not less than one. Secondly, this construction method is applied to resolvable perfect Mendelsohn designs. Thirdly, cardinalities of such sets of units are investigated. Finally, composition theorems for free difference families via difference matrices are described. They can be utilized to produce some new examples of resolvable designs.

Key Words and Phrases: resolvable; balanced incomplete block design; free difference family; frame; (modified) group divisible design; difference matrix; perfect Mendelsohn design. 

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Copyright information

© Springer-Verlag Tokyo 1998

Authors and Affiliations

  • Sanpei Kageyama
    • 1
  • Ying Miao
    • 1
  1. 1.Department of Mathematics, Hiroshima University, 1-1-1 Kagamiyama, Higashi-Hiroshima 739, JapanJP

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