Group divisible designs with block size four and group type g um1 for more small g

Hengjia Wei, Gennian Ge

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

Non-uniform group divisible designs are instrumental in the constructions for other types of designs. Most of the progress for the existence of {4}-GDDs of type gum1 is on the case when gu is even, where the existence for small g has played a key role. In order to determine the spectrum for {4}-GDDs of type gum1 with gu being odd, we continue to investigate the small cases with g {7, 9, 21} in this paper. We show that, for each g {7, 9, 21}, the necessary conditions for the existence of a {4}-GDD of type gum1 are also sufficient. As the applications of these GDDs, we obtain a few pairwise balanced designs with minimum block size 4. Meanwhile, we also improve the existence result for frame self-orthogonal Mendelsohn triple systems of type hn by reducing an infinite class of possible exceptions, namely n = 9 and h 2 mod 6, to eight undetermined cases.

Original languageEnglish
Pages (from-to)2065-2083
Number of pages19
JournalDiscrete Mathematics
Volume313
Issue number20
DOIs
StatePublished - 1 Jan 2013
Externally publishedYes

Keywords

  • Double group divisible designs
  • Frame self-orthogonal Mendelsohn triple
  • Group divisible designs
  • Incomplete group divisible designs
  • Pairwise balanced designs
  • Systems

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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