Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4647544 | Discrete Mathematics | 2013 | 19 Pages |
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 gâ{7,9,21} in this paper. We show that, for each gâ{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 hâ¡2mod6, to eight undetermined cases.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Hengjia Wei, Gennian Ge,