کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4647544 | 1342359 | 2013 | 19 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Group divisible designs with block size four and group type gum1 for more small g
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات گسسته و ترکیبات
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
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.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Discrete Mathematics - Volume 313, Issue 20, 28 October 2013, Pages 2065-2083
Journal: Discrete Mathematics - Volume 313, Issue 20, 28 October 2013, Pages 2065-2083
نویسندگان
Hengjia Wei, Gennian Ge,