Changyuan Wang , R. Julian R. Abel , Thomas Britz , Yudhistira A. Bunjamin , Diana Combe
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Abstract
In this paper, we consider the existence of group divisible designs (GDDs) with block size 4 and group sizes 4 and 10. We show that a 4-GDD of type exists when the necessary conditions are satisfied, except possibly for a finite number of cases with . We also give some new examples of 4-GDDs for which the number of points is 51, 54 or some value less than or equal to 50.
期刊介绍：
Discrete Mathematics provides a common forum for significant research in many areas of discrete mathematics and combinatorics. Among the fields covered by Discrete Mathematics are graph and hypergraph theory, enumeration, coding theory, block designs, the combinatorics of partially ordered sets, extremal set theory, matroid theory, algebraic combinatorics, discrete geometry, matrices, and discrete probability theory.
Items in the journal include research articles (Contributions or Notes, depending on length) and survey/expository articles (Perspectives). Efforts are made to process the submission of Notes (short articles) quickly. The Perspectives section features expository articles accessible to a broad audience that cast new light or present unifying points of view on well-known or insufficiently-known topics.
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