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A New Construction of Group Divisible Designs with Nonuniform Group Type
Author(s) -
Ge Gennian,
Li Shuxing,
Wei Hengjia
Publication year - 2016
Publication title -
journal of combinatorial designs
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.618
H-Index - 34
eISSN - 1520-6610
pISSN - 1063-8539
DOI - 10.1002/jcd.21513
Subject(s) - mathematics , type (biology) , block (permutation group theory) , group (periodic table) , block size , construct (python library) , combinatorics , product (mathematics) , discrete mathematics , computer science , geometry , key (lock) , physics , ecology , computer security , quantum mechanics , biology , programming language
The construction of group divisible designs (GDDs) is a basic problem in design theory. While there have been some methods concerning the constructions of uniform GDDs, the construction of nonuniform GDDs remains a challenging problem. In this paper, we present a new approach to the construction of nonuniform GDDs with group typeg k m 1and block size k . We make a progress by proposing a new construction, in which generalized difference sets, a truncating technique, and a difference method are combined to construct nonuniform GDDs. Moreover, we present a variation of this new construction by employing Rees' product constructions. We obtain several infinite families of nonuniform GDDs, as well as many examples whose block sizes are relatively large.