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- Title
Group divisible designs of four groups and block size five with configuration (1, 1, 1, 2).
- Authors
Mwesigwa, Ronald; Sarvate, Dinesh G.; Li Zhang
- Abstract
We present constructions and results about GDDs with four groups and block size five in which each block has Configuration (1; 1; 1; 2), that is, each block has exactly one point from three of the four groups and two points from the fourth group. We provide the necessary conditions of the existence of a GDD(n; 4; 5; λ1; λ2) with Configuration (1; 1; 1; 2), and show that the necessary conditions are sufficient for a GDD(n; 4; 5; λ1; λ2) with Configuration (1; 1; 1; 2) if n 6≠ 0(mod 6), respectively. We also show that a GDD(n; 4; 5; 2n; 6(n - 1)) with Configuration (1; 1; 1; 2) exists, and provide constructions for a GDD(n = 2t; 4; 5; n; 3(n = 1)) with Configuration (1; 1; 1; 2) where n 6= 12, and a GDD(n = 6t; 4; 5; 4t; 2(6t - 1)) with Configuration (1; 1; 1; 2) where n 6= 6 and 18, respectively.
- Subjects
BLOCKS (Group theory); DIGITAL divide; CONFIGURATIONS (Geometry); MATHEMATICAL analysis; COMPUTER science
- Publication
Journal of Algebra Combinatorics Discrete Structures & Applications, 2017, Vol 4, Issue 3, p187
- ISSN
2148-838X
- Publication type
Article
- DOI
10.13069/jacodesmath.70490