An application of modified group divisible designs
type: Item
instance of: scholarly article
title: An application of modified group divisible designs
zbMATH Open document ID: 0814.05014
DOI: 10.1016/0097-3165(94)90095-7
author: Ahmed M. Assaf
published in: Journal of Combinatorial Theory. Series A
publication date: 1995-06-08T00:00:00Z
review text: Let \(\kappa\), \(\lambda\), \(m\), \(\upsilon\) be positive integers. A group divisible design of order \(\kappa\), \(\lambda\), \(m\), \(\upsilon\) consists of a finite set \(V\) of points, a partition \(\gamma= \{G_ 1,\dots, G_ r\}\) of \(V\) into \(r\) subsets of \(V\) called groups and a collection \(\beta= \{B_ 1, B_ 2,\dots\}\) consisting of \(\kappa\)-subsets of \(V\) called blocks satisfying the following properties: (1) \(| G_ i|= m\), \(i= 1,\dots, r\). (2) \(| B\cap G|\leq 1\) for \(B\in \beta\) and \(G\in \gamma\). (3) Every 2-subset \(\{x,y\}\subset V\) whose elements \(x\), \(y\) belong to different groups \(G_ i\), \(G_ j\) is contained in exactly \(\lambda\) blocks. Group divisible designs with block sizes 3 and 4 are known to exist. In this paper the author constructs group divisible designs with block size 5 and several other covering designs and packing designs.
reviewed by: Joachim Rosenthal
Mathematics Subject Classification ID: 05B05
Mathematics Subject Classification ID: 05B40
Mathematics Subject Classification ID: 51E05
Mathematics Subject Classification ID: 62K10
zbMATH DE Number: 665830
zbMATH Keywords: block designs
zbMATH Keywords: group divisible design
zbMATH Keywords: covering designs
zbMATH Keywords: packing designs
MaRDI profile type: Publication
full work available at URL: 0097-3165(94)90095-7
OpenAlex ID: W2060374617
cites work: Four mutually orthogonal Latin squares of orders \(28\) and \(52\)
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cites work: Q4865125
cites work: Packing pairs by quintuples with index 2: \(v\) odd, \(v\not\equiv 13\pmod{20}\)
cites work: Q3686719
cites work: Q5725147
cites work: Optimal packings of \(K_4\)'s into a \(K_n\)
cites work: Four MOLS of order 10 with a hole of order 2
cites work: Group divisible designs with block-size four
cites work: Minimal coverings of pairs by triples
cites work: Q5682334
cites work: Q4288149
cites work: Balanced incomplete block designs and related designs
cites work: On resolvable designs
cites work: Covering triples by quadruples: an asymptotic solution
cites work: Coverings of pairs by quintuples
cites work: On the covering of pairs by quadruples. I
cites work: On the covering of pairs by quadruples. II
cites work: Q4079614
cites work: Q4065553
cites work: Q3216667
cites work: Coverings pairs by quintuples: The case v congruent to 3 (mod 4)
cites work: Q3773899
cites work: Q3829564
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description: scientific article; zbMATH DE number 665830