The existence of doubly resolvable \((v,3,2)\)-BIBDs
type: Item
instance of: scholarly article
title: The existence of doubly resolvable \((v,3,2)\)-BIBDs
zbMATH Open document ID: 0836.05008
DOI: 10.1016/0097-3165(95)90028-4
published in: Journal of Combinatorial Theory. Series A
publication date: 1995-10-04T00:00:00Z
review text: The author shows that the necessary conditions for the existence of doubly resolvable \((v,3,2)\) balanced incomplete block designs, \(\text{DR} (v,3,2)\)-BIBDs, are also sufficient for \(v \geq 12\) with at most six possible exceptions. Specifically, such designs exist provided \(v \equiv 0 \pmod 3\), \(v \neq 6\), 9, except possibly for \(v \in \{72, 78, 90, 114, 117, 126\}\). Note that repeated blocks are allowed. Several direct and recursive constructions are employed.
Mathematics Subject Classification ID: 05B05
Mathematics Subject Classification ID: 05B15
zbMATH DE Number: 802349
zbMATH Keywords: doubly resolvable design
zbMATH Keywords: Kirkman square
zbMATH Keywords: partitioned generalized balanced tournament design
zbMATH Keywords: balanced incomplete block designs
author: Esther R. Lamken
reviewed by: Chester J. Salwach
MaRDI profile type: Publication
full work available at URL: 0097-3165(95)90028-4
OpenAlex ID: W2062060070
cites work: Four mutually orthogonal Latin squares of orders \(28\) and \(52\)
cites work: Resolvable BIBD and SOLS
cites work: Q4190650
cites work: More mutually orthogonal latin squares
cites work: Q3781762
cites work: Q3216660
cites work: Doubly resolvable designs from generalized Bhaskar Rao designs
cites work: Q4026147
cites work: Q3991272
cites work: Q3904616
cites work: Resolvable BIBDs with block size 8 and index 7
cites work: Q4888375
cites work: Q4723751
cites work: Resolvable balanced incomplete block designs with block size 8
cites work: Balanced incomplete block designs and related designs
cites work: On resolvable balanced incomplete block designs
cites work: On resolvable designs
cites work: Q3788022
cites work: Q4374720
cites work: Generalized Balanced Tournament Designs
cites work: Constructions for generalized balanced tournament designs
cites work: Existence results for generalized balanced tournament designs with block size 3
cites work: The existence of partitioned generalized balanced tournament designs with block size 3
cites work: The existence of doubly near resolvable (v,3,2)‐BIBDs
cites work: 3-complementary frames and doubly near resolvable (v,3,2)-BIBDs
cites work: The existence of 3 orthogonal partitioned incomplete Latin squares of type \(t^ n\)
cites work: Four pairwise balanced designs
cites work: Q3735718
cites work: Q3783307
cites work: Q3783308
cites work: Existence results for doubly near resolvable \((v,3,2)\)-BIBDs
cites work: Q3820612
cites work: Q3708811
cites work: Q3708812
cites work: Q3682493
cites work: Existence of resolvable BIBDs with \(k=5\) and \(\lambda=4\)
cites work: Q4175291
cites work: The existence of Room squares
cites work: Q4742798
cites work: Q4140221
cites work: Q3794191
cites work: Q3758837
cites work: Q3735717
cites work: A Kirkman square of order 51 and block size 3
cites work: Q4017168
cites work: Doubly resolvable designs
cites work: On Mutually Orthogonal Resolutions and Near-Resolutions
cites work: Q4071247
cites work: Q3309839
description: scientific article; zbMATH DE number 802349