Group divisible designs with block size 4 and type gum1

被引：12

作者：

Forbes, A. D. ^{[1
]}

Forbes, K. A. ^{[2
]}

机构：

[1] Open Univ, Sch Math & Stat, Walton Hall, Milton Keynes MK7 6AA, Bucks, England

[2] Univ Kingston, Res Business & Innovat, Kingston Upon Thames KT1 2EE, Surrey, England

来源：

JOURNAL OF COMBINATORIAL DESIGNS | 2018年 / 26卷 / 11期

关键词：

double group divisible design; group divisible design; GRAPH; HGDDS;

D O I：

10.1002/jcd.21607

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Building upon the work of Wei and Ge (Designs, Codes, and Cryptography 74, 2015), we extend the range of positive integer parameters g, u, and m for which group divisible designs with block size 4 and type gum1 are known to exist. In particular, we show that the necessary conditions for the existence of these designs when m>0 and mg are sufficient in the following cases: , g=2 with one exception, 2(6)5(1), g=10, and g=11.

引用

页码：519 / 539

页数：21

共 47 条

[21] Super-simple group divisible designs with block size 4 and index 2
Cao, H.
Yan, F.
Wei, R.
JOURNAL OF STATISTICAL PLANNING AND INFERENCE, 2010, 140 (09) : 2497 - 2503
[22] Super-simple group divisible designs with block size 4 and index 9
Zhang, Yong
Chen, Kejun
JOURNAL OF STATISTICAL PLANNING AND INFERENCE, 2011, 141 (09) : 3231 - 3243
[23] Super-simple group divisible designs with block size 4 and index 5
Cao, H.
Yan, F.
DISCRETE MATHEMATICS, 2009, 309 (16) : 5111 - 5119
[24] Incomplete group divisible designs with block size four and general index
Wang, Li-dong
Kong, Hai-rong
Liu, Hong-juan
ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES, 2011, 27 (03): : 407 - 418
[25] Incomplete Group Divisible Designs with Block Size Four and General Index
Li-dong Wang 1
Acta Mathematicae Applicatae Sinica, 2011, 27 (03) : 407 - 418
[26] Modified group divisible designs with block size 5 and even index
Abel, R. Julian R.
Assaf, Ahmed M.
DISCRETE MATHEMATICS, 2008, 308 (15) : 3335 - 3351
[27] Super-simple group divisible designs with block size 4 and index λ=7, 8
Chen, Guangzhou
Chen, Kejun
Zhang, Yong
Jiang, Ning
DISCRETE MATHEMATICS, 2021, 344 (12)
[28] Incomplete group divisible designs with block size four and general index
Li-dong Wang
Hai-rong Kong
Hong-juan Liu
Acta Mathematicae Applicatae Sinica, English Series, 2011, 27
[29] Embeddings of resolvable group divisible designs with block size 3 and for all λ
Shen, Jun
Shen, Hao
ARS COMBINATORIA, 2009, 91 : 271 - 287
[30] α-Resolvable Group Divisible Designs with Block Size Four and Groups Size Six and Nine
Meng, Zhaoping
Du, Beiliang
UTILITAS MATHEMATICA, 2009, 78 : 203 - 237

← 1 2 3 4 5 →