组块大小为 4、组块大小为 4 和 10 的可分设计,以及其他一些 4-GDD 设计

IF 0.7 3区 数学 Q2 MATHEMATICS
Changyuan Wang , R. Julian R. Abel , Thomas Britz , Yudhistira A. Bunjamin , Diana Combe
{"title":"组块大小为 4、组块大小为 4 和 10 的可分设计,以及其他一些 4-GDD 设计","authors":"Changyuan Wang ,&nbsp;R. Julian R. Abel ,&nbsp;Thomas Britz ,&nbsp;Yudhistira A. Bunjamin ,&nbsp;Diana Combe","doi":"10.1016/j.disc.2024.114254","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we consider the existence of group divisible designs (GDDs) with block size 4 and group sizes 4 and 10. We show that a 4-GDD of type <span><math><msup><mrow><mn>4</mn></mrow><mrow><mi>t</mi></mrow></msup><msup><mrow><mn>10</mn></mrow><mrow><mi>s</mi></mrow></msup></math></span> exists when the necessary conditions are satisfied, except possibly for a finite number of cases with <span><math><mn>4</mn><mi>t</mi><mo>+</mo><mn>10</mn><mi>s</mi><mo>≤</mo><mn>178</mn></math></span>. We also give some new examples of 4-GDDs for which the number of points is 51, 54 or some value less than or equal to 50.</p></div>","PeriodicalId":50572,"journal":{"name":"Discrete Mathematics","volume":"348 2","pages":"Article 114254"},"PeriodicalIF":0.7000,"publicationDate":"2024-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0012365X24003856/pdfft?md5=0cc847d0e63ce2f36a39c3a9c8057cf4&pid=1-s2.0-S0012365X24003856-main.pdf","citationCount":"0","resultStr":"{\"title\":\"Group divisible designs with block size 4 and group sizes 4 and 10 and some other 4-GDDs\",\"authors\":\"Changyuan Wang ,&nbsp;R. Julian R. Abel ,&nbsp;Thomas Britz ,&nbsp;Yudhistira A. Bunjamin ,&nbsp;Diana Combe\",\"doi\":\"10.1016/j.disc.2024.114254\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In this paper, we consider the existence of group divisible designs (GDDs) with block size 4 and group sizes 4 and 10. We show that a 4-GDD of type <span><math><msup><mrow><mn>4</mn></mrow><mrow><mi>t</mi></mrow></msup><msup><mrow><mn>10</mn></mrow><mrow><mi>s</mi></mrow></msup></math></span> exists when the necessary conditions are satisfied, except possibly for a finite number of cases with <span><math><mn>4</mn><mi>t</mi><mo>+</mo><mn>10</mn><mi>s</mi><mo>≤</mo><mn>178</mn></math></span>. We also give some new examples of 4-GDDs for which the number of points is 51, 54 or some value less than or equal to 50.</p></div>\",\"PeriodicalId\":50572,\"journal\":{\"name\":\"Discrete Mathematics\",\"volume\":\"348 2\",\"pages\":\"Article 114254\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2024-09-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.sciencedirect.com/science/article/pii/S0012365X24003856/pdfft?md5=0cc847d0e63ce2f36a39c3a9c8057cf4&pid=1-s2.0-S0012365X24003856-main.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Discrete Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0012365X24003856\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discrete Mathematics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0012365X24003856","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0

摘要

在本文中,我们考虑了块大小为 4、组大小为 4 和 10 的组可分割设计(GDD)的存在性。我们证明,在满足必要条件的情况下,4t10s 类型的 4-GDD 是存在的,4t+10s≤178 的有限个例除外。我们还给出了一些点数为 51、54 或小于等于 50 的 4-GDD 的新例子。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Group divisible designs with block size 4 and group sizes 4 and 10 and some other 4-GDDs

In this paper, we consider the existence of group divisible designs (GDDs) with block size 4 and group sizes 4 and 10. We show that a 4-GDD of type 4t10s exists when the necessary conditions are satisfied, except possibly for a finite number of cases with 4t+10s178. We also give some new examples of 4-GDDs for which the number of points is 51, 54 or some value less than or equal to 50.

求助全文
通过发布文献求助,成功后即可免费获取论文全文。 去求助
来源期刊
Discrete Mathematics
Discrete Mathematics 数学-数学
CiteScore
1.50
自引率
12.50%
发文量
424
审稿时长
6 months
期刊介绍: Discrete Mathematics provides a common forum for significant research in many areas of discrete mathematics and combinatorics. Among the fields covered by Discrete Mathematics are graph and hypergraph theory, enumeration, coding theory, block designs, the combinatorics of partially ordered sets, extremal set theory, matroid theory, algebraic combinatorics, discrete geometry, matrices, and discrete probability theory. Items in the journal include research articles (Contributions or Notes, depending on length) and survey/expository articles (Perspectives). Efforts are made to process the submission of Notes (short articles) quickly. The Perspectives section features expository articles accessible to a broad audience that cast new light or present unifying points of view on well-known or insufficiently-known topics.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信