{"title":"Cyclic balanced sampling plans avoiding adjacent units with block size four","authors":"Zian Zhang, Yanxun Chang , Tao Feng","doi":"10.1016/j.disc.2025.114490","DOIUrl":null,"url":null,"abstract":"<div><div>Balanced sampling plans avoiding adjacent units can be utilized for survey sampling when the units are arranged in one-dimensional ordering and the adjacent units in this ordering provide similar information. The existence of such a balanced sampling plan is equivalent to the existence of a <em>k</em>-clique decomposition of a special Cayley graph over a cyclic group. This paper completely determines the spectrum of cyclic balanced sampling plans avoiding adjacent units with maximum distance five and block size four.</div></div>","PeriodicalId":50572,"journal":{"name":"Discrete Mathematics","volume":"348 7","pages":"Article 114490"},"PeriodicalIF":0.7000,"publicationDate":"2025-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discrete Mathematics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0012365X25000986","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
Abstract
Balanced sampling plans avoiding adjacent units can be utilized for survey sampling when the units are arranged in one-dimensional ordering and the adjacent units in this ordering provide similar information. The existence of such a balanced sampling plan is equivalent to the existence of a k-clique decomposition of a special Cayley graph over a cyclic group. This paper completely determines the spectrum of cyclic balanced sampling plans avoiding adjacent units with maximum distance five and block size four.
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.
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