{"title":"On products of strong Skolem starters","authors":"Oleg Ogandzhanyants, Margarita Kondratieva, Nabil Shalaby","doi":"10.1002/jcd.21943","DOIUrl":null,"url":null,"abstract":"<p>In 1991, Shalaby conjectured that any <span></span><math>\n \n <mrow>\n <msub>\n <mi>Z</mi>\n \n <mi>n</mi>\n </msub>\n </mrow></math>, where <span></span><math>\n \n <mrow>\n <mi>n</mi>\n \n <mo>≡</mo>\n \n <mn>1</mn>\n </mrow></math> or <span></span><math>\n \n <mrow>\n <mn>3</mn>\n <mspace></mspace>\n \n <mrow>\n <mo>(</mo>\n \n <mrow>\n <mi>mod</mi>\n <mspace></mspace>\n \n <mn>8</mn>\n </mrow>\n \n <mo>)</mo>\n </mrow>\n \n <mo>,</mo>\n \n <mi>n</mi>\n \n <mo>≥</mo>\n \n <mn>11</mn>\n </mrow></math>, admits a strong Skolem starter. In 2018, the authors fully described and explicitly constructed the infinite “cardioidal” family of strong Skolem starters. No other infinite family of these combinatorial designs was known to date. Statements regarding the products of starters, proven in this paper give a new way of generating strong or skew Skolem starters of composite orders. This approach extends our previous result by generating new infinite families of these starters that are not cardioidal.</p>","PeriodicalId":15389,"journal":{"name":"Journal of Combinatorial Designs","volume":"32 8","pages":"464-487"},"PeriodicalIF":0.5000,"publicationDate":"2024-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Combinatorial Designs","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/jcd.21943","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
In 1991, Shalaby conjectured that any , where or , admits a strong Skolem starter. In 2018, the authors fully described and explicitly constructed the infinite “cardioidal” family of strong Skolem starters. No other infinite family of these combinatorial designs was known to date. Statements regarding the products of starters, proven in this paper give a new way of generating strong or skew Skolem starters of composite orders. This approach extends our previous result by generating new infinite families of these starters that are not cardioidal.
期刊介绍：
The Journal of Combinatorial Designs is an international journal devoted to the timely publication of the most influential papers in the area of combinatorial design theory. All topics in design theory, and in which design theory has important applications, are covered, including:
block designs, t-designs, pairwise balanced designs and group divisible designs
Latin squares, quasigroups, and related algebras
computational methods in design theory
construction methods
applications in computer science, experimental design theory, and coding theory
graph decompositions, factorizations, and design-theoretic techniques in graph theory and extremal combinatorics
finite geometry and its relation with design theory.
algebraic aspects of design theory.
Researchers and scientists can depend on the Journal of Combinatorial Designs for the most recent developments in this rapidly growing field, and to provide a forum for both theoretical research and applications. All papers appearing in the Journal of Combinatorial Designs are carefully peer refereed.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
