{"title":"Further results on large sets plus of partitioned incomplete Latin squares","authors":"","doi":"10.1016/j.disc.2024.114215","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we continue to study the existence of large sets plus of partitioned incomplete Latin squares of type <span><math><msup><mrow><mi>g</mi></mrow><mrow><mi>n</mi></mrow></msup><msup><mrow><mo>(</mo><mi>u</mi><mi>g</mi><mo>)</mo></mrow><mrow><mn>1</mn></mrow></msup></math></span>, denoted by LSPILS<span><math><msup><mrow></mrow><mrow><mo>+</mo></mrow></msup><mo>(</mo><msup><mrow><mi>g</mi></mrow><mrow><mi>n</mi></mrow></msup><msup><mrow><mo>(</mo><mi>u</mi><mi>g</mi><mo>)</mo></mrow><mrow><mn>1</mn></mrow></msup><mo>)</mo></math></span>. We almost solve the existence of an LSPILS<span><math><msup><mrow></mrow><mrow><mo>+</mo></mrow></msup><mo>(</mo><msup><mrow><mi>g</mi></mrow><mrow><mi>n</mi></mrow></msup><msup><mrow><mo>(</mo><mi>u</mi><mi>g</mi><mo>)</mo></mrow><mrow><mn>1</mn></mrow></msup><mo>)</mo></math></span> for any integer <span><math><mi>g</mi><mo>≥</mo><mn>1</mn></math></span> and <span><math><mi>u</mi><mo>=</mo><mn>3</mn><mo>,</mo><mn>4</mn></math></span> with some possible exceptions.</p></div>","PeriodicalId":50572,"journal":{"name":"Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2024-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0012365X24003467/pdfft?md5=a7bdcbba4d2ea5621caf6949ac6fa294&pid=1-s2.0-S0012365X24003467-main.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discrete Mathematics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0012365X24003467","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
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Abstract
In this paper, we continue to study the existence of large sets plus of partitioned incomplete Latin squares of type , denoted by LSPILS. We almost solve the existence of an LSPILS for any integer and with some possible exceptions.
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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