Shangzhao Li , Xiran Zhang , Jing Chen , Shaojun Dai
{"title":"A note on block-transitive 2 − (v,k,1) designs","authors":"Shangzhao Li , Xiran Zhang , Jing Chen , Shaojun Dai","doi":"10.1016/j.amc.2025.129314","DOIUrl":null,"url":null,"abstract":"<div><div>Let <em>G</em> act block-transitively on a <span><math><mn>2</mn><mo>−</mo><mo>(</mo><mi>v</mi><mo>,</mo><mn>12</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></span> design. If <em>G</em> is solvable, then (1) if <span><math><mn>3</mn><mo>|</mo><mi>v</mi></math></span>, then <span><math><mi>v</mi><mo>=</mo><msup><mrow><mn>3</mn></mrow><mrow><mi>n</mi></mrow></msup></math></span>, <span><math><mi>G</mi><mo>≤</mo><mi>A</mi><mi>Γ</mi><mi>L</mi><mo>(</mo><mn>1</mn><mo>,</mo><msup><mrow><mn>3</mn></mrow><mrow><mi>n</mi></mrow></msup><mo>)</mo></math></span>, where <span><math><msup><mrow><mi>p</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>≡</mo><mn>1</mn><mspace></mspace><mo>(</mo><mrow><mi>mod</mi></mrow><mspace></mspace><mn>44</mn><mo>)</mo></math></span>; (2) if <span><math><mn>3</mn><mo>∤</mo><mi>v</mi></math></span>, then <span><math><mi>v</mi><mo>=</mo><msup><mrow><mi>p</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span>, <span><math><mi>G</mi><mo>≤</mo><mi>A</mi><mi>Γ</mi><mi>L</mi><mo>(</mo><mn>1</mn><mo>,</mo><msup><mrow><mi>p</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>)</mo></math></span>, where <span><math><mi>p</mi><mo>≠</mo><mn>2</mn></math></span> and <span><math><msup><mrow><mi>p</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>≡</mo><mn>1</mn><mspace></mspace><mo>(</mo><mrow><mi>mod</mi></mrow><mspace></mspace><mn>132</mn><mo>)</mo></math></span>.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"495 ","pages":"Article 129314"},"PeriodicalIF":3.5000,"publicationDate":"2025-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Mathematics and Computation","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0096300325000414","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
Let G act block-transitively on a design. If G is solvable, then (1) if , then , , where ; (2) if , then , , where and .
期刊介绍：
Applied Mathematics and Computation addresses work at the interface between applied mathematics, numerical computation, and applications of systems – oriented ideas to the physical, biological, social, and behavioral sciences, and emphasizes papers of a computational nature focusing on new algorithms, their analysis and numerical results.
In addition to presenting research papers, Applied Mathematics and Computation publishes review articles and single–topics issues.
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
