Shangzhao Li , Xiran Zhang , Jing Chen , Shaojun Dai
{"title":"关于块传递2 − （v,k,1）设计的注释","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":3.4000,"publicationDate":"2025-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"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\":3.4000,\"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}","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}
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.
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
