{"title":"关于雅各布有非三角 p 扭转的公因子矩阵的比例","authors":"Sergio Ricardo Zapata Ceballos","doi":"10.1016/j.jcta.2024.105953","DOIUrl":null,"url":null,"abstract":"<div><p>We study the proportion of metric matroids whose Jacobians have nontrivial <em>p</em>-torsion. We establish a correspondence between these Jacobians and the <span><math><msub><mrow><mi>F</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span>-rational points on configuration hypersurfaces, thereby relating their proportions. By counting points over finite fields, we prove that the proportion of these Jacobians is asymptotically equivalent to <span><math><mn>1</mn><mo>/</mo><mi>p</mi></math></span>.</p></div>","PeriodicalId":50230,"journal":{"name":"Journal of Combinatorial Theory Series A","volume":"210 ","pages":"Article 105953"},"PeriodicalIF":0.9000,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S009731652400092X/pdfft?md5=d8e2893424d34795a1338a7aa80035a5&pid=1-s2.0-S009731652400092X-main.pdf","citationCount":"0","resultStr":"{\"title\":\"On the proportion of metric matroids whose Jacobians have nontrivial p-torsion\",\"authors\":\"Sergio Ricardo Zapata Ceballos\",\"doi\":\"10.1016/j.jcta.2024.105953\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We study the proportion of metric matroids whose Jacobians have nontrivial <em>p</em>-torsion. We establish a correspondence between these Jacobians and the <span><math><msub><mrow><mi>F</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span>-rational points on configuration hypersurfaces, thereby relating their proportions. By counting points over finite fields, we prove that the proportion of these Jacobians is asymptotically equivalent to <span><math><mn>1</mn><mo>/</mo><mi>p</mi></math></span>.</p></div>\",\"PeriodicalId\":50230,\"journal\":{\"name\":\"Journal of Combinatorial Theory Series A\",\"volume\":\"210 \",\"pages\":\"Article 105953\"},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2024-09-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.sciencedirect.com/science/article/pii/S009731652400092X/pdfft?md5=d8e2893424d34795a1338a7aa80035a5&pid=1-s2.0-S009731652400092X-main.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Combinatorial Theory Series A\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S009731652400092X\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Combinatorial Theory Series A","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S009731652400092X","RegionNum":2,"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
摘要
我们研究了雅各布具有非难 p 扭转的度量矩阵的比例。我们在这些雅各布与配置超曲面上的 Fp 有理点之间建立了对应关系，从而将它们的比例联系起来。通过计算有限域上的点，我们证明这些雅各布的比例在渐近上等同于 1/p。
On the proportion of metric matroids whose Jacobians have nontrivial p-torsion
We study the proportion of metric matroids whose Jacobians have nontrivial p-torsion. We establish a correspondence between these Jacobians and the -rational points on configuration hypersurfaces, thereby relating their proportions. By counting points over finite fields, we prove that the proportion of these Jacobians is asymptotically equivalent to .
期刊介绍：
The Journal of Combinatorial Theory publishes original mathematical research concerned with theoretical and physical aspects of the study of finite and discrete structures in all branches of science. Series A is concerned primarily with structures, designs, and applications of combinatorics and is a valuable tool for mathematicians and computer scientists.
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