数环面上的三脚架

Q3 Mathematics
Jayadev S. Athreya, David Aulicino, Harry Richman
{"title":"数环面上的三脚架","authors":"Jayadev S. Athreya,&nbsp;David Aulicino,&nbsp;Harry Richman","doi":"10.1007/s40598-022-00216-z","DOIUrl":null,"url":null,"abstract":"<div><p>Motivated by the problem of counting finite BPS webs, we count certain immersed metric graphs, <i>tripods</i>, on the flat torus. Classical Euclidean geometry turns this into a lattice point counting problem in <span>\\({\\mathbb {C}}^2\\)</span>, and we give an asymptotic counting result using lattice point counting techniques.</p></div>","PeriodicalId":37546,"journal":{"name":"Arnold Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2022-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Counting Tripods on the Torus\",\"authors\":\"Jayadev S. Athreya,&nbsp;David Aulicino,&nbsp;Harry Richman\",\"doi\":\"10.1007/s40598-022-00216-z\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Motivated by the problem of counting finite BPS webs, we count certain immersed metric graphs, <i>tripods</i>, on the flat torus. Classical Euclidean geometry turns this into a lattice point counting problem in <span>\\\\({\\\\mathbb {C}}^2\\\\)</span>, and we give an asymptotic counting result using lattice point counting techniques.</p></div>\",\"PeriodicalId\":37546,\"journal\":{\"name\":\"Arnold Mathematical Journal\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-08-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Arnold Mathematical Journal\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s40598-022-00216-z\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Arnold Mathematical Journal","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1007/s40598-022-00216-z","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 0

摘要

受有限BPS网计数问题的启发,我们在平面环面上计数某些浸入度量图,即三脚架。经典欧几里得几何将其转化为\({\mathbb{C}}^2)中的格点计数问题,并使用格点计数技术给出了渐近计数结果。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Counting Tripods on the Torus

Counting Tripods on the Torus

Motivated by the problem of counting finite BPS webs, we count certain immersed metric graphs, tripods, on the flat torus. Classical Euclidean geometry turns this into a lattice point counting problem in \({\mathbb {C}}^2\), and we give an asymptotic counting result using lattice point counting techniques.

求助全文
通过发布文献求助,成功后即可免费获取论文全文。 去求助
来源期刊
Arnold Mathematical Journal
Arnold Mathematical Journal Mathematics-Mathematics (all)
CiteScore
1.50
自引率
0.00%
发文量
28
期刊介绍: The Arnold Mathematical Journal publishes interesting and understandable results in all areas of mathematics. The name of the journal is not only a dedication to the memory of Vladimir Arnold (1937 – 2010), one of the most influential mathematicians of the 20th century, but also a declaration that the journal should serve to maintain and promote the scientific style characteristic for Arnold''s best mathematical works. Features of AMJ publications include: Popularity. The journal articles should be accessible to a very wide community of mathematicians. Not only formal definitions necessary for the understanding must be provided but also informal motivations even if the latter are well-known to the experts in the field. Interdisciplinary and multidisciplinary mathematics. AMJ publishes research expositions that connect different mathematical subjects. Connections that are useful in both ways are of particular importance. Multidisciplinary research (even if the disciplines all belong to pure mathematics) is generally hard to evaluate, for this reason, this kind of research is often under-represented in specialized mathematical journals. AMJ will try to compensate for this.Problems, objectives, work in progress. Most scholarly publications present results of a research project in their “final'' form, in which all posed questions are answered. Some open questions and conjectures may be even mentioned, but the very process of mathematical discovery remains hidden. Following Arnold, publications in AMJ will try to unhide this process and made it public by encouraging the authors to include informal discussion of their motivation, possibly unsuccessful lines of attack, experimental data and close by research directions. AMJ publishes well-motivated research problems on a regular basis.  Problems do not need to be original; an old problem with a new and exciting motivation is worth re-stating. Following Arnold''s principle, a general formulation is less desirable than the simplest partial case that is still unknown.Being interesting. The most important requirement is that the article be interesting. It does not have to be limited by original research contributions of the author; however, the author''s responsibility is to carefully acknowledge the authorship of all results. Neither does the article need to consist entirely of formal and rigorous arguments. It can contain parts, in which an informal author''s understanding of the overall picture is presented; however, these parts must be clearly indicated.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信