{"title":"随机链配合物的一个模型","authors":"Michael J. Catanzaro, Matthew J. Zabka","doi":"10.1007/s12188-021-00248-w","DOIUrl":null,"url":null,"abstract":"<div><p>We introduce a model for random chain complexes over a finite field. The randomness in our complex comes from choosing the entries in the matrices that represent the boundary maps uniformly over <span>\\(\\mathbb {F}_q\\)</span>, conditioned on ensuring that the composition of consecutive boundary maps is the zero map. We then investigate the combinatorial and homological properties of this random chain complex.</p></div>","PeriodicalId":50932,"journal":{"name":"Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg","volume":null,"pages":null},"PeriodicalIF":0.4000,"publicationDate":"2021-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s12188-021-00248-w.pdf","citationCount":"0","resultStr":"{\"title\":\"A model for random chain complexes\",\"authors\":\"Michael J. Catanzaro, Matthew J. Zabka\",\"doi\":\"10.1007/s12188-021-00248-w\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We introduce a model for random chain complexes over a finite field. The randomness in our complex comes from choosing the entries in the matrices that represent the boundary maps uniformly over <span>\\\\(\\\\mathbb {F}_q\\\\)</span>, conditioned on ensuring that the composition of consecutive boundary maps is the zero map. We then investigate the combinatorial and homological properties of this random chain complex.</p></div>\",\"PeriodicalId\":50932,\"journal\":{\"name\":\"Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2021-11-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://link.springer.com/content/pdf/10.1007/s12188-021-00248-w.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s12188-021-00248-w\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s12188-021-00248-w","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
We introduce a model for random chain complexes over a finite field. The randomness in our complex comes from choosing the entries in the matrices that represent the boundary maps uniformly over \(\mathbb {F}_q\), conditioned on ensuring that the composition of consecutive boundary maps is the zero map. We then investigate the combinatorial and homological properties of this random chain complex.
期刊介绍：
The first issue of the "Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg" was published in the year 1921. This international mathematical journal has since then provided a forum for significant research contributions. The journal covers all central areas of pure mathematics, such as algebra, complex analysis and geometry, differential geometry and global analysis, graph theory and discrete mathematics, Lie theory, number theory, and algebraic topology.
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
