{"title":"From Abel’s Binomial Theorem to Cayley’s Tree Formula","authors":"Marc Zucker","doi":"10.1080/00029890.2023.2276637","DOIUrl":null,"url":null,"abstract":"AbstractWe derive Abel’s generalization of the binomial theorem and use it to present a short proof of Cayley’s theorem on the number of trees on n labeled vertices.MSC: 05C30 DISCLOSURE STATEMENTNo potential conflict of interest was reported by the author(s).","PeriodicalId":7761,"journal":{"name":"American Mathematical Monthly","volume":"13 5","pages":"0"},"PeriodicalIF":0.4000,"publicationDate":"2023-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"American Mathematical Monthly","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1080/00029890.2023.2276637","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
AbstractWe derive Abel’s generalization of the binomial theorem and use it to present a short proof of Cayley’s theorem on the number of trees on n labeled vertices.MSC: 05C30 DISCLOSURE STATEMENTNo potential conflict of interest was reported by the author(s).
期刊介绍:
The Monthly''s readers expect a high standard of exposition; they look for articles that inform, stimulate, challenge, enlighten, and even entertain. Monthly articles are meant to be read, enjoyed, and discussed, rather than just archived. Articles may be expositions of old or new results, historical or biographical essays, speculations or definitive treatments, broad developments, or explorations of a single application. Novelty and generality are far less important than clarity of exposition and broad appeal. Appropriate figures, diagrams, and photographs are encouraged.
Notes are short, sharply focused, and possibly informal. They are often gems that provide a new proof of an old theorem, a novel presentation of a familiar theme, or a lively discussion of a single issue.
Abstracts for articles or notes should entice the prospective reader into exploring the subject of the paper and should make it clear to the reader why this paper is interesting and important. The abstract should highlight the concepts of the paper rather than summarize the mechanics. The abstract is the first impression of the paper, not a technical summary of the paper. Excessive use of notation is discouraged as it can limit the interest of the broad readership of the MAA, and can limit search-ability of the article.