{"title":"An identity involving derangement numbers and bell numbers","authors":"Z. Du, Fonseca da","doi":"10.2298/aadm200705010d","DOIUrl":null,"url":null,"abstract":"The aim of this paper is to establish a new identity between derangement numbers and Bell numbers. Two known identities can be recovered. We provide a combinatorial interpretation for the new identity and a representation of the derangement numbers in terms of the determinants of Hessenberg matrices.","PeriodicalId":51232,"journal":{"name":"Applicable Analysis and Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applicable Analysis and Discrete Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.2298/aadm200705010d","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
The aim of this paper is to establish a new identity between derangement numbers and Bell numbers. Two known identities can be recovered. We provide a combinatorial interpretation for the new identity and a representation of the derangement numbers in terms of the determinants of Hessenberg matrices.
期刊介绍：
Applicable Analysis and Discrete Mathematics is indexed, abstracted and cover-to cover reviewed in: Web of Science, Current Contents/Physical, Chemical & Earth Sciences (CC/PC&ES), Mathematical Reviews/MathSciNet, Zentralblatt für Mathematik, Referativny Zhurnal-VINITI. It is included Citation Index-Expanded (SCIE), ISI Alerting Service and in Digital Mathematical Registry of American Mathematical Society (http://www.ams.org/dmr/).
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