{"title":"A general formula in composition theory","authors":"Rafael Jakimczuk","doi":"10.1515/ms-2024-0043","DOIUrl":null,"url":null,"abstract":"We prove general formulae in composition theory. We study the number of restricted compositions of a positive integer <jats:italic>n</jats:italic> in <jats:italic>k</jats:italic> parts, where the parts are in very general integer sequences. Note that in compositions the order of the parts is considered.","PeriodicalId":18282,"journal":{"name":"Mathematica Slovaca","volume":"24 1","pages":""},"PeriodicalIF":0.9000,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematica Slovaca","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1515/ms-2024-0043","RegionNum":3,"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
Abstract
We prove general formulae in composition theory. We study the number of restricted compositions of a positive integer n in k parts, where the parts are in very general integer sequences. Note that in compositions the order of the parts is considered.
期刊介绍：
Mathematica Slovaca, the oldest and best mathematical journal in Slovakia, was founded in 1951 at the Mathematical Institute of the Slovak Academy of Science, Bratislava. It covers practically all mathematical areas. As a respectful international mathematical journal, it publishes only highly nontrivial original articles with complete proofs by assuring a high quality reviewing process. Its reputation was approved by many outstanding mathematicians who already contributed to Math. Slovaca. It makes bridges among mathematics, physics, soft computing, cryptography, biology, economy, measuring, etc. The Journal publishes original articles with complete proofs. Besides short notes the journal publishes also surveys as well as some issues are focusing on a theme of current interest.
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