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Selected Chapters of Number Theory: Special Numbers最新文献

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Catalan Numbers 加泰罗尼亚语数字
Selected Chapters of Number Theory: Special Numbers Pub Date : 2024-03-22 DOI: 10.1142/13840
Elena Deza
{"title":"Catalan Numbers","authors":"Elena Deza","doi":"10.1142/13840","DOIUrl":"https://doi.org/10.1142/13840","url":null,"abstract":"Suppose you have n pairs of parentheses and you would like to form valid groupings of them, where “valid” means that each open parenthesis has a matching closed parenthesis. For example, “(()())” is valid, but “())()(” is not. How many groupings are there for each value of n? Perhaps a more precise definition of the problem would be this: A string of parentheses is valid if there are an equal number of open and closed parentheses and if you begin at the left as you move to the right, add 1 each time you pass an open and subtract 1 each time you pass a closed parenthesis, then the sum is always non-negative. Table 1 shows the possible groupings for 0 ≤ n ≤ 5.","PeriodicalId":260761,"journal":{"name":"Selected Chapters of Number Theory: Special Numbers","volume":" 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140218353","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Stirling Numbers 斯特灵的数字
Selected Chapters of Number Theory: Special Numbers Pub Date : 2023-04-17 DOI: 10.1142/13463
E. Deza
{"title":"Stirling Numbers","authors":"E. Deza","doi":"10.1142/13463","DOIUrl":"https://doi.org/10.1142/13463","url":null,"abstract":"","PeriodicalId":260761,"journal":{"name":"Selected Chapters of Number Theory: Special Numbers","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121989486","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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