{"title":"E","authors":"A. Mohamed, D. Chenaf, S. El-Shahed","doi":"10.1201/9781003211396-5","DOIUrl":null,"url":null,"abstract":".G A bstract. O ne form ofthe inclusion-exclusion principle assertsthat if A and B are functions of (cid:12)nite sets then the form ulas A ( S ) = P T (cid:18) S B ( T ) and B ( S ) = P T (cid:18) S ( (cid:0) 1) j S j(cid:0) j T j A ( T ) are equivalent. If we replace B ( S ) by ( (cid:0) 1) j S j B ( S ) then these form ulastake on the sym m etric form which we call sym m etric inclusion-exclusion . W e study instances of sym m etric inclusion-exclusion in which thefunctions A and B havecom binatorialorprobabilistic interpretations.In particular,we study casesrelated to the P(cid:19)olya-Eggenberger urn m odelin which A ( S )and B ( S )depend only on the cardinality of S .","PeriodicalId":275113,"journal":{"name":"DARE’s Dictionary of Environmental Sciences and Engineering","volume":"131 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"DARE’s Dictionary of Environmental Sciences and Engineering","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1201/9781003211396-5","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
.G A bstract. O ne form ofthe inclusion-exclusion principle assertsthat if A and B are functions of (cid:12)nite sets then the form ulas A ( S ) = P T (cid:18) S B ( T ) and B ( S ) = P T (cid:18) S ( (cid:0) 1) j S j(cid:0) j T j A ( T ) are equivalent. If we replace B ( S ) by ( (cid:0) 1) j S j B ( S ) then these form ulastake on the sym m etric form which we call sym m etric inclusion-exclusion . W e study instances of sym m etric inclusion-exclusion in which thefunctions A and B havecom binatorialorprobabilistic interpretations.In particular,we study casesrelated to the P(cid:19)olya-Eggenberger urn m odelin which A ( S )and B ( S )depend only on the cardinality of S .
摘要。包含-不相容原理的一种形式断言，如果A和B是(cid:12)个集合的函数，则形式A (S) = P T (cid:18) S B (T)和B (S) = P T (cid:18) S ((cid:0) 1) j S j(cid:0) j T j A (T)是等价的。如果我们用((cid:0) 1) j S j B (S)来代替B (S)那么这些形式就变成了矩阵形式我们称之为矩阵的包容-排斥。我们研究了函数A和函数B具有二元或概率解释的系统包含-不相容的实例。特别地，我们研究了与P(cid:19)olya-Eggenberger模型相关的情况，其中A (S)和B (S)仅依赖于S的基数。
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