E

DARE’s Dictionary of Environmental Sciences and Engineering Pub Date : 1900-01-01 DOI:10.1201/9781003211396-5

A. Mohamed, D. Chenaf, S. El-Shahed

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引用次数: 0

摘要

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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.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 .

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DARE’s Dictionary of Environmental Sciences and Engineering

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