تسجيل الدخول

تسجيل

Complete Product

المؤلف:  Comtet, L

المصدر:  Advanced Combinatorics: The Art of Finite and Infinite Expansions, rev. enl. ed. Dordrecht, Netherlands: Reidel

الجزء والصفحة:  p. 186

11-1-2022

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Complete Product

The complete products of a Boolean algebra of subsets generated by a set {A_k}_(k=1)^p" src="https://mathworld.wolfram.com/images/equations/CompleteProduct/Inline1.gif" style="height:19px; width:41px" /> of cardinal number  are the  Boolean functions

(1)

where each  may equal  or its complement . For example, the  complete products of {A_1,A_2,A_3}" src="https://mathworld.wolfram.com/images/equations/CompleteProduct/Inline8.gif" style="height:16px; width:94px" /> are

(2)

Each Boolean function has a unique representation (up to order) as a union of complete products. For example,

			(3)
			(4)
			(5)

(Comtet 1974, p. 186).

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REFERENCES:

Comtet, L. Advanced Combinatorics: The Art of Finite and Infinite Expansions, rev. enl. ed. Dordrecht, Netherlands: Reidel, p. 186, 1974.