Connecting two rings underlying the inclusion-exclusion principle (Q1069942)
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scientific article; zbMATH DE number 3933083
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Connecting two rings underlying the inclusion-exclusion principle |
scientific article; zbMATH DE number 3933083 |
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Connecting two rings underlying the inclusion-exclusion principle (English)
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1985
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In [\textit{O. D'Antona} and \textit{G.-C. Rota}, J. Comb. Theory, Ser. A 24, 395-402 (1978; Zbl 0392.05009)] two rings (the segment ring R and the square-free ring L) are described that provide an algebraic background for symbolic computations dealing with the inclusion-exclusion principle. In this paper a relationship between R and L is presented through two maps \(\phi\) : \(R\to L\) and \(\psi\) : \(L\to R\) which preserve the combinatorial interpretation of R and L, resp. and which are the inverse of each other.
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segment ring
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square-free ring
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symbolic computations
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inclusion- exclusion principle
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