On the number of tournaments with prescribed score vector (Q1076686)
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scientific article; zbMATH DE number 3954954
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the number of tournaments with prescribed score vector |
scientific article; zbMATH DE number 3954954 |
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On the number of tournaments with prescribed score vector (English)
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1986
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Let f(S) denote the number of tournament matrices with non-increasing column sum vector \(S=(s_ 1,...,s_ n)\). The authors show that if f(S')\(\neq 0\) and S' is majorized by S where \(S\neq S'\), then \(f(S')>f(S)\). From this they deduce an improved lower bound for \(f(\bar S)\) where \(\bar S\) denotes the column sum vector of a regular (or an almost regular) tournament matrix.
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score vectors
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tournament matrices
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