On the enumeration of bipartite simple games (Q2022519)
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scientific article; zbMATH DE number 7341238
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the enumeration of bipartite simple games |
scientific article; zbMATH DE number 7341238 |
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On the enumeration of bipartite simple games (English)
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29 April 2021
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The authors provide a classification of all bipartite simple games, up to isomorphism. The obtained classification can be implemented in an algorithm able to enumerate bipartite simple games. These numbers provide some light on enumerations of several subclasses of bipartite simple games, for which formulas are obtained. They also deduce a procedure for bipartite non-complete games, which allows enumerating the number of bipartite simple games. Several formulas are obtained by the authors, in particular polynomial expressions for the number of bicameral meet games and the number of bicameral join games, two of the most widely used voting systems.
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Dedekind numbers and simple games
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inequivalent monotonic Boolean functions
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classification of bipartite simple games and bipartite Boolean functions
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enumeration of bipartite simple games and bipartite Boolean functions
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enumeration of the bicameral meet and bicameral join voting systems
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