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Beatpath: Difference between revisions
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Updated link to [http://en.wikipedia.org/wiki/Preorder#Constructions natural partial order generated from that preorder] in order to reflect reorganization of that Wikipedia article
imported>DCary (Fix links to examples and algorithms so they use standard capitalization) |
imported>DCary m (Updated link to [http://en.wikipedia.org/wiki/Preorder#Constructions natural partial order generated from that preorder] in order to reflect reorganization of that Wikipedia article) |
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:(X,Y) is in ''Beat'' if and only if candidate X pair-wise beats candidate Y
The [http://en.wikipedia.org/wiki/Binary_relation#Operations_on_binary_relations transitive-reflexive closure] of ''Beat'' is a [http://en.wikipedia.org/wiki/Preorder preorder] on the set of candidates, and the [http://en.wikipedia.org/wiki/Preorder#
Typically, ''Beat'' is [http://en.wikipedia.org/wiki/Irreflexive irreflexive] and [http://en.wikipedia.org/wiki/Antisymmetric_relation anti-symmetric], but this formulation does not depend on those properties. When ''Beat'' is irreflexive and anti-symmetric, the cycle equivalence classes can have 1, 3, or more candidates, but never exactly 2 candidates.
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