Partial order

English

Hasse diagram of a set with the partial order "is divisible by"

Noun

1. Template:Lb Template:Lb An ordering of the elements of a collection that behaves like that of the natural numbers by size, except that some elements may not be comparable (if all elements are comparable, it is called a total order); Template:Lb a binary relation that is reflexive, antisymmetric, and transitive.
   • 1986, Kenneth R. Goodearl, Partially Ordered Abelian Groups with Interpolation, Template:W, Softcover reprint 2010, page xxi,

     A partial order on a set X is any reflexive, antisymmetric, transitive relation on X. In most cases, partial orders are denoted ≤.

   • 1999, Paul A. S. Ward, An Online Algorithm for Dimension-Bound Analysis, Patrick Amestoy, P. Berger, M. Daydé, I. Duff, V. Frayssé, L. Giraud, D. Ruiz (editors), Euro-Par ’99 Parallel Processing: 5th International Euro-Par Conference, Proceedings, Springer, Template:W 1685, page 144,

     The vector-clock size necessary to characterize causality in a distributed computation is bounded by the dimension of the partial order induced by that computation.

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Synonyms

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Hypernyms

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Hyponyms

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  • well-order

Related terms

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Translations

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References

• B. Dushnik and E. W. Miller, Partially Ordered Sets, Amer. J. Math. 63 (1941), 600-610.

Further reading

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