partial order
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See also: partialorder
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English[edit]
Noun[edit]
partial order (plural partial orders)
 (set theory, order theory) A binary relation that is reflexive, antisymmetric, and transitive.
 1986, Kenneth R. Goodearl, Partially Ordered Abelian Groups with Interpolation, American Mathematical Society, 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 DimensionBound Analysis, Patrick Amestoy, P. Berger, M. Daydé, I. Duff, V. Frayssé, L. Giraud, D. Ruiz (editors), EuroPar ’99 Parallel Processing: 5th International EuroPar Conference, Proceedings, Springer, LNCS 1685, page 144,
 The vectorclock size necessary to characterize causality in a distributed computation is bounded by the dimension of the partial order induced by that computation.
 2008, David Eppstein, JeanClaude Falmagne, Sergei Ovchinnikov, Media Theory: Interdisciplinary Applied Mathematics, Springer, page 7,
 Consider an arbitrary finite set S. The family of all strict partial orders (asymmetric, transitive, cf. 1.8.3, p. 14) on S enjoys a remarkable property: any partial order P can be linked to any other partial order P’ by a sequence of steps each of which consists of changing the order either by adding one ordered pair of elements of S (imposing an ordering between two previouslyincomparable elements) or by removing one ordered pair (causing two previously related elements to become incomparable), without ever leaving the family .
 1986, Kenneth R. Goodearl, Partially Ordered Abelian Groups with Interpolation, American Mathematical Society, Softcover reprint 2010, page xxi,
Synonyms[edit]
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Related terms[edit]
Translations[edit]
binary relation that is reflexive, antisymmetric, and transitive


Further reading[edit]
 Partially ordered set on Wikipedia.Wikipedia
 Complete partial order on Wikipedia.Wikipedia
References[edit]
 B. Dushnik and E. W. Miller, Partially Ordered Sets, Amer. J. Math. 63 (1941), 600610.