partial order
See also: partialorder
Contents
EnglishEdit
NounEdit
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,
SynonymsEdit
HypernymsEdit
HyponymsEdit
Related termsEdit
TranslationsEdit
binary relation that is reflexive, antisymmetric, and transitive


Further readingEdit
 Partially ordered set on Wikipedia.Wikipedia
 Complete partial order on Wikipedia.Wikipedia
ReferencesEdit
 B. Dushnik and E. W. Miller, Partially Ordered Sets, Amer. J. Math. 63 (1941), 600610.