partial order

Noun

This text is extracted from the Wiktionary and it is available under the CC BY-SA 3.0 license | Terms and conditions | Privacy policy 0.020

Noun

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

- A
**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, LNCS 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.

- The vector-clock size necessary to characterize causality in a distributed computation is bounded by the dimension of the
**2008**, David Eppstein, Jean-Claude Falmagne, Sergei Ovchinnikov,*Media Theory: Interdisciplinary Applied Mathematics*, Springer, page 7 ↗,- Consider an arbitrary finite set
*S*. The family \mathcal{P} 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 previously-incomparable elements) or by removing one ordered pair (causing two previously related elements to become incomparable), without ever leaving the family \mathcal{P}.

- Consider an arbitrary finite set

- German: partielle Ordnung
- Russian: части́чный поря́док

This text is extracted from the Wiktionary and it is available under the CC BY-SA 3.0 license | Terms and conditions | Privacy policy 0.020