# partially ordered set

(redirected from Posets)

## partially ordered set

[′pär·shə·lē ¦ōr·dərd ′set]
(mathematics)
A set on which a partial order is defined. Also known as poset.

## partially ordered set

References in periodicals archive ?
In a standard way, every poset can be considered as a category, and monotone mappings between posets can be considered as functors.
It develops that there is a close connection between algebraic and combinatorial invariants of these monoids: certain homological invariants of the monoid algebra coincide with the cohomology of order complexes of posets naturally associated with a monoid.
The SheafSystem(TM) uses advanced mathematics - posets, lattices, sheaves, and fiber bundles - to revolutionize data management for this highly structured region of the data complexity spectrum.
Waszkiewicz: Partial metrizebility of continuous posets, Math.
He covers Konig's Lemma (including two ways of looking at mathematics), posets and maximal elements (including order), formal systems (including post systems and compatibility as bonuses), deduction in posets (including proving statements about a poset), Boolean algebras, propositional logic (including a system for proof about propositions), valuations (including semantics for propositional logic), filters and ideals (including the algebraic theory of Boolean algebras), first-order logic, completeness and compactness, model theory (including countable models) and nonstandard analysis (including infinitesimal numbers).
Final segments play for posets the same role than ideals for rings.
Quasisymmetric functions were first defined by Gessel [Ges84] in the 1980s as weight enumerators for labelled posets.
Waszkiewicz: Partial metrisability of continuous posets, Math.
categories with morphism posets and monotone composition, and monotone functors, respectively.
For the entirety of this paper let us assume that all our posets are finite and contain a [?
These categories are enriched over the category Pos of posets (with order preserving mappings as morphisms), that is, the morphism sets are posets with respect to pointwise order.
For some family of ranked posets P, it is natural to consider an analog [N.

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