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.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.

partially ordered set

References in periodicals archive ?
For instance, for real and complex hyperplane face monoids, the subposets B[X, Y) are the face posets of spheres (see [section][section] 5.3-5.4).
[2] Das, Tarun, On posets of certain classes of maps, Math.
Theorem 3.4 s[[LAMBDA].sub.y]s that if a permutation has a principal order ideal that can decompose nontrivially into a direct product of posets, then there are ways for that principal order ideal to appear as an interval in an "interesting" way, as described in Remark 1.6.
Quasisymmetric functions were first defined by Gessel [Ges84] in the 1980s as weight enumerators for labelled posets. Since then, the Hopf algebra of quasisymmetric functions, QSym, has arisen in a variety of contexts including the study of Lie representations, riffle shuffles, random walks, and the representation theory of Hecke algebras.
Matveev presents a set of problems in combinatorics, combinatorial optimization, posets, graphs, elementary number theory, and other areas that represent a far-reaching extension of the arsenal of committee methods in pattern recognition.
The following notion of regularity is borrowed from Alfuraidan and Khamsi in [16] that considered it for posets.
Subsequently, a new proof was found by Bjorner and Wachs [2, Theorem 6.1] using their theory of CL-shellable posets. A simpler proof of Farmer's result was given by Kerz [6, Theorem 1] in 2004.
In section 2, one considers examples and properties of the Stokes posets. In particular, one proves that the Tamari lattice is recovered as a special case, for a very regular quadrangulation.
In a standard way, every poset can be considered as a category, and monotone mappings between posets can be considered as functors.
The former class is associated to finite posets, while the latter corresponds to dedekind complete finite posets.
further generalized the concept of countably approximating lattices to the concept of countably approximating posets and characterized countably approximating posets via the cr-Scott topology.

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