Boolean Dimension and Local Dimension

Dimension is a standard and well-studied measure of complexity of posets. Recent research has provided many new upper bounds on the dimension for various structurally restricted classes of posets. Bounded dimension gives a succinct representation of the poset, admitting constant response time for qu...

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Bibliographic Details
Published inElectronic notes in discrete mathematics Vol. 61; pp. 1047 - 1053
Main Authors Trotter, William T., Walczak, Bartosz
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.08.2017
Subjects
order dimension
Partially ordered sets
Partially ordered sets
order dimension
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ISSN1571-0653
1571-0653
DOI10.1016/j.endm.2017.07.071

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Summary:Dimension is a standard and well-studied measure of complexity of posets. Recent research has provided many new upper bounds on the dimension for various structurally restricted classes of posets. Bounded dimension gives a succinct representation of the poset, admitting constant response time for queries of the form “is x>y?”. This application motivates looking for stronger notions of dimension, possibly leading to succinct representations for more general classes of posets. We focus on two: boolean dimension, introduced in the 1980s and revisited in recent research, and local dimension, a very new one. We determine precisely which values of dimension/boolean dimension/local dimension imply that the two other parameters are bounded. This is an extended abstract; see arXiv:1705.09167 for a full version.
ISSN:1571-0653
1571-0653
DOI:10.1016/j.endm.2017.07.071