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arXiv · 1705.09167

Boolean dimension and local dimension

William T. Trotter·Bartosz Walczak
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Abstract

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.

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William T. Trotter, Bartosz Walczak. 2017-05-25. Boolean dimension and local dimension. https://arxiv.org/abs/1705.09167

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