Boolean dimension and local dimension
Combinatorics
2017-05-26 v1 Discrete Mathematics
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 ?". 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.
Cite
@article{arxiv.1705.09167,
title = {Boolean dimension and local dimension},
author = {William T. Trotter and Bartosz Walczak},
journal= {arXiv preprint arXiv:1705.09167},
year = {2017}
}