Abstract
Dorais asked for the maximum guaranteed size of a subposet with dimension at most d of an n-element poset. A lower bound of order \(\sqrt {n}\) was found by Goodwillie. We provide a sublinear upper bound for each d. For d = 2, our bound is n 0.8295.
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Reiniger, B., Yeager, E. Large Subposets with Small Dimension. Order 33, 81–84 (2016). https://doi.org/10.1007/s11083-015-9353-0
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DOI: https://doi.org/10.1007/s11083-015-9353-0