Large subposets with small dimension

2014/03/31 by Benjamin Reiniger, Reiniger, Benjamin, Elyse Yeager +1
Mathematics · #06A07 #Advanced Topology and Set Theory #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory #Rings, Modules, and Algebras #math.CO #msc:06A07

paper · pdf · doi:10.48550/arxiv.1404.0021

4 pages

arxiv created 2014/03/31 · openalex publication_date 2014/03/31 · arxiv updated 2014/04/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Dorais asked for the maximum guaranteed size of a dimension d subposet of an n-element poset. A lower bound of order √(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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