对于具有平面覆盖图的偏置集，维度是高度的多项式

IF 1.2 1区数学 Q1 MATHEMATICS

Journal of Combinatorial Theory Series B Pub Date : 2023-11-29 DOI:10.1016/j.jctb.2023.10.009

Jakub Kozik , Piotr Micek , William T. Trotter

引用次数: 8

摘要

我们证明了具有平面覆盖图的高度为h的偏置集的维数为O(h6)。以前，最佳上界为2O(h3)。平面性在我们的论证中起着关键作用，因为存在这样的假设集(1)维度在高度上是指数级的，(2)封面图不包括K5作为次要项。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Dimension is polynomial in height for posets with planar cover graphs

We show that height h posets that have planar cover graphs have dimension $O (h^{6})$ . Previously, the best upper bound was $2^{O (h^{3})}$ . Planarity plays a key role in our arguments, since there are posets such that (1) dimension is exponential in height and (2) the cover graph excludes $K_{5}$ as a minor.

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来源期刊

Journal of Combinatorial Theory Series B 数学-数学

CiteScore

2.70

自引率

14.30%

发文量

审稿时长

6-12 weeks

期刊介绍： The Journal of Combinatorial Theory publishes original mathematical research dealing with theoretical and physical aspects of the study of finite and discrete structures in all branches of science. Series B is concerned primarily with graph theory and matroid theory and is a valuable tool for mathematicians and computer scientists.