Dimension is polynomial in height for posets with planar cover graphs

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research 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

Abstract

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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对于具有平面覆盖图的偏置集，维度是高度的多项式

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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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.

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