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arXiv · 2512.10413

Local dimension of a Boolean lattice

Jędrzej Hodor·Jakub Sordyl
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Abstract

For every integer $n$ with $n \geq 4$, we prove that the local dimension of a poset consisting of all the subsets of $\{1,\dots,n\}$ equipped with the inclusion relation is strictly less than $n$, answering a question of Kim, Martin, Masařík, Shull, Smith, Uzzell, and Wang (Eur. J. Comb. 2020). We also study several related problems.

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Jędrzej Hodor, Jakub Sordyl. 2025-12-15. Local dimension of a Boolean lattice. https://arxiv.org/abs/2512.10413

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