Local dimension of a Boolean lattice

Jędrzej Hodor; Jakub Sordyl

Local dimension of a Boolean lattice

Combinatorics 2025-12-16 v2

Authors: Jędrzej Hodor , Jakub Sordyl

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, Masa\v{r}\'ik, Shull, Smith, Uzzell, and Wang (Eur. J. Comb. 2020). We also study several related problems.

Keywords

set theory and dimension theory lattice theory

Cite

@article{arxiv.2512.10413,
  title  = {Local dimension of a Boolean lattice},
  author = {Jędrzej Hodor and Jakub Sordyl},
  journal= {arXiv preprint arXiv:2512.10413},
  year   = {2025}
}

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