Local dimension of a Boolean lattice

Published 11 Dec 2025 in math.CO | (2512.10413v1)

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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