Local dimension of a Boolean lattice
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915674544144384 |
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| author | Hodor, Jędrzej Sordyl, Jakub |
| author_facet | Hodor, Jędrzej Sordyl, Jakub |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_10413 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Local dimension of a Boolean lattice Hodor, Jędrzej Sordyl, Jakub Combinatorics 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. |
| title | Local dimension of a Boolean lattice |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2512.10413 |