On the number of antichains in $\{0,1,2\}^n$
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866914248437792768 |
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| author | Jenssen, Matthew Park, Jinyoung Sarantis, Michail |
| author_facet | Jenssen, Matthew Park, Jinyoung Sarantis, Michail |
| contents | We provide precise asymptotics for the number of antichains in the poset $\{0,1,2\}^n$, answering a question of Sapozhenko. Finding improved estimates for this number was also a problem suggested by Noel, Scott, and Sudakov, who obtained asymptotics for the logarithm of the number. Key ingredients for the proof include a graph-container lemma to bound the number of expanding sets in a class of irregular graphs, isoperimetric inequalities for generalizations of the Boolean lattice, and methods from statistical physics based on the cluster expansion. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_07650 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the number of antichains in $\{0,1,2\}^n$ Jenssen, Matthew Park, Jinyoung Sarantis, Michail Combinatorics We provide precise asymptotics for the number of antichains in the poset $\{0,1,2\}^n$, answering a question of Sapozhenko. Finding improved estimates for this number was also a problem suggested by Noel, Scott, and Sudakov, who obtained asymptotics for the logarithm of the number. Key ingredients for the proof include a graph-container lemma to bound the number of expanding sets in a class of irregular graphs, isoperimetric inequalities for generalizations of the Boolean lattice, and methods from statistical physics based on the cluster expansion. |
| title | On the number of antichains in $\{0,1,2\}^n$ |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2601.07650 |