On the number of families avoiding a subposet
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866911541922627584 |
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| author | Jiang, Tao Longbrake, Sean Yepremyan, Liana |
| author_facet | Jiang, Tao Longbrake, Sean Yepremyan, Liana |
| contents | In this paper we show that for any poset $P$ that is not an antichain, the number of induced $P$-free families in the Boolean lattice $2^{[n]}$ is at most $ 2^{O(\mathrm{La}^*(n,P))}$, where $\mathrm{La}^*(n,P)$ denotes the the largest size of an induced $P$-free subfamily of $2^{[n]}$. We also obtain related supersaturation results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_23431 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the number of families avoiding a subposet Jiang, Tao Longbrake, Sean Yepremyan, Liana Combinatorics 05D05 In this paper we show that for any poset $P$ that is not an antichain, the number of induced $P$-free families in the Boolean lattice $2^{[n]}$ is at most $ 2^{O(\mathrm{La}^*(n,P))}$, where $\mathrm{La}^*(n,P)$ denotes the the largest size of an induced $P$-free subfamily of $2^{[n]}$. We also obtain related supersaturation results. |
| title | On the number of families avoiding a subposet |
| topic | Combinatorics 05D05 |
| url | https://arxiv.org/abs/2603.23431 |