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arXiv · 2603.23431

On the number of families avoiding a subposet

Tao Jiang·Sean Longbrake·Liana Yepremyan
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Abstract

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.

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Tao Jiang, Sean Longbrake, Liana Yepremyan. 2026-03-24. On the number of families avoiding a subposet. https://arxiv.org/abs/2603.23431

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