[2603.23431] On the number of families avoiding a subposet
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.
On the number of families avoiding a subposet Tao Jiang ∗ Sean Longbrake † Liana Yepremyan ‡ arXiv:2603.23431v1 [math.CO] 24 Mar 2026 March 25, 2026 Abstract In this paper we show that for any poset P that is not an antichain, the number of…
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