[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…
saved by
related reading
- [2604.06521] The Exact Saturation Number for the Diamondarxiv.org
- balogh containersarxiv.org
- nullstellensatzweb.math.princeton.edu
- Random Turán Problems for Graphs with a Vertex Complete to One Partarxiv.org
- 02_GyarfasLehel_AHellyTypeProblemInTrees.pdfusers.renyi.hu
- Forbidding Exactly One Hamming Distancearxiv.org
- Helly Theorems for Generalized Turán Problemsarxiv.org
- rainbow-turan-full-version.pdfpeople.maths.ox.ac.uk
- piercing intervals - gyarfasarxiv.org
- Exact Stability for Turan's Theoremarxiv.org
- 2-reachable subsets in two-colored graphsarxiv.org
- Induced rational exponents near twoarxiv.org