# Induced Poset Saturation

• Maria Ivan (Cambridge)
• Thursday 11 November 2021, 14:30-15:30
• MR12.

Given a fixed poset $\mathcal P$, we say that a family $\mathcal F$ of subsets of $[n]$ is \textit{$\mathcal P$-free} if it does not contain an (induced) copy of$\mathcal P$. And we say that $\mathcal F$ is \textit{$\mathcal P$-saturated} if it is maximal $\mathcal P$-free. How small can a $\mathcal P$-saturated family be? The smallest such size is the \textit{induced saturation number} of $\mathcal P$, $\text{sat}$. Even for very small posets, the question of the growth speed of $\text{sat}(n,\mathcal P)$ seems to be hard. We present background on this problem and some recent results.

This talk is part of the Combinatorics Seminar series.