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Department of Applied Mathematics and Theoretical Physics

For a fixed poset $\mathcal P$ we say that a family $\mathcal F\subseteq\mathcal P([n])$ is $\mathcal P$-saturated if it does not contain an induced copy of $\mathcal P$, but whenever we add a new set to $\mathcal F$, we form an induced copy of $\mathcal P$. The size of the smallest such family is denoted by $\text{sat}^*(n, \mathcal P)$.\par For the diamond poset $\mathcal D_2$ (the two-dimensional Boolean lattice), while it is easy to see that the saturation number is at most $n+1$, the best known lower bound stayed at $O(\sqrt n)$ until last year. I will go over the proof that $sat^*(n,\mathcal D_2) = \Theta(n)$. This is joint work with Maria Ivan.


Further information

Time:

07May
May 7th 2026
14:30 to 15:30

Venue:

MR12

Speaker:

Sean Jaffe (Cambridge)

Series:

Combinatorics Seminar