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# Casey Tompkins, Ramsey numbers of Boolean lattices

## Tuesday, November 23, 2021 @ 4:30 PM - 5:30 PM KST

Room B232,
IBS (기초과학연구원)

The *poset Ramsey number* $R(Q_{m},Q_{n})$ is the smallest integer $N$ such that any blue-red coloring of the elements of the Boolean lattice $Q_{N}$ has a blue induced copy of $Q_{m}$ or a red induced copy of $Q_{n}$. Axenovich and Walzer showed that $n+2\le R(Q_{2},Q_{n})\le2n+2$. Recently, Lu and Thompson

improved the upper bound to $\frac{5}{3}n+2$. In this paper, we solve this problem asymptotically by showing that $R(Q_{2},Q_{n})=n+O(n/\log n)$.

Joint work with Dániel Grósz and Abhishek Methuku.