Description
A family $\mathcal{G}$ of sets is a weak copy of a poset $P$ if there is a bijection $f:P\rightarrow \mathcal{G}$ such that $p\leqslant q$ implies $f(p)\subseteq f(q)$. If $f$ satisfies $p\leqslant q$ if and only if $f(p)\subseteq f(q)$, then $\mathcal{G}$ is a strong copy of $P$. We study the anti-Ramsey numbers $ar(n,P), ar^*(n,P)$, the maximum number of colors used in a coloring of $2^{[n]}$ that does not admit a rainbow weak or strong copy of $P$, respectively. We establish connections to the well-studied extremal numbers $LA(n,P)$ and $LA^*(n,P)$ and determine asymptotically $ar(n,T)$ for all tree posets $T$ and $ar(n,O_{2k})$ for all crown posets $O_{2k}$.
Meeting ID: 895 2960 8626
Passcode: 627606
Link: https://us06web.zoom.us/j/89529608626?pwd=Y4YMgg9b3QvdPmbym7JPMTvyNMpPwb.1