Nagy Kartal: Chain-dependent families

Abstract:
A condition is called chain-dependent, if it is satisfied for a family if and only if it is satisfied for its intersections with the $n!$ full chains. We introduce a method to handle problems with such conditions, then show how it can be used to prove three classic theorems. Then, a theorem about families containing no two sets such that $A\subset B$ and $\lambda \cdot |A| \le |B|$ is proved. Finally, we investigate problems where instead of the size of the family, the number of $\ell$-chains is maximized. This is joint work with Daniel Nagy.

The lecture can be followed by zoom:

• Zoom link: https://us06web.zoom.us/j/89547528463?pwd=Z0ZiU1NXZkpyY2NNUy9PYXptY0JuZz09
• Meeting ID: 895 4752 8463
• Passcode: 890941