A set system
A set system is , if it does not contain a chain of length .
Our main result is the following:
Suppose that and are fixed positive integers, where is even with and is large enough.
If is a -intersecting -Sperner family, then has size at most the size of the sum of
layers, of sizes .
This bound is best possible. The case whenis odd remains open.
Joint work with Józsi Balogh and Will Linz.