Xiao Jimeng: Largest family without a pair of posets

Let Y be the poset with elements a, b , c, d such that a < b < c, d,

and let Y' be the same poset but all relations reversed. We say a family of

subsets of [n] contains a copy of Y on three consecutive levels if it contains

4 subsets A, B, C, D such that A < B < C, D and |D| = |C| = |B|+1 =|A|+ 2.

We denote by $La_{c}(n, Y, Y')$ the largest size of a family of subsets of [n]

without both Y and Y'on three consecutive levels. In this talk, we will show

the exact value of $La _{c}(n, Y, Y')$.