Georgia Institute of Technology College of Sciences

We say a partially ordered set $P$ is a tree poset if its Hasse diagram, the graph drawn by joining $x$ with $y$ if there is no $z$ such that $x > z > y$, is a tree. In this talk, we will be discussing a tool for embedding tree posets $P$ into subsets of the Boolean lattice, and some applications of it to counting copies of $P$ in subsets of the Boolean lattice, counting $P$-free subsets of the Boolean lattice, and largest $P$-free subsets of the Boolean lattice. This talk is based on joint work with Tao Jiang, Sam Spiro, and Liana Yepremyan.