UCLA

In this dissertation, we study poset associahedra and the combinatorics surrounding them. We provide a simple realization of poset associahedra and affine poset cyclohedra. Furthermore, we show that the f-vector of a poset associahedron depends only on the comparability graph of the poset. We investigate a connection between certain poset associahedra and the theory of stack-sorting. Finally, we show that when the poset is a rooted tree, the 1-skeleton of the poset associahedronorients to a lattice. These lattices generalize both the weak Bruhat order and the Tamari lattice.