Susanna Fishel, Arizona State University 

Title: Maximal length chains in lattices from graph associahedra

ABSTRACT: Tubing posets are orientations of the 1-skeleton of graph associahedra. For the complete graph on n vertices, the poset is the weak order on the symmetric group. When the graph is the path on n vertices, the poset is the Tamari lattice. We consider tubing posets of a family of graphs which interpolates between the complete and the path graphs. We discuss enumeration of the maximal length chains of the lattices corresponding to this graph family, first in terms of standard Young tableaux, then using quasisymmetric functions. I will also discuss recent results for more general graphs.  We assume no prior knowledge of any of the topics in the talk. This is joint work with Samantha Dahlberg and with Manuel Concha, Hsin-Chieh Liao, and Andrew Reimer-Berg.