Combinatorics and Algebra Seminar- Order polynomial product formulas and poset dynamics
Wednesday, October 15, 2025
4:00 pm - 5:00 pm
Title: Order polynomial product formulas and poset dynamics
Speaker: Sam Hopkins, Howard University
Date and time: Wednesday 10/15, 4–5pm
Place: Phillips 108
Abstract: I'll present a heuristic for finding special families of partially ordered sets. The heuristic says that the posets with order polynomial product formulas are the same as the posets with good dynamical behavior. Here the order polynomial is a certain enumerative invariant of the poset. Meanwhile, the dynamics includes promotion of linear extensions, and rowmotion of order ideals and P-partitions. The heuristic is useful both for finding new posets with good enumerative behavior and for finding new posets with good dynamical behavior. It also directly leads to many remarkable cyclic sieving conjectures.
Speaker: Sam Hopkins, Howard University
Date and time: Wednesday 10/15, 4–5pm
Place: Phillips 108
Abstract: I'll present a heuristic for finding special families of partially ordered sets. The heuristic says that the posets with order polynomial product formulas are the same as the posets with good dynamical behavior. Here the order polynomial is a certain enumerative invariant of the poset. Meanwhile, the dynamics includes promotion of linear extensions, and rowmotion of order ideals and P-partitions. The heuristic is useful both for finding new posets with good enumerative behavior and for finding new posets with good dynamical behavior. It also directly leads to many remarkable cyclic sieving conjectures.