Title: Introducing the interval poset associahedron
| Speaker: | Jette Gutzeit |
| Affiliation: | University of Greifswald |
| Location: | MC 5479 |
There will be a pre-seminar presenting relevant background at the beginning graduate level starting at 1pm.
Abstract: Given a permutation, we define its interval poset to be the set of all intervals ordered by inclusion. In this framework, a 'tube' is a convex connected subset, while a 'tubing' denotes a collection of tubes, that are pairwise either nested or disjoint. The interval poset associahedron is a polytope, whose faces correspond to proper tubes and whose vertices correspond to maximal tubings of the interval poset of a given permutation.
If we start with a simple permutation, the resulting interval poset associahedron will be isomorphic to the permutahedron. And if we consider inverse permutations, it turns out, that they yield identical associahedra.
If there is time, I will discuss another order on permutations, the Bruhat order, and compare it to the permutahedron.