|Date: Friday, October 11, 2013
Location: 3866 East Hall (4:10 PM to 5:00 PM)
Title: Linear extensions of posets to polytopes
Abstract: Postnikov showed that the set of vectors formed by entries on the diagonal of Shifted Young Tableaux of staircase shape is exactly the set of integer lattice points of an associahedron. In a joint work with Dorian Croitoru and Alexander Postnikov (arxiv.org:1309.1994), we generalize this to linear extensions of arbitrary poset P restricted to a subposet Q. We show that the possible vectors that can appear by restricting linear extensions of P to Q can be described by integer lattice points of some polytope, determined by P and Q.
In particular, when Q is a chain of P, Stanley showed that the number of linear extensions which restricts to a fixed vector can be interpreted as mixed volume of certain polytopes. I will also introduce a recent joint project with Jangsoo Kim on combinatorial interpretation of the Selberg integral, which is related to this interpretation.
Speaker: Suho Oh
Institution: U. Michigan