Math Seminar Series
(Conferences / Seminars / Lectures)
Combinatorics and Graph Theory more information...
Nicholas Ovenhouse, University of Minnesota, will be speaking.
The presentation is titled "Laurent Polynomials from the Super Ptolemy Relation."
Contact Bruce E Sagan (email@example.com) for more information.
In classical geometry, Ptolemy's theorem relates the lengths of the sides of a quadrilateral to the lengths of the diagonals. Fixing a triangulation of a polygon, the length of any diagonal can be expressed (using Ptolemy's theorem) as a Laurent polynomial in the lengths of diagonals in the triangulation. There is a combinatorial description of the terms in this Laurent polynomial due to Schiffler, in terms of "T-paths". Recently, Penner and Zeitlin constructed a super-algebra from a triangulation, and an analogue of the Ptolemy relation in this situation. I will describe a generalization of "T-paths" which enumerate the terms in the corresponding super Laurent polynomials. This is joint work with Gregg Musiker and Sylvester Zhang.