Department of Mathematics

Combinatorics and Graph Theory

  •  Nicholas Ovenhouse, University of Minnesota
  •  Laurent Polynomials from the Super Ptolemy Relation
  •  02/10/2021
  •  3:00 PM - 3:50 PM
  •  Online (virtual meeting) (Virtual Meeting Link)
  •  Bruce E Sagan (bsagan@msu.edu)

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.

 

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