Discrete CATS Seminar

Speaker:  Richard Ehrenborg

Title:         Uniform flag triangulations of the Legendre polytope

                (or how I spent my summer holiday)

Abstract:

The Legendre polytope, also known as the full root polytope of type A,

is the convex hull of all pairwise differences of the basis vectors.

We describe all flag triangulations of this polytope that are uniform,

that is, the edges are described in terms of the relative order of the

indices of the four basis vectors involved.  We obtain three classes

of triangulations: the lex class, the revlex class and the Simion

class. We also do a refined enumeration of faces of these

triangulations that keeps track of the number of forward and backward

arrows, and surprisingly the enumeration result only depends on which

class the triangulation belongs to.



Joint work with Gabor Hetyei and Margaret Readdy.