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Triangulations of root polytopes and subdivision algebras
Algebra & Discrete Mathematics| Speaker: | Karola Meszaros, MIT |
| Location: | 2112 MSB |
| Start time: | Fri, Apr 24 2009, 1:10PM |
Description
A type A_{n-1} root polytope is the convex hull in R^n of the origin
and a subset of the points e_i-e_j, 1\leq i< j \leq n. A collection
of triangulations of these polytopes can be described by reduced
forms of monomials in the subdivision algebra, which is a commutative
algebra generated by n^2 variables x_{ij}, for 1\leq i< j \leq n. In
a closely related noncommutative algebra, the reduced forms of
monomials are unique, and correspond to shellable triangulations
whose simplices are indexed by noncrossing alternating trees. Using
these triangulations Ehrhart polynomials are computed. The results
are extended to a more general family of polytopes.