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MIT Combinatorics Seminar

Bergman Complexes, Coxeter Arrangements, and Graph Associahedra

Lauren Williams (Massachusetts Institute of Technology)
lauren@math.mit.edu

Wednesday, April 6, 2005   4:15 pm    Room 2-338

ABSTRACT

The Bergman complex B(M) and the positive Bergman complex B+(M) of an oriented matroid M generalize to matroids the notions of tropical varieties and positive tropical varieties. Our main result is that if M is the oriented matroid of a Coxeter arrangement, then B(M) equals the nested set complex of that arrangement, and B+(M) is dual to the corresponding graph associahedron. This recovers Carr and Devadoss' tiling of the minimal blowup of a Coxeter complex by graph associahedra.

This is joint work with Federico Ardila and Vic Reiner.