Bergman complexes, coxeter arrangements, and graph associahedra

Federico Ardila, Victor Reiner, Lauren Williams

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Scopus citations

Abstract

Tropical varieties play an important role in algebraic geometry. The Bergman complex B(M) and the positive Bergman complex B +(M) of an oriented matroid M generalize to matroids the notions of the tropical variety and positive tropical variety associated to a linear ideal. Our main result is that if A is a Coxeter arrangement of type φ with corresponding oriented matroid Mφ, then B +(Mφ) is dual to the graph associahedron of type φ, and B(M) equals the nested set complex of A.

Original languageEnglish (US)
Title of host publicationFPSAC Proceedings 2005 - 17th Annual International Conference on Formal Power Series and Algebraic Combinatorics
Pages47-58
Number of pages12
StatePublished - Dec 1 2005
Event17th Annual International Conference on Algebraic Combinatorics and Formal Power Series, FPSAC'05 - Taormina, Italy
Duration: Jun 20 2005Jun 25 2005

Other

Other17th Annual International Conference on Algebraic Combinatorics and Formal Power Series, FPSAC'05
CountryItaly
CityTaormina
Period6/20/056/25/05

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