## 218 Citations

Bergman complexes, Coxeter arrangements, and graph associahedra.

- Mathematics
- 2005

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…

COXETER ARRANGEMENTS , AND GRAPH ASSOCIAHEDRA

- Mathematics
- 2006

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…

Complexes of trees and nested set complexes

- Mathematics
- 2004

We exhibit an identity of abstract simplicial complexes between the well-studied complex of trees Tn and the reduced minimal nested set complex of the partition lattice. We conclude that the order…

Matroid polytopes, nested sets and Bergman fans

- Mathematics
- 2004

The tropical variety defined by linear equations with constant coefficients is the Bergman fan of the corresponding matroid. Building on a self-contained introduction to matroid polytopes, we present…

Lagrangian geometry of matroids

- Mathematics
- 2020

We introduce the conormal fan of a matroid M, which is a Lagrangian analog of the Bergman fan of M. We use the conormal fan to give a Lagrangian interpretation of the Chern-Schwartz-MacPherson cycle…

The Orlik-Solomon algebra and the Bergman fan of a Matroid

- Mathematics
- 2013

Given a matroid M one can define its Orlik-Solomon algebra OS(M) and the Bergman fan �0(M). On the other hand to any rational polyhedral fan � one can associate its tropical homology and cohomology…

Tropical fans and normal complexes

- Mathematics
- 2021

Associated to any divisor in the Chow ring of a simplicial tropical fan, we construct a family of polytopal complexes, called normal complexes, which we propose as an analogue of the well-studied…

## References

SHOWING 1-10 OF 24 REFERENCES

The tropical Grassmannian

- Mathematics
- 2003

In tropical algebraic geometry, the solution sets of polynomial equations are piecewise-linear. We introduce the tropical variety of a polynomial ideal, and we identify it with a polyhedral…

The Pre-WDVV Ring of Physics and its Topology

- Mathematics
- 2005

We show how a simplicial complex arising from the WDVV (Witten-Dijkgraaf-Verlinde-Verlinde) equations of string theory is the Whitehouse complex. Using discrete Morse theory, we give an elementary…

Homotopy of Non-Modular Partitions and the Whitehouse Module

- Mathematics
- 1999

AbstractWe present a class of subposets of the partition lattice Πn with the following property: The order complex is homotopy equivalent to the order complex of Πn − 1, and the Sn-module structure…

Local structure of some Out ( F n )-complexes

- Mathematics
- 1990

In previous work of the author and M. Culler, contractible simplicial complexes were constructed on which the group of outer automorphisms of a free group of finite rank acts with finite stabilizers…

Geometry of the Space of Phylogenetic Trees

- MathematicsAdv. Appl. Math.
- 2001

We consider a continuous space which models the set of all phylogenetic trees having a fixed set of leaves. This space has a natural metric of nonpositive curvature, giving a way of measuring…

Non-archimedean amoebas and tropical varieties

- Mathematics
- 2004

Abstract We study the non-archimedean counterpart to the complex amoeba of an algebraic variety, and show that it coincides with a polyhedral set defined by Bieri and Groves using valuations. For…

Shellability of Complexes of Trees

- MathematicsJ. Comb. Theory, Ser. A
- 1998

We show that for allk?1 andn?0 the simplicial complexes T(k)nof all leaf-labelled trees withnk+2 leaves and all interior vertices of degreeskl+2 (l?1) are shellable. This yields a direct…

The logarithmic limit-set of an algebraic variety

- Mathematics
- 1971

Let C be the field of complex numbers and V a subvariety of (C{O})n. To study the "exponential behavior of Vat infinity", we define V(a) as the set of limitpoints on the unit sphere Sn-1 of the set…

The geometry of the set of characters iduced by valuations.

- Mathematics
- 1984

1. 1. Let k be a field endowed with a real valuation v: k-^R^. That is, a map which assigns to each non-zero element a e k a real number v (a) and to 0 e k the symbol i;(0) = GO, such that v(ab) =…