22 citations · 61 across the 10 of their papers we have counts for
10 papers
Bergman Complexes, Coxeter Arrangements, and Graph Associahedra
Federico Ardila, Victor Reiner, Lauren Williams
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…
The coefficients of a Fibonacci power series
Federico Ardila
We give a short proof of the result that all the coefficients of the series (1-x)(1-x^2)(1-x^3)(1-x^5)(1-x^8)(1-x^13)(1-x^21)... are equal to -1, 0, or 1, and most of them are equa…
Computing the Tutte polynomial of a hyperplane arrangement
Federico Ardila
We define and study the Tutte polynomial of a hyperplane arrangement. We introduce a method for computing it by solving an enumerative problem in a finite field. For specific arran…
Semimatroids and their Tutte polynomials
Federico Ardila
We define and study "semimatroids", a class of objects which abstracts the dependence properties of an affine hyperplane arrangement. We show that geometric semilattices are precis…
The number of halving circles
Federico Ardila
A set S of 2n+1 points in the plane is said to be in general position if no three points of S are collinear and no four are concyclic. A circle is called halving with respect to S…
The Positive Bergman Complex of an Oriented Matroid
Federico Ardila, Caroline Klivans, Lauren Williams
We study the positive Bergman complex B+(M) of an oriented matroid M, which is a certain subcomplex of the Bergman complex B(M) of the underlying unoriented matroid. The positive B…