69 citations · 209 across the 37 of their papers we have counts for
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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…
Subdominant matroid ultrametrics
Federico Ardila
Given a matroid M on the ground set E, the Bergman fan B(M), or space of M-ultrametrics, is a polyhedral complex in R^E which arises in several different areas, such as tropical al…
A tropical morphism related to the hyperplane arrangement of the complete bipartite graph
Federico Ardila
We undertake a combinatorial study of the piecewise linear map g : R^{2m+2n} --> R^{mn} which assigns to the four vectors a, A in R^m and b, B in R^n the m by n matrix given by g_{…