6 papers
Combinatorics of the Cosmohedron
Federico Ardila-Mantilla, Nima Arkani-Hamed, Carolina Figueiredo +1
The cosmohedron was recently proposed as a polytope underlying the cosmological wavefunction for theory. Its faces were conjectured to be in bijection with Matryos…
Tree metrics and log-concavity for matroids
Federico Ardila-Mantilla, Sergio Cristancho, Graham Denham +3
We show that a set function satisfies the gross substitutes property if and only if its homogeneous generating polynomial is a Lorentzian polynomial for all positive…
Markov chains, CAT(0) cube complexes, and enumeration: monotone paths in a strip mix slowly
Federico Ardila-Mantilla, Naya Banerjee, Coleson Weir
We prove that two natural Markov chains on the set of monotone paths in a strip mix slowly. To do so, we make novel use of the theory of non-positively curved (CAT(0)) cubical comp…
Intersection theory of matroids: variations on a theme
Federico Ardila-Mantilla
Chow rings of toric varieties, which originate in intersection theory, feature a rich combinatorial structure of independent interest. We survey four different ways of computing in…
The tropical critical points of an affine matroid
Federico Ardila-Mantilla, Christopher Eur, Raul Penaguiao
We prove that the number of tropical critical points of an affine matroid (M,e) is equal to the beta invariant of M. Motivated by the computation of maximum likelihood degrees, thi…
The Degree of a Tropical Root Surface of Type
Federico Ardila-Mantilla, Mont Cordero-Aguilar
We prove that the tropical surface of the root system has degree .