41 citations · 74 across the 5 of their papers we have counts for
9 papers
Varieties of Tropical Ideals are Balanced
Diane Maclagan, Felipe Rincón
Tropical ideals, introduced in arXiv:1609.03838, define subschemes of tropical toric varieties. We prove that the top-dimensional parts of their varieties are balanced polyhedral c…
Positively Hyperbolic Varieties, Tropicalization, and Positroids
Felipe Rincón, Cynthia Vinzant, Josephine Yu
A variety of codimension in complex affine space is called positively hyperbolic if the imaginary part of any point in it does not lie in any positive linear subspace of dimens…
Tropical ideals do not realise all Bergman fans
Jan Draisma, Felipe Rincón
Every tropical ideal in the sense of Maclagan-Rincón has an associated tropical variety, a finite polyhedral complex equipped with positive integral weights on its maximal cells. T…
Tropical Ideals
Diane Maclagan, Felipe Rincón
We introduce and study a special class of ideals, called tropical ideals, in the semiring of tropical polynomials, with the goal of developing a useful and solid algebraic foundati…
Compressed sensing of data with a known distribution
Mateo Díaz, Mauricio Junca, Felipe Rincón +1
Compressed sensing is a technique for recovering an unknown sparse signal from a small number of linear measurements. When the measurement matrix is random, the number of measureme…
Tropical schemes, tropical cycles, and valuated matroids
Diane Maclagan, Felipe Rincón
We show that the weights on a tropical variety can be recovered from the tropical scheme structure proposed by the Giansiracusas in arXiv:1308.0042, so there is a well-defined Hilb…
Positively oriented matroids are realizable
Federico Ardila, Felipe Rincón, Lauren Williams
We prove da Silva's 1987 conjecture that any positively oriented matroid is a positroid; that is, it can be realized by a set of vectors in a real vector space. It follows from thi…
Positroids and non-crossing partitions
Federico Ardila, Felipe Rincón, Lauren Williams
We investigate the role that non-crossing partitions play in the study of positroids, a class of matroids introduced by Postnikov. We prove that every positroid can be constructed…
Valuations for matroid polytope subdivisions
Federico Ardila, Alex Fink, Felipe Rincón
We prove that the ranks of the subsets and the activities of the bases of a matroid define valuations for the subdivisions of a matroid polytope into smaller matroid polytopes.