17 citations · 73 across the 26 of their papers we have counts for
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Enumerating neighborly polytopes and oriented matroids
Hiroyuki Miyata, Arnau Padrol
Neighborly polytopes are those that maximize the number of faces in each dimension among all polytopes with the same number of vertices. Despite their extremal properties they form…
Universality theorems for inscribed polytopes and Delaunay triangulations
Karim A. Adiprasito, Arnau Padrol, Louis Theran
We prove that every primary basic semialgebraic set is homotopy equivalent to the set of inscribed realizations (up to Möbius transformation) of a polytope. If the semialgebraic se…
Polygons as sections of higher-dimensional polytopes
Arnau Padrol, Julian Pfeifle
We show that every heptagon is a section of a -polytope with vertices. This implies that every -gon with can be obtained as a section of a $(2+\lfloor\frac{n}{7…
Dyck path triangulations and extendability
Cesar Ceballos, Arnau Padrol, Camilo Sarmiento
We introduce the Dyck path triangulation of the cartesian product of two simplices . The maximal simplices of this triangulation are given by Dyck paths, and…
The universality theorem for neighborly polytopes
Karim A. Adiprasito, Arnau Padrol
In this note, we prove that every open primary basic semialgebraic set is stably equivalent to the realization space of an even-dimensional neighborly polytope. This in particular…