17 citations · 73 across the 26 of their papers we have counts for
4 papers · 1 filter
Geometry of -Tamari lattices in types and
Cesar Ceballos, Arnau Padrol, Camilo Sarmiento
In this paper, we exploit the combinatorics and geometry of triangulations of products of simplices to derive new results in the context of Catalan combinatorics of -Tamari latt…
Colorful simplicial depth, Minkowski sums, and generalized Gale transforms
Karim Adiprasito, Philip Brinkmann, Arnau Padrol +3
The colorful simplicial depth of a collection of d+1 finite sets of points in Euclidean d-space is the number of choices of a point from each set such that the origin is contained…
Extension complexity of polytopes with few vertices or facets
Arnau Padrol
We study the extension complexity of polytopes with few vertices or facets. On the one hand, we provide a complete classification of -polytopes with at most vertices accor…
Extension complexity and realization spaces of hypersimplices
Francesco Grande, Arnau Padrol, Raman Sanyal
The (n,k)-hypersimplex is the convex hull of all 0/1-vectors of length n with coordinate sum k. We explicitly determine the extension complexity of all hypersimplices as well as of…