6 papers
The graph of implicit edge dependencies for indecomposability and beyond
Arnau Padrol, Germain Poullot
A polytope is called indecomposable if it cannot be expressed nontrivially as a Minkowski sum of other polytopes. Since Gale introduced the concept in 1954, several increasingly st…
Indecomposability of 0/1-polytopes
Akihiro Higashitani, Arnau Padrol, Raman Sanyal
We prove that every 0/1-polytope has a unique Minkowski decomposition into indecomposable polytopes, up to translation of summands. The summands lie in pairwise orthogonal subspace…
Many rays of the submodular cone
Georg Loho, Arnau Padrol, Germain Poullot
The study of the cone of submodular functions goes back to Jack Edmonds' seminal 1970 paper, which already highlighted the difficulty of characterizing its extreme rays. Since then…
Framed Polytopes and Higher Categories
Guillaume Laplante-Anfossi, Anibal M. Medina-Mardones, Arnau Padrol
In the early 1990s, Kapranov and Voevodsky proposed a geometric method for constructing higher-categorical pasting diagrams from generically framed convex polytopes. This work revi…
Facial nested complexes and acyclonestohedra
Chiara Mantovani, Arnau Padrol, Vincent Pilaud
We study nested complexes of building sets on the Las Vergnas face lattices of oriented matroids. Such a nested complex is the face lattice of an oriented matroid, obtained by iter…
An asymptotic rigidity property from the realizability of chirotope extensions
Xavier Goaoc, Arnau Padrol
Let be a finite full-dimensional point configuration in . We show that if a point configuration has the property that all finite chirotopes realizable by addi…