6 papers · 1 filter
Ample sets in Cartesian products
Victor Chepoi, Matthew Maat
Ample sets of hypercubes, introduced by A. Dress in 1995, constitute a combinatorial structure with rich properties and important examples. Ample sets can be characterized in a mul…
Geometry of ample/lopsided sets
Hans--Jürgen Bandelt, Victor Chepoi, Andreas Dress +1
Lopsided sets were introduced by Jim Lawrence in 1983 when he studied the subsets of that encode the intersection pattern of a convex set with the orthants of ${\…
Cell structure of mediangle graphs
Victor Chepoi, Anthony Genevois, Kolja Knauer
Mediangle graphs are a common generalization of median graphs (1-sekeleta of CAT(0) cube complexes) and Coxeter graphs (Cayley graphs of Coxeter systems). Answering a question moti…
Separation axiom for geodesic convexity in graphs
Victor Chepoi
Semispaces of a convexity space are maximal convex sets missing a point. The separation axiom asserts that any point and any convex set not containing…
Geometry of convex geometries
Jérémie Chalopin, Victor Chepoi, Kolja Knauer
We prove that any convex geometry on points and any ideal of can be realized as the intersection pat…
Boundary rigidity of finite CAT(0) cube complexes
Jérémie Chalopin, Victor Chepoi
In this note, we prove that finite CAT(0) cube complexes can be reconstructed from their boundary distances (computed in their 1-skeleta). This result was conjectured by Haslegrave…