13 citations · 63 across the 13 of their papers we have counts for
5 papers · 1 filter
Realizing convex codes with axis-parallel boxes
Miguel Benitez, Siran Chen, Tianhui Han +3
Every ordered collection of sets in Euclidean space can be associated to a combinatorial code, which records the regions cut out by the sets in space. Given two ordered collections…
Recognizing and Realizing Inductively Pierced Codes
Ryan Curry, R. Amzi Jeffs, Nora Youngs +1
We prove algebraic and combinatorial characterizations of the class of inductively pierced codes, resolving a conjecture of Gross, Obatake, and Youngs. Starting from an algebraic i…
Planar convex codes are decidable
Boris Bukh, R. Amzi Jeffs
We show that every convex code realizable by compact sets in the plane admits a realization consisting of polygons, and analogously every open convex code in the plane can be reali…
Colorful Words and d-Tverberg Complexes
Florian Frick, R. Amzi Jeffs
We give a complete combinatorial characterization of weakly -Tverberg complexes. These complexes record which intersection combinatorics of convex hulls necessarily arise in any…
Enumeration of interval graphs and -representable complexes
Boris Bukh, R. Amzi Jeffs
For each fixed , we obtain asymptotic estimates for the number of -representable simplicial complexes on vertices as a function of . The case corresponds to…