English

Flips in Two-dimensional Hypertriangulations

Combinatorics 2025-09-29 v5 Metric Geometry

Abstract

We study flips in hypertriangulations of planar points sets. Here a level-kk hypertriangulation of nn points in the planes is a subdivision induced by the projection of a kk-hypersimplex, which is the convex hull of the barycenters of the (k1)(k-1)-dimensional faces of the standard (n1)(n-1)-simplex. In particular, we introduce four types of flips and prove that the level-2 hypertriangulations are connected by these flips.

Keywords

Cite

@article{arxiv.2212.11380,
  title  = {Flips in Two-dimensional Hypertriangulations},
  author = {Herbert Edelsbrunner and Alexey Garber and Mohadese Ghafari and Teresa Heiss and Morteza Saghafian},
  journal= {arXiv preprint arXiv:2212.11380},
  year   = {2025}
}
R2 v1 2026-06-28T07:47:52.920Z