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math.CO2022★ 1 cited
Flips in Two-dimensional Hypertriangulations
Herbert Edelsbrunner, Alexey Garber, Mohadese Ghafari +2
We study flips in hypertriangulations of planar points sets. Here a level- hypertriangulation of points in the planes is a subdivision induced by the projection of a -hyp…
math.CO2022
On Angles in Higher Order Brillouin Tessellations and Related Tilings in the Plane
Herbert Edelsbrunner, Alexey Garber, Mohadese Ghafari +2
For a locally finite set in , the order- Brillouin tessellations form an infinite sequence of convex face-to-face tilings of the plane. If the set is coarsely dens…
math.CO2022★ 1 cited
Brillouin Zones of Integer Lattices and Their Perturbations
Herbert Edelsbrunner, Alexey Garber, Mohadese Ghafari +3
For a locally finite set, , the -th Brillouin zone of is the region of points for which is the -th smallest…