23 citations · 112 across the 26 of their papers we have counts for
5 papers · 1 filter
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…
Catalan numbers as discrepancies for a family of substitutions on infinite alphabets
Dirk Frettlöh, Alexey Garber, Neil Mañibo
In this work, we consider a class of substitutions on infinite alphabets and show that they exhibit a growth behaviour which is impossible for substitutions on finite alphabets. Wh…
Substitution tilings with transcendental inflation factor
Dirk Frettlöh, Alexey Garber, Neil Mañibo
For any , we construct a substitution on an infinite alphabet which gives rise to a substitution tiling with inflation factor . In particular, we obtain the first class of…
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…
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…