1 citations · 1 across the 3 of their papers we have counts for
6 papers
Inscribable Fans II: Inscribed zonotopes, simplicial arrangements, and reflection groups
Sebastian Manecke, Raman Sanyal
An arrangement of hyperplanes is strongly inscribable if it has an inscribed (or ideal hyperbolic) zonotope. We characterize inscribed zonotopes and prove that the family of strong…
Fan Valuations and spherical intrinsic volumes
Spencer Backman, Sebastian Manecke, Raman Sanyal
We generalize valuations on polyhedral cones to valuations on fans. For fans induced by hyperplane arrangements, we show a correspondence between rotation-invariant valuations and…
Coprime Ehrhart theory and counting free segments
Sebastian Manecke, Raman Sanyal
A lattice polytope is "free" (or "empty") if its vertices are the only lattice points it contains. In the context of valuation theory, Klain (1999) proposed to study the functions…
Angle sums of simplicial polytopes
Sebastian Manecke
The interior angle vector (-vector) of a polytope is a metric analogue of the -vector in which faces are weighted by their solid angle. For simplicial polytopes, Dehn…
Eberhard-type theorems with two kinds of polygons
Sebastian Manecke
Eberhard-type theorems are statements about the realizability of a polytope (or more general polyhedral maps) given the valency of its vertices and sizes of its polygonal faces up…
S-hypersimplices, pulling triangulations, and monotone paths
Sebastian Manecke, Raman Sanyal, Jeonghoon So
An -hypersimplex for is the convex hull of all -vectors of length with coordinate sum in . These polytopes generalize the classical hy…