Sebastian Manecke

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20182022

most citedInscribable Fans II: Inscribed zonotopes, simplicial arrangements, and reflection groups

1 citations · 1 across the 3 of their papers we have counts for

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math.CO2021

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…

math.CO2020

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…

math.CO2020

Angle sums of simplicial polytopes

Sebastian Manecke

The interior angle vector ( $α$ -vector) of a polytope is a metric analogue of the $f$ -vector in which faces are weighted by their solid angle. For simplicial polytopes, Dehn…

math.CO2019

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…

math.CO2018

S-hypersimplices, pulling triangulations, and monotone paths

Sebastian Manecke, Raman Sanyal, Jeonghoon So

An $S$ -hypersimplex for $S \subseteq {0, 1, \dots, d}$ is the convex hull of all $0/1$ -vectors of length $d$ with coordinate sum in $S$ . These polytopes generalize the classical hy…

math.CO2018

Generalized angle vectors, geometric lattices, and flag-angles

Spencer Backman, Sebastian Manecke, Raman Sanyal

Interior and exterior angle vectors of polytopes capture curvature information at faces of all dimensions and can be seen as metric variants of $f$ -vectors. In this context, Gram's…