3 papers
math.MG2026
On polynomial inequalities for cone-volumes of polytopes
Tom Baumbach, Martin Henk
Motivated by the discrete logarithmic Minkowski problem we study for a given matrix its cone-volume set consisting of all the cone-volu…
math.MG2026
On the discrete logarithmic Minkowski problem in the plane
Tom Baumbach
The paper characterizes the convex hull of the closure of the cone-volume set $C_\cv(U)$, consisting of all cone-volume vectors of polygons with outer unit normals vectors containe…
math.CO2025
The canonical form, scissors congruence and adjoint degrees of polytopes
Tom Baumbach, Ansgar Freyer, Julian Weigert +1
We study the canonical form as a valuation in the context of scissors congruence for polytopes. We identify the degree of its numerator - the adjoint polynomial $\operatorname…