6 papers
Exponential valuations on lattice polygons valued at formal power series
Karoly J. Boroczky, Matyas Domokos, Ansgar Freyer +2
We classify valuations on lattice polygons with values in the ring of formal power series that commute with the action of the affine unimodular group. A typical example of such val…
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{…
Pal's isominwidth problem in the hyperbolic space
Karoly J. Boroczky, Ansgar Freyer, Adam Sagmeister
The paper focuses on possible hyperbolic versions of the classical Pal isominwidth inequality in R^2 from 1921, which states that for a fixed minimal width, the regular triangle ha…
The isominwidth problem on the 2-sphere
Ansgar Freyer, Ádám Sagmeister
Pál's isominwidth theorem states that for a fixed minimal width, the regular triangle has minimal area. A spherical version of this theorem was proven by Bezdek and Blekherman, if…
Exponential valuations on lattice polygons
Karoly J. Boroczky, Matyas Domokos, Ansgar Freyer +3
We classify translatively exponential and GL(2,Z) covariant valuations on lattice polygons valued at measurable real functions. A typical example of such valuations is induced by t…
Bounds on the lattice point enumerator via slices and projections
Ansgar Freyer, Martin Henk
Gardner, Gronchi and Zong posed the problem to find a discrete analogue of M. Meyer's inequality bounding the volume of a convex body from below by the geometric mean of the volume…