6 papers
Exact Flatness Constant for One-Point Convex Bodies and the Discrete Isominwidth Problem: The Planar Case
Gennadiy Averkov, Giulia Codenotti, Ansgar Freyer +1
A variant of the flatness problem from integer programming is studied, in which one considers convex bodies in with at most interior lattice points. The maximum…
Minimal covering bodies and Brunn-Minkowski type inequalities for the covering radius
Giulia Codenotti, Ansgar Freyer, Katarina KrivokuÄa
Inclusion minimal convex bodies with the property that the integer translates of cover the space are studied. Such bodies are referred to as minimal covering bodies and it…
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…
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 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…
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…