A closer look at lattice points in rational simplices.
A finite calculus approach to Ehrhart polynomials.
A Markoff-Type Chain for the View-Obstruction Problem for Spheres in R4.
A mean-square bound for the lattice discrepancy of bodies of rotation with flat points on the boundary
An Ehrhart series formula for reflexive polytopes.
An Example Concerning the Translative Kissing Number of a Convex Body.
Computing parametric rational generating functions with a primal Barvinok algorithm.
Computing the period of an Ehrhart quasi-polynomial.
Convexity in subsets of lattices.
The notion of convex set for subsets of lattices in one particular case was introduced in [1], where it was used to study Paretto's principle in the theory of group choice. This notion is based on a betweenness relation due to Glivenko [2]. Betweenness is used very widely in lattice theory as basis for lattice geometry (see [3], and, especially [4 part 1]).In the present paper the relative notions of convexity are considered for subsets of an arbitrary lattice.In section 1 certain relative notions...
Curvature and Flow in Digital Space
We first define the curvature indices of vertices of digital objects. Second, using these indices, we define the principal normal vectors of digital curves and surfaces. These definitions allow us to derive the Gauss-Bonnet theorem for digital objects. Third, we introduce curvature flow for isothetic polytopes defined in a digital space.
Discrete convexity.
Distribution of lattice points on hyperbolic surfaces
Let two lattices have the same number of points on each hyperbolic surface . We investigate the case when Λ’, Λ” are sublattices of of the same prime index and show that then Λ’ and Λ” must coincide up to renumbering the coordinate axes and changing their directions.
Economical Coverings of Sets of Lattice Points.
Ein dreidimensionales Gitterpunktproblem.
Formes quadratiques encapsulées
Gröbner bases of lattices, corner polyhedra, and integer programming.
Integer Points on Curves and Surfaces.
Integral Self-Affine Tiles in ... Part II: Lattice Tilings.
Intrinsic Volumes and Lattice Points of Crosspolytopes.
Klein polyhedra and lattices with positive norm minima
A Klein polyhedron is defined as the convex hull of nonzero lattice points inside an orthant of . It generalizes the concept of continued fraction. In this paper facets and edge stars of vertices of a Klein polyhedron are considered as multidimensional analogs of partial quotients and quantitative characteristics of these “partial quotients”, so called determinants, are defined. It is proved that the facets of all the Klein polyhedra generated by a lattice have uniformly bounded determinants...