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.