With the increasing number of parts that manufacturers need to place on a piece of material
such as sheet metal, the need increases for more sophisticated algorithms for part …

The present paper is devoted to discrete analogues of Sobolev spaces of smooth functions.
The discrete analogues that we consider are spaces of functions on vertex sets of graphs. …

… If K is a polytope then PK is a zonotope, which is shown by the following geometric interpretation:
Let F1, y, Fm be the facets of K, and let vi be the exterior normal to Fi whose Euclidean …

Using methods developed in multivariate splines, we present an explicit formula for discrete
truncated powers, which are defined as the number of non-negative integer solutions of …

We give some new enumerations of indegree sequences of orientations of a graph using
the Tutte polynomial. Then we introduce some discrete dynamical systems in digraphs …

We introduce a new encoding of the face numbers of a simplicial complex, its Stirling
polynomial, that has a simple expression obtained by multiplying each face number with an …

The aim of the present chapter is to describe in some detail certain polytopes and families of
polytopes. This should serve the double purpose of familiarizing the reader with geometric …

… [19] SJ LV, GS LENG, Extended Affine Surface Area and Zonotopes, J.Kore.Math.…

Kontur-Toleranzbereiche werden um ein Zentrum θ∈ IRd einer Verteilung F∈ F konstruiert.
Dieses Zentrum kann zum Beispiel dem Erwartungswert oder einem multivariaten Median …

When solving a difficult problem it is a natural idea to decompose complicated objects into
smaller, easy-tohandle pieces. In this book we study such decompositions: triangulations of …