Given a finite collection S of geometric objects such as hyperplanes or spheres in R , the arrangement A(S) is the decomposition of R into connected open cells of dimensions 0, 1, . . . , d induced by S. Besides being interesting in their own right, arrangements of hyperplanes have served as a unifying structure for many problems in discrete and computational geometry. With the recent advances ...

We derermine the cd-index of the induced subdivision arising from a manifold arrangement. This generalizes earlier results in several directions: (i) One can work with manifolds other than the n-sphere and n-torus, (ii) the induced subdivision is a Whitney stratification, and (iii) the submanifolds in the arrangement are no longer required to be codimension one. 2010 Mathematics Subject Classif...

This note considers possible arrangements of the sectors of a generalised dartboard. The sum of the pth powers of the absolute differences of the numbers on adjacent sectors is introduced as a penalty cost function and a string reversal algorithm is used to determine all arrangements that maximise the penalty, for any p ≥ 1. The maximum value of the penalty function for p = 1 is well known in t...

The mega trend individualization drives productmanufacturers towards offering more and more variants of theirproducts. As seen in mass customization scenarios, productconfiguration based on a modular strategy is an enabler for thistrend. The key idea of variant management is to optimize the number of product variants that can be offered to a specific market segment, i.e. outer v...