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Entering the Extranet Era

Combinatorics entering the third millennium

In the later part of the century, attitudes changed. When the 1998 film Good Will Hunting featured a famous mathematician at the Massachusetts Institute of Technology who had won a Fields Medal for combinatorics, many found this somewhat unbelievable.2 However, life followed art in this case when, later in the same year, Fields Medals were awarded to Richard Borcherds and Tim Gowers for work mu...

Entering and Leaving j-Facets

Let S be a set of n points in d-space, no i + 1 points on a common (i − 1)-flat for 1 ≤ i ≤ d. An oriented (d − 1)-simplex spanned by d points in S is called jfacet of S, if there are exactly j points from S on the positive side of its affine hull. We show: (*) For j ≤ n/2 − 2, the total number of (≤ j)-facets (i.e. the number of i-facets with 0 ≤ i ≤ j) in 3-space is maximized in convex positi...

Constructing customized process views

To enable effective cross-organizational collaborations, process providers have to offer external views on their internal processes to their partners. A process view hides details of an internal process that are secret to or irrelevant for the partners. This paper describes a formal two-step approach for constructing customized process views on structured process models. First, a non-customized...