Abstract: Consider n points in general position in d-dimensional space. For a k-element subset the degree is the number of empty simplices with this k-set as base. The k-degree of the set of n points is defined as the maximum degree over all k-element subset. An old (and still unsolved) question by Erdös asks whether the 2-degree of a planar point sets is unbounded as n tends to infinity.
We investigate the degree of random point sets consisting of n independently and uniformly chosen points from a compact set. We state the optimal order of the vertex- and facet-degree and state some open questions.
Mittwoch, 29.05.2024
| 16.15 bis 18.00 Uhr