Ober­se­mi­nar "Sto­chas­tik": Matt­hi­as Reitz­ner (Os­na­brück), Stars of em­pty sim­pli­ces

Ort: J3.330

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.