Upper bounds for Heilbronn's triangle problem in higher dimensions
Dmitrii Zakharov
Abstract:We develop a new simple approach to prove upper bounds for generalizations of the Heilbronn's triangle problem in higher dimensions. Among other things, we show the following: for fixed , any subset of of size contains
points that span a simplex of volume at most ,
points whose convex hull has volume at most ,
points that span a ‐dimensional simplex of volume at most .
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