Sierksma's Dutch Cheese Problem

Details Sierksma's Dutch Cheese Problem Sierksma's Dutch Cheese Problem

1997-03-24

arxiv.org/abs/math/9703208v1

Mathematics

Combinatorics

Scientific paper

Consider partitions, of a cardinality $(q-1)(d+1)+1$ generic subset of
euclidean $d$-space, into $q$ parts whose convex hulls have a nonempty
intersection. We show that if these partitions are counted with appropriate
signs $\pm 1$ then the answer is always $((q-1)!)^d$. Also some other related
results are given.

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