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Sierksma's Dutch Cheese Problem

K. S. Sarkaria
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Abstract

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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K. S. Sarkaria. 1997-03-24. Sierksma's Dutch Cheese Problem. https://arxiv.org/abs/math/9703208

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