Sierksma的荷兰奶酪问题

摘要：

考虑将欧氏$d$ -空间的基数$(q-1)(d+1)+1$类属子集划分为凸包具有非空交集的$q$部分。我们表明，如果这些分区计数与适当的符号$\pm 1$，那么答案总是$((q-1)!)^d$。同时也给出了其它一些相关结果。

英文摘要：

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.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。