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Given a ﬁnite number of masses in the Euclidean space, one could ask is it possible to equipartition these masses into equal parts. Fixing the collection of masses, and the amount of hyperplanes, the equipartition-ability depends on the dimension, and there exists a dimension of such equipartition is possible. In this paper, topology and combinatorics method are used for estimating the lower bound and upper bound of the dimension. In particular, we are looking equipartition problem together with Cascading Makeev Constrain.
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Zhang, Jialin, "Hyperplanes Equipartition with Cascading Makeev" (2018). Senior Projects Spring 2018. 262.