Abstract
Birch and Tverberg partitions are closely related concepts from discrete geometry. We show two properties for the number of Birch partitions: Evenness and a lower bound. This implies the first nontrivial lower bound for the number of Tverberg partitions that holds for arbitrary q, where q is the number of partition blocks. The proofs are based on direct arguments and do not use the equivariant method from topological combinatorics.
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Hell, S. On the Number of Birch Partitions. Discrete Comput Geom 40, 586–594 (2008). https://doi.org/10.1007/s00454-008-9083-9
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DOI: https://doi.org/10.1007/s00454-008-9083-9