On the Number of Birch Partitions |
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Authors: | Stephan Hell |
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Institution: | (1) Institut für Mathematik, MA 6–2, TU Berlin, 10623 Berlin, Germany |
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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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Keywords: | Tverberg’ s theorem Sierksma’ s conjecture |
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