On the number of Birch partitions

Details On the number of Birch partitions On the number of Birch partitions

2006-12-28

arxiv.org/abs/math/0612823v2

Mathematics

Combinatorics

8 pages, shortened version for publication in Discrete & Computational Geometry

Scientific paper

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 non-trivial 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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