On the Number of Birch Partitions

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. We furthermore investigate whether these results admit a topological version.

• Type: Journal
• Year: 2008
• Where: DCG
• Authors: Stephan Hell
• Keywords: DCG 2008, Discrete Geometry, Lower Bound, Tverberg Partitions