On the number of Birch partitions
Combinatorics
2008-04-17 v2
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 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.
Keywords
Cite
@article{arxiv.math/0612823,
title = {On the number of Birch partitions},
author = {Stephan Hell},
journal= {arXiv preprint arXiv:math/0612823},
year = {2008}
}
Comments
8 pages, shortened version for publication in Discrete & Computational Geometry