2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/158988Birch 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.8 pages, shortened version for publication in Discrete & Computational GeometryCombinatorics05A18; 52A37text