On the number of Tverberg partitions in the prime power case

We give an extension of the lower bound of A. Vućić, R. Živaljević [Notes on a conjecture of Sierksma, Discrete Comput. Geom. 9 (1993) 339–349] for the number of Tverberg partitions from the prime to the prime power case. Our proof is inspired by the Z p -index version of the proof in [J. Matoušek, Using the Borsuk–Ulam Theorem, in: Lectures on Topological Methods in Combinatorics and Geometry, Universitext, Springer-Verlag, Heidelberg, 2003] and uses Volovikov’s Lemma. Analogously, one obtains an extension of the lower bound for the number of different splittings of a generic necklace to the prime power case.