  We give an extension of the lower bound of Vucic and Zivaljevic 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 Matousek's book "Using the
Borsuk-Ulam Theorem" 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.
