Tverberg's Transversal Conjecture and Analogues of Nonembeddability Theorems for Transversals
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In this paper we prove a special case of the transversal conjecture of Tverberg and Vrecica. We consider the case when the numbers of parts ri in this conjecture are powers of the same prime. We also prove some results on common transversals that generalize the classical nonembeddability theorems. We also prove an analogue of the colored Tverberg's theorem by Zivaljevic and Vrecica. Instead of multicolor simplices with a common point it gives multicolor simplices with a common m-transversal.