Discrete Math Seminar: Imre Barany

Let B be the unit ball of a norm in the d-dimensional space and assume that V is a finite subset of B, and the sum of the vectors in V is the zero vector. A theorem of Steinitz from 1914 says that there is an ordering v_1,...,v_n of the vectors in V such that every partial sum along this ordering has norm at most 2d. In the lecture several versions and various extensions of this theorem will be explained.