Department of Computer Science | Institute of Theoretical Computer Science | CADMO

Theory of Combinatorial Algorithms

Prof. Emo Welzl and Prof. Bernd Gärtner

No Title


Simultaneous partitions of measures by k-fans

Jirí Matousek (joint work with Imre Bárány)

A k-fan is a point in the plane and k semilines emanating from it. Motivated by a neat question of A. Kaneko and M. Kano, we study equipartitions by k-fans of two or more probability measures in the plane, as well as partitions in other prescribed ratios. One of our results: for any two measures there is a 4-fan such that one of its sectors contains $\frac 25$of both measures, and each of the the remaining three sectors contains $\frac 15$ of both measures.


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