FYI (Department Colloquium)
Rendezvous numbers and von Neumann’s min-max theorem
Carsten Thomassen
Department of Mathematics, Technical University of Denmark, Lyngby, Denmark
Department of Mathematics, Technical University of Denmark, Lyngby, Denmark
2010/04/01 Thursday 4:30PM-5:30PM (Room 1501)
A rendezvous number for a metric space M is a number a such that, for every finite subset Q of M, there is an element p in M, such that the average distance from p to the elements in Q is a.
O. Gross showed in 1964 that every compact connected metric space has precisely one rendezvous number. This result is a consequence of von Neumann’s min-max theorem in game theory.
In an article in the American Math. Monthly 93(1986) 260-275, J. Cleary and A. A. Morris asked if a (more) elementary proof of Gross’ result exists.
In this talk I shall formulate a min-max result for real matrices which immediately implies these results of Gross and von Neumann.
The proof is easy and involves only mathematical induction.