[Turkmath:9817] Sabancı Üniv. Math. Colloquium (May 15 Thursday, 15:40): Jonathan Jedwab, The n-card problem

[wmeidl]

Dear All

please see below the abstract of the Sabancı University Math. Colloquium 
talk by*

Jonathan Jedwab,* Simon Fraser University, Canada*
Title: *The n-card problem
*Date: *Thursday, 15.05.2014, 15:40
*Place:* Sabanci University, FENS 2008


All interested are welcome to attend. For directions to Sabancı 
University please visit

http://www.sabanciuniv.edu/tr/?kampus_hayati/hizmet_ve_olanaklar/ulasim.html 




*Abstract:* The n-card problem is to determine the minimal intervals 
[u,v] such that for every stochastic matrix A of order n there is a 
permutation matrix P
of order n (depending on A) such that tr(PA) lies in [u,v]. This problem 
is closely related to classical mathematical problems from industry and 
management,
including the linear assignment problem and the travelling salesman 
problem. The minimal intervals for the n-card problem are known only for 
n < 5.
I shall describe a method of analysis for the n-card problem that makes 
repeated use of the Extreme Principle. This method answers a question 
posed by
Sands, by showing that [1,2] is a solution to the n-card problem for all 
n. The method also shows that each closed interval of length n/(n-1) 
contained in [0,2)
is a solution to the n-card problem for all n.

This is joint work with Justin Chan.


Greetings, Wilfried Meidl
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