Event Details

Who Can Solve This Problem About Permutations of a Finite Set?

Presenter: Christine Mynhardt - Department of Mathematics, University of South Africa
Supervisor:

Date: Mon, January 29, 2001
Time: 15:30:00 - 00:00:00
Place: Clearihue A-215

ABSTRACT

For which values of n does there exist a permutation f of the set N = {0, 1, ..., n-1} such that the functions g,h : N -> N defined by

g(x) = (f(x)+x) mod n and h(x) = (f(x) - x) mod n
are also permutations?

Suppose n is an integer for which no such permutation f exists. What is the cardinality of a largest subset N' of N for which there exists a 1-1 function f : N' -> N such that the functions g,h : N' -> N (defined as above) are also 1-1? Why do we want to know this, anyway?