The order of a permutation is the number of times that permutation must be repeated until the objects return to their original positions. For example the permutation (2,3,1) on the letters ABC successively generates BCA, CAB and ABC, so its order is 3.
What is the highest possible order of a permutation on a list of 100 elements?
Every permutation is either a cycle or is composed of subintervals that are cycles. The order of the permutation is the LCM of its sub-intervals.
So we require a set sub-intervals with sum 100 and to maximize the order, they shouldn't have common factors.
My guess is 2x3x5x7x11x13x17x19x23 = 223092870 should do it.
|
|
Posted by Jer
on 2024-01-24 09:08:56 |
A quick guess
