Related to the paper: http://arxiv.org/PS_cache/arxiv/pdf/0809/0809.0400v1.pdf and coin-change problem in general.
We say that a coin system of coins canonical if the greedy algorithm to the coin change-making problem (https://en.wikipedia.org/wiki/Change-making_problem) indeed produces the optimal solution.
Now instead I want to make a canonical coin system consisting of some positive integer $k$ coins (so I want to know for any $k$) such that a greedy solution is the only possible optimal solution.
How can this be done? Would the spacing between two coin denomations explode?