Combinatorics of the change-making problem

Details Combinatorics of the change-making problem Combinatorics of the change-making problem

2007-12-30

arxiv.org/abs/0801.0120v2

Mathematics

Combinatorics

18 pages, 4 figures Added a partial proof of conjecture 7.6 + some minor changes

Scientific paper

10.1016/j.ejc.2009.05.002

We investigate the structure of the currencies (systems of coins) for which
the greedy change-making algorithm always finds an optimal solution (that is, a
one with minimum number of coins). We present a series of necessary conditions
that must be satisfied by the values of coins in such systems. We also uncover
some relations between such currencies and their sub-currencies.

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