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{\bf L.J. Cowen, Robert Cowen and Arthur Steinberg }
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{\bf Totally Greedy Coin Sets and Greedy Obstructions}
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A coin set is a strictly increasing list of positive integers that
always begins with 1. A coin set is called {\em greedy\/} when the
simple greedy change-making algorithm always produces the fewest
number of coins in change. Here, the greedy change-making algorithm
repeatedly selects the largest denomination coin less than the
remaining amount until it has assembled the correct change. Pearson
has provided an efficient algorithm for determining whether a coin set
is greedy. We study a stricter property on coin sets, called total
greediness, which requires that all initial subsequences of the coin
set also be greedy, and a simple property makes it easy
to test if a coin set is totally greedy. We begin to explore
the theory of greedy obstructions-- those coin sets that cannot be
extended to greedy coin sets by the addition of coins in larger
denominations.
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