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The Computer Journal 1989 32(4):374-376; doi:10.1093/comjnl/32.4.374
© 1989 by British Computer Society
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Another Postage Stamp Problem

C. Mitchell *

Hewlett-Packard Laboratories, Filton Road, Stoke Gifford, Bristol BS12 6QZ, UK

The postage stamp problem requires the selection of a set of k postage stamp denominations such that sums of h (or fewer) of these denominations can realise all the numbers 1,2,...,n for n as large as possible (given k). In this paper we consider a natural analogue of this problem to the case where each stamp denomination is allowed to occur a negative number of times, so long as the sum of the absolute values of the numbers of occurrences is at most h. Interestingly, for the case h=2, the problem considered here is also an analogue of the Golomb Ruler problem. For the case h=2, constructions are shown which give a lower bound on the maximum n achievable.

Received August 1987. revised January 1988.

* Hewlett-Packard Laboratories, Filton Road, Stoke Gifford, Bristol BS12 6QZ


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