Abstract
We consider systems of sets of integers (of given cardinality n) whose sets of differences cover a sequence of consecutive integers 1,2,... , t. We show that lim t→∞ s n ( t) 2/ t and lim t→∞ m n ( t)/ t exist, where s n ( t) is the minimum number cardinality of the union of such a collection of sets and m n ( t) is the minimum number of sets in such a systems. Our results show that for large t there is a system for which both the number of sets and the cardinality of the union are close to the minimum.
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