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Difference basis systems

✍ Scribed by Peter Wild

Book ID
103058026
Publisher
Elsevier Science
Year
1987
Tongue
English
Weight
498 KB
Volume
63
Category
Article
ISSN
0012-365X

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✦ Synopsis

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 fim~_,~s,,(t)2/t and lim~_~ mn(t)/t exist, where s,,(t) is the minimum cardinality of the union of such a collection of sets and m,(t) is the minimum number of sets in such a system. 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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