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Permutations of the positive integers with specified differences

โœ Scribed by Richard Stong

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
460 KB
Volume
176
Category
Article
ISSN
0012-365X

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โœฆ Synopsis

In this paper, we show that given any finite set, D = {D 1, D2, ..., D.}, of positive integers, with gcd (D~, D 2 .... ,D.) = 1, there is a permutation of the positive integers such that the absolute value of the difference between any two consecutive values is in D. Further, it is possible to choose the permutation so that each element of D occurs infinitely often as a difference. This answers in the affirmative a conjecture of Slater and Velez (1977, 1979).

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