Permutations of the positive integers with specified differences Original Research Article

In this paper, we show that given any finite set, D = {D1, D2, … , Dn}, of positive integers, with gcd (D1, D2, … , Dn) = 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).