#### Vol. 82, No. 2, 1979

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Permutations of the positive integers with restrictions on the sequence of differences. II

### Peter John Slater and William Yslas Vélez

Vol. 82 (1979), No. 2, 527–531
##### Abstract

In this paper we discuss the following conjecture:

Conjecture: Let D = {D1,,Dn}, D N, N the set of positive integers. Then there exists a permutation of N, call it (ak : k N) such that {|ak+1 ak| : k N} = D iff (D1,,Dn) = 1.

We also consider the following question:

Question: For what sets D = {D1,,Dn} does there exist an integer M N and a permutation {bk : k = 1,,M} of {1,,M} such that {|bk+1 bk| : k = 1,,M 1} = D.

We answer the conjecture and the following question in the affirmative if the set D has the following property: For each Dr D there is a Ds D such that (Dr,Ds) = 1.

Primary: 05A05
##### Milestones 