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

Peter J. Slater, William Yslas Vélez

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3 Scopus citations

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 ϵ N) such that (|αfk+1 − ak| : k ϵ N) = D iff (D1, …, Dn) = l. We also consider the following question: Question: For what sets D = (D1, ‖, Dn) does there exist an integer M ϵ N and a permutation (|bk:+1: k = 1,… , M) of (1, …, M) such that (|bk+1 − bk|: k = 1, …, M - l) = D. We answer the conjecture and the following question in the affirmative if the set D has the following property: For each DrEspilon; D there is a Dsϵ D such that (Dr, Ds) = 1.

Original languageEnglish (US)
Pages (from-to)527-531
Number of pages5
JournalPacific Journal of Mathematics
Volume82
Issue number2
DOIs
StatePublished - Jan 1 1979

ASJC Scopus subject areas

  • Mathematics(all)

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