TY - JOUR

T1 - Permutations of the positive integers with restrictions on the sequence of differences, II

AU - Slater, Peter J.

AU - Vélez, William Yslas

N1 - Copyright:
Copyright 2017 Elsevier B.V., All rights reserved.

PY - 1979

Y1 - 1979

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0040624485&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0040624485&partnerID=8YFLogxK

U2 - 10.2140/pjm.1979.82.527

DO - 10.2140/pjm.1979.82.527

M3 - Article

AN - SCOPUS:0040624485

VL - 82

SP - 527

EP - 531

JO - Pacific Journal of Mathematics

JF - Pacific Journal of Mathematics

SN - 0030-8730

IS - 2

ER -