TY - JOUR
T1 - Permutations of the positive integers with restrictions on the sequence of differences, II
AU - Slater, Peter J.
AU - Vélez, William Yslas
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.
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U2 - 10.2140/pjm.1979.82.527
DO - 10.2140/pjm.1979.82.527
M3 - Article
AN - SCOPUS:0040624485
SN - 0030-8730
VL - 82
SP - 527
EP - 531
JO - Pacific Journal of Mathematics
JF - Pacific Journal of Mathematics
IS - 2
ER -