Vol. 71, No. 1, 1977

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

Peter John Slater and William Yslas Vélez

Vol. 71 (1977), No. 1, 193–196
Abstract

Let {ak} be a sequence of positive integers and dk = |ak+1 ak|. We say that {ak} is a permutation if every positive integer appears once and only once in the sequence, {ak}. We prove the following: Let {mi} be any sequence of positive integers, then there exists a permutation {ak} such that |{k|dk = i}| = mi.

Mathematical Subject Classification 2000
Primary: 05A05
Milestones
Received: 28 April 1976
Revised: 22 November 1976
Published: 1 July 1977
Authors
Peter John Slater
William Yslas Vélez