Rearrangements of bounded variation sequences (Q1331186)

Let \(p\) be a permutation of \(N\), the set of all positive integers. Then \(p\) is said to be bounded variation preserving (BVP) if the rearrangement induced by \(p\), \(a_ p= (a_{p(k)})\), is of bounded variation for all \(a= (a_ k)\in \text{BV}\). In this paper the author has established a necessary and sufficient condition for \(p\) to be BVP which is deduced from a result of \textit{F. M. Mears} [Duke Math. J. 13, 579-585 (1946)].