# interleave sequence

Let $S$ be a set, and let $\{x_{i}\},\ i=0,1,2,\dots$ and $\{y_{i}\},\ i=0,1,2,\dots$ be two sequences in $S$. The interleave sequence is defined to be the sequence $x_{0},y_{0},x_{1},y_{1},\dots$. Formally, it is the sequence $\{z_{i}\},\ i=0,1,2,\dots$ given by

 $z_{i}:=\begin{cases}x_{k}&\text{\ \ if }i=2k\text{ is even,}\\ y_{k}&\text{\ \ if }i=2k+1\text{ is odd.}\end{cases}$
Title interleave sequence InterleaveSequence 2013-03-22 11:52:12 2013-03-22 11:52:12 djao (24) djao (24) 7 djao (24) Definition msc 26A03 msc 40-00 msc 11A15