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
Canonical name	InterleaveSequence
Date of creation	2013-03-22 11:52:12
Last modified on	2013-03-22 11:52:12
Owner	djao (24)
Last modified by	djao (24)
Numerical id	7
Author	djao (24)
Entry type	Definition
Classification	msc 26A03
Classification	msc 40-00
Classification	msc 11A15