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# 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

$z_{i}:=\begin{cases}x_{k}&\text{\ \ if }i=2k\text{ is even,}\\ y_{k}&\text{\ \ if }i=2k+1\text{ is odd.}\end{cases}$ |

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## Mathematics Subject Classification

26A03*no label found*40-00

*no label found*11A15

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