PlanetMath: interleave sequence

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interleave sequence

(Definition)

Let be a set, and let $\{x_i\},\ i=0,1,2,\dots$ and $\{y_i\},\ i=0,1,2,\dots$ be two sequences in . 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

$\begin{displaymath} z_i := \begin{cases} x_k & \text{\ \ if } i=2k \text{ is even,}\ y_k & \text{\ \ if } i=2k+1 \text{ is odd.} \end{cases}\end{displaymath}$

"interleave sequence" is owned by djao.

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Cross-references: sequences
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This is version 2 of interleave sequence, born on 2001-10-21, modified 2003-11-05.
Object id is 449, canonical name is InterleaveSequence.
Accessed 6485 times total.

Classification:

AMS MSC:	26A03 (Real functions :: Functions of one variable :: Foundations: limits and generalizations, elementary topology of the line)
	40-00 (Sequences, series, summability :: General reference works )

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