InterleaveSequence 2001-10-21 02:33:56 2003-11-05 17:40:36 Definition \usepackage{amssymb} \usepackage{amsmath} \usepackage{amsfonts} \usepackage{graphicx} \usepackage{xypic} 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 {\em 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 $$ z_i := \begin{cases} x_k & \text{\ \ if } i=2k \text{ is even,}\\ y_k & \text{\ \ if } i=2k+1 \text{ is odd.} \end{cases} $$