Dynamic Datastructures

Abstract

Imagine that we have an infinite number of boxes labelled 0, 1, 2,.... In the boxes there are a finite number of pebbles. Now start the following process. At each stage you are allowed to remove one pebble from a box with label n and then replace it with as many pebbles as you like as long as those pebbles are introduced in boxes with lower labels than n. A stage in the process can be visualized by

$$\begin{array}{*{20}{c}}{12}&{23}\end{array}\begin{array}{*{20}{c}} 8&0&0 \end{array} \ldots $$