Let’s use generating functions to count the average number of leaves in a binary tree with \(N\) internal nodes. Definitions Let \(P\)...
Let’s use generating functions to count the average number of 1’s in a binary string of length \(N\). Definitions Let \(P\) be the set...
Generating functions can be used for counting. Consider the problem of finding the number of trees with internal nodes. Let \(T\) be the...
Technique The basic technique is to multiply the equation with \(z^{N}\), sum over all \(N\), recast in terms of the generating function...
Definition An ordinary generating function of a sequence \(\left\{a_{k}\right\}\) is: \begin{equation*} A(z) = \sum_{k\ge 0}a_{k}z^{k}...
Problem How many bits are needed to represent a binary tree with \(n\) nodes? A lower bound is given by the fact that \(m\) bits can...