### Enumeration of words by the sum of differences between adjacent letters

*Toufik Mansour*

#### Abstract

We consider the sum $u$ of differences between adjacent letters
of a word of $n$ letters, chosen uniformly at random from a given alphabet.
This paper obtains the enumerating generating function for the number of such
words with respect to the sum $u$, as well as explicit formulas
for the mean and variance of $u$.

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