Discrete Mathematics & Theoretical Computer Science, Vol 11, No 1 (2009)

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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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