# Combinatorics of geometrically distributed random variables: Length of ascending runs

Abstract.For $n$ independently distributed geometric random variables we consider the average length of the $m$--th run, for fixed $m$ and $n\to\infty$. One particular result is that this parameter approaches $1+q$. In the limiting case $q\to1$ we thus rederive known results about runs in permutations.
I submitted this paper for LATIN 2000 in Uruguay. I did not travel much last year, but I want to pick it up again. Thus, let us hope for success.
Added February 2001: There is a slight error in the double generating function R(z,w), because I forgot a factor z^{k-1} somewhere. It does not affect the computation of the average, however.

helmut@gauss.cam.wits.ac.za,

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