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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