  In this paper we investigate the problem of detecting, counting, and
enumerating (generating) all maximum length plateau-$k$-rollercoasters
appearing as a subsequence of some given word (sequence, string), while
allowing for plateaus. We define a plateau-$k$-rollercoaster as a word
consisting of an alternating sequence of (weakly) increasing and decreasing
\emph{runs}, with each run containing at least $k$ \emph{distinct} elements,
allowing the run to contain multiple copies of the same symbol consecutively.
This differs from previous work, where runs within rollercoasters have been
defined only as sequences of distinct values. Here, we are concerned with
rollercoasters of \emph{maximum} length embedded in a given word $w$, that is,
the longest rollercoasters that are a subsequence of $w$.
  We present algorithms allowing us to determine the longest
plateau-$k$-roller\-coasters appearing as a subsequence in any given word $w$
of length $n$ over an alphabet of size $\sigma$ in $O(n \sigma k)$ time, to
count the number of plateau-$k$-rollercoasters in $w$ of maximum length in $O(n
\sigma k)$ time, and to output all of them with $O(n)$ delay after $O(n \sigma
k)$ preprocessing. Furthermore, we present an algorithm to determine the
longest common plateau-$k$-rollercoaster within a set of words in $O(N k
\sigma)$ where $N$ is the product of all word lengths within the set.
