  In this paper, several variants of the ascent-plateau statistic are
introduced, including flag ascent-plateau, double ascent and descent-plateau.
We first study the flag ascent-plateau statistic on Stirling permutations by
using context-free grammars. We then present a unified refinement of the ascent
polynomials and the ascent-plateau polynomials. In particular, by using Foata
and Strehl's group action, we prove two bistatistics over the set of Stirling
permutations of order n are equidistributed.
