The 1/k-Eulerian polynomials and k-Stirling permutations

In a recent work of Savage and Viswanathan (2012), during studies of the set of n-dimensional k-inversion sequences, the so-called 1/k-Eulerian polynomials have been introduced, which are given as generating polynomials of the number of ascents in such inversion sequences. In this paper, we discover that the 1/k-polynomials are also generating polynomials of the number of the longest ascent plateaus of k-Stirling permutations. Moreover, we also introduce the dual set of Stirling permutations.