  Recently, Kitaev and Remmel [Classifying descents according to parity, Annals
of Combinatorics, to appear 2007] refined the well-known permutation statistic
``descent'' by fixing parity of one of the descent's numbers. Results in that
paper were extended and generalized in several ways. In this paper, we shall
fix a set partition of the natural numbers $N$, $(N_1, ..., N_t)$, and we study
the distribution of descents, levels, and rises according to whether the first
letter of the descent, rise, or level lies in $N_i$ over the set of words over
the alphabet $[k]$. In particular, we refine and generalize some of the results
in [Counting occurrences of some subword patterns, Discrete Mathematics and
Theoretical Computer Science 6 (2003), 001-012.].
