Recently, Kitaev and Remmel  re¯ned the well-known permutation statistic \descent" by ¯xing parity of one of the descent's numbers. Results in  were extended and generalized in several ways in [7, 10, 11, 12]. In this paper, we shall ¯x a set partition of the natural numbers N, (N1; : : : ;Ns), and we study the distribution of descents, levels, and rises according to whether the ¯rst letter of the descent, rise, or level lies in Ni over the set of words over the alphabet [k] = f1; : : : ; kg. In particular, we re¯ne and generalize some of the results in .
|Number of pages||22|
|Journal||Discrete Mathematics and Theoretical Computer Science|
|Publication status||Published - 2008|
- distribution of descents
- permutation statistics