%0 Journal Article
%T Counting descents, rises, and levels, with prescribed first element, in words
%A Sergey Kitaev
%A Toufik Mansour
%A Jeffrey B. Remmel
%J Mathematics
%D 2006
%I arXiv
%X 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.].
%U http://arxiv.org/abs/math/0701032v2