%0 Journal Article
%T Counting descents, rises, and levels, with prescribed first element, in words
%A Sergey Kitaev
%A Toufik Mansour
%A Jeff Remmel
%J Discrete Mathematics & Theoretical Computer Science
%D 2008
%I Discrete Mathematics & Theoretical Computer Science
%X Recently, Kitaev and Remmel refined the well-known permutation statistic ``descent'' by fixing parity of one of the descent's numbers which was extended and generalized in several ways in the literature. In this paper, we shall fix a set partition of the natural numbers  , (  1, бн,   s), and we study the distribution of descents, levels, and rises according to whether the first letter of the descent, rise, or level lies in   i over the set of words over the alphabet [k]= {1,бн,k}. In particular, we refine and generalize some of the results by Burstein and Mansour.
%U http://www.dmtcs.org/dmtcs-ojs/index.php/dmtcs/article/view/680