Counting Descents, Rises, and Levels, with Prescribed First Element, in Words

Recently, Kitaev and Remmel [8] refined the well-known permutation statistic "descent" by fixing parity of one of the descent's numbers. Results in [8] were extended and generalized in several ways in [7, 9, 10, 11]. In this paper, we shall fix a set partition of the natural numbers N, (N1, . . . , Nt), and we study the distribution of descents, levels, and rises according to whether the first letter of the descent, rise, or level lies in Ni over the set of words over the alphabet [k] = {1, . . . , k}. In particular, we refine and generalize some of the results in [4].

• Type: Journal
• Year: 2008
• Where: DMTCS
• Authors: Sergey Kitaev, Toufik Mansour, Jeffrey B. Remmel
• Keywords: DMTCS 2003, DMTCS 2008, Set Partition, Statistic, Well-known Permutation