Kitaev, Sergey and Mansour, Toufik and Remmel, Jeff - Counting descents, rises, and levels, with prescribed first element, in words

dmtcs:432 - Discrete Mathematics & Theoretical Computer Science, January 1, 2008, Vol. 10 no. 3
Counting descents, rises, and levels, with prescribed first element, in words

Authors: Kitaev, Sergey and Mansour, Toufik and Remmel, Jeff

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 N,(N1, ..., Ns), 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 by Burstein and Mansour


Source : oai:HAL:hal-00972336v1
Volume: Vol. 10 no. 3
Section: Combinatorics
Published on: January 1, 2008
Submitted on: March 26, 2015
Keywords: [INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]


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