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Discrete Mathematics & Theoretical Computer Science |
Sergey Kitaev ; Toufik Mansour ; Jeff Remmel - 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 - https://doi.org/10.46298/dmtcs.432Counting descents, rises, and levels, with prescribed first element, in wordsArticle
Authors: Sergey Kitaev 
1; Toufik Mansour 2; Jeff Remmel 3
- 1 The Mathematics Institute, Reyjavik University
- 2 Department of Mathematics [Haïfa]
- 3 Department of Mathematics [Univ California San Diego]
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: HAL:hal-00972336v1
Volume: Vol. 10 no. 3
Section: Combinatorics
Published on: January 1, 2008
Imported on: March 26, 2015
Keywords: [INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]
Funding:
- Source : OpenAIRE Graph
- Combinatorial Structures for Permutation Enumeration and Macdonald Polynomials; Funder: National Science Foundation; Code: 0654060
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