Counting descents, rises, and levels, with prescribed first element, in words
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, (ℕ 1...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Discrete Mathematics & Theoretical Computer Science
2008-08-01
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| Series: | Discrete Mathematics & Theoretical Computer Science |
| Online Access: | http://www.dmtcs.org/dmtcs-ojs/index.php/dmtcs/article/view/680 |
| Summary: | 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, (ℕ 1, …, ℕ 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 ℕ i 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. |
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| ISSN: | 1462-7264 1365-8050 |