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 |
| _version_ | 1818551567364653056 |
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| author | Sergey Kitaev Toufik Mansour Jeff Remmel |
| author_facet | Sergey Kitaev Toufik Mansour Jeff Remmel |
| author_sort | Sergey Kitaev |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-12T09:01:37Z |
| format | Article |
| id | doaj.art-19e9894456cd4eb09a12fc9b32b3f852 |
| institution | Directory Open Access Journal |
| issn | 1462-7264 1365-8050 |
| language | English |
| last_indexed | 2024-12-12T09:01:37Z |
| publishDate | 2008-08-01 |
| publisher | Discrete Mathematics & Theoretical Computer Science |
| record_format | Article |
| series | Discrete Mathematics & Theoretical Computer Science |
| spelling | doaj.art-19e9894456cd4eb09a12fc9b32b3f8522022-12-22T00:29:49ZengDiscrete Mathematics & Theoretical Computer ScienceDiscrete Mathematics & Theoretical Computer Science1462-72641365-80502008-08-01103Counting descents, rises, and levels, with prescribed first element, in wordsSergey KitaevToufik MansourJeff RemmelRecently, 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.http://www.dmtcs.org/dmtcs-ojs/index.php/dmtcs/article/view/680 |
| spellingShingle | Sergey Kitaev Toufik Mansour Jeff Remmel Counting descents, rises, and levels, with prescribed first element, in words Discrete Mathematics & Theoretical Computer Science |
| title | Counting descents, rises, and levels, with prescribed first element, in words |
| title_full | Counting descents, rises, and levels, with prescribed first element, in words |
| title_fullStr | Counting descents, rises, and levels, with prescribed first element, in words |
| title_full_unstemmed | Counting descents, rises, and levels, with prescribed first element, in words |
| title_short | Counting descents, rises, and levels, with prescribed first element, in words |
| title_sort | counting descents rises and levels with prescribed first element in words |
| url | http://www.dmtcs.org/dmtcs-ojs/index.php/dmtcs/article/view/680 |
| work_keys_str_mv | AT sergeykitaev countingdescentsrisesandlevelswithprescribedfirstelementinwords AT toufikmansour countingdescentsrisesandlevelswithprescribedfirstelementinwords AT jeffremmel countingdescentsrisesandlevelswithprescribedfirstelementinwords |