Counting descents, rises, and levels, with prescribed first element, in words

Sergey Kitaev, Toufik Mansour, Jeffrey Remmel

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

Recently, Kitaev and Remmel [9] re¯ned the well-known permutation statistic \descent" by ¯xing parity of one of the descent's numbers. Results in [9] were extended and generalized in several ways in [7, 10, 11, 12]. In this paper, we shall ¯x a set partition of the natural numbers N, (N1; : : : ;Ns), and we study the distribution of descents, levels, and rises according to whether the ¯rst letter of the descent, rise, or level lies in Ni over the set of words over the alphabet [k] = f1; : : : ; kg. In particular, we re¯ne and generalize some of the results in [4].
LanguageEnglish
Number of pages22
JournalDiscrete Mathematics and Theoretical Computer Science
Volume10
Issue number3
Publication statusPublished - 2008

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Descent
Counting
Statistics
Permutation Statistics
Set Partition
Natural number
Parity
Generalise

Keywords

  • distribution of descents
  • rises
  • levels
  • permutation statistics

Cite this

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abstract = "Recently, Kitaev and Remmel [9] re¯ned the well-known permutation statistic \descent{"} by ¯xing parity of one of the descent's numbers. Results in [9] were extended and generalized in several ways in [7, 10, 11, 12]. In this paper, we shall ¯x a set partition of the natural numbers N, (N1; : : : ;Ns), and we study the distribution of descents, levels, and rises according to whether the ¯rst letter of the descent, rise, or level lies in Ni over the set of words over the alphabet [k] = f1; : : : ; kg. In particular, we re¯ne and generalize some of the results in [4].",
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Counting descents, rises, and levels, with prescribed first element, in words. / Kitaev, Sergey; Mansour, Toufik; Remmel, Jeffrey.

In: Discrete Mathematics and Theoretical Computer Science, Vol. 10, No. 3, 2008.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Counting descents, rises, and levels, with prescribed first element, in words

AU - Kitaev, Sergey

AU - Mansour, Toufik

AU - Remmel, Jeffrey

PY - 2008

Y1 - 2008

N2 - Recently, Kitaev and Remmel [9] re¯ned the well-known permutation statistic \descent" by ¯xing parity of one of the descent's numbers. Results in [9] were extended and generalized in several ways in [7, 10, 11, 12]. In this paper, we shall ¯x a set partition of the natural numbers N, (N1; : : : ;Ns), and we study the distribution of descents, levels, and rises according to whether the ¯rst letter of the descent, rise, or level lies in Ni over the set of words over the alphabet [k] = f1; : : : ; kg. In particular, we re¯ne and generalize some of the results in [4].

AB - Recently, Kitaev and Remmel [9] re¯ned the well-known permutation statistic \descent" by ¯xing parity of one of the descent's numbers. Results in [9] were extended and generalized in several ways in [7, 10, 11, 12]. In this paper, we shall ¯x a set partition of the natural numbers N, (N1; : : : ;Ns), and we study the distribution of descents, levels, and rises according to whether the ¯rst letter of the descent, rise, or level lies in Ni over the set of words over the alphabet [k] = f1; : : : ; kg. In particular, we re¯ne and generalize some of the results in [4].

KW - distribution of descents

KW - rises

KW - levels

KW - permutation statistics

UR - http://www.dmtcs.org/dmtcs-ojs/index.php/dmtcs/article/view/680

UR - https://personal.cis.strath.ac.uk/sergey.kitaev/index_files/Papers/deslevris-words.pdf

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JO - Discrete Mathematics and Theoretical Computer Science

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JF - Discrete Mathematics and Theoretical Computer Science

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