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

Sergey Kitaev; Toufik Mansour; Jeff Remmel

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

Sergey Kitaev, Toufik Mansour, Jeff Remmel

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

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,... , 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.

Original language	English
Pages (from-to)	1-22
Number of pages	22
Journal	Discrete Mathematics and Theoretical Computer Science
Volume	10
Issue number	3
State	Published - 2008

Keywords

Composition
Descent
Level
Multivariate generating function
Rise
Set partition
Word

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science
Discrete Mathematics and Combinatorics

Cite this

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AU - Mansour, Toufik

AU - Remmel, Jeff

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AB - 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.

KW - Composition

KW - Descent

KW - Level

KW - Multivariate generating function

KW - Rise

KW - Set partition

KW - Word

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SN - 1462-7264

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JO - Discrete Mathematics and Theoretical Computer Science

JF - Discrete Mathematics and Theoretical Computer Science

IS - 3

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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