Motzkin numbers of higher rank: Generating function and explicit expression

Toufik Mansour; Matthias Schork; Yidong Sun

Motzkin numbers of higher rank: Generating function and explicit expression

Toufik Mansour
, Matthias Schork
, Yidong Sun

Department of Mathematics

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

Abstract

The generating function for the (colored) Motzkin numbers of higher rank introduced recently is discussed. Considering the special case of rank one yields the corresponding results for the conventional colored Motzkin numbers for which in addition a recursion relation is given. Some explicit expressions are given for the higher rank case in the first few instances.

Original language	English
Article number	07.7.4
Journal	Journal of Inequalities in Pure and Applied Mathematics
Volume	8
Issue number	2
State	Published - 2007

Keywords

Catalan number
Generating function
Motzkin number
Recursion relation

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

Cite this

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title = "Motzkin numbers of higher rank: Generating function and explicit expression",

abstract = "The generating function for the (colored) Motzkin numbers of higher rank introduced recently is discussed. Considering the special case of rank one yields the corresponding results for the conventional colored Motzkin numbers for which in addition a recursion relation is given. Some explicit expressions are given for the higher rank case in the first few instances.",

keywords = "Catalan number, Generating function, Motzkin number, Recursion relation",

author = "Toufik Mansour and Matthias Schork and Yidong Sun",

year = "2007",

language = "English",

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journal = "Journal of Inequalities in Pure and Applied Mathematics",

issn = "1443-5756",

publisher = "Victoria University of Technology",

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T1 - Motzkin numbers of higher rank

T2 - Generating function and explicit expression

AU - Mansour, Toufik

AU - Schork, Matthias

AU - Sun, Yidong

PY - 2007

Y1 - 2007

N2 - The generating function for the (colored) Motzkin numbers of higher rank introduced recently is discussed. Considering the special case of rank one yields the corresponding results for the conventional colored Motzkin numbers for which in addition a recursion relation is given. Some explicit expressions are given for the higher rank case in the first few instances.

AB - The generating function for the (colored) Motzkin numbers of higher rank introduced recently is discussed. Considering the special case of rank one yields the corresponding results for the conventional colored Motzkin numbers for which in addition a recursion relation is given. Some explicit expressions are given for the higher rank case in the first few instances.

KW - Catalan number

KW - Generating function

KW - Motzkin number

KW - Recursion relation

UR - https://www.scopus.com/pages/publications/34547317245

M3 - Article

AN - SCOPUS:34547317245

SN - 1443-5756

VL - 8

JO - Journal of Inequalities in Pure and Applied Mathematics

JF - Journal of Inequalities in Pure and Applied Mathematics

IS - 2

M1 - 07.7.4

ER -

Motzkin numbers of higher rank: Generating function and explicit expression

Abstract

Keywords

ASJC Scopus subject areas

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