Some combinatorial identities of the r-whitney-eulerian numbers

Toufik Mansour; José L. Ramírez; Mark Shattuck; Sergio N. Villamarín

doi:10.2298/AADM180420012M

Some combinatorial identities of the r-whitney-eulerian numbers

Toufik Mansour
, José L. Ramírez
, Mark Shattuck
, Sergio N. Villamarín

Department of Mathematics

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

Abstract

In this paper, we study further properties of a recently introduced generalized Eulerian number, denoted by A_m;r(n; k), which reduces to the classical Eulerian number when m = 1 and r = 0. Among our results is a generalization of an earlier symmetric Eulerian number identity of Chung, Graham and Knuth. Using the row generating function for A_m;r(n; k) for a fixed n, we introduce the r-Whitney-Euler-Frobenius fractions, which generalize the Euler-Frobenius fractions. Finally, we consider a further four-parameter combinatorial generalization of A_m;r(n; k) and find a formula for its exponential generating function in terms of the Lambert-W function.

Original language	English
Pages (from-to)	378-398
Number of pages	21
Journal	Applicable Analysis and Discrete Mathematics
Volume	13
Issue number	2
DOIs	https://doi.org/10.2298/AADM180420012M
State	Published - 2019

Bibliographical note

Publisher Copyright:
© 2019 University of Belgrade.

Keywords

Combinatorial identity
Euler-Frobenius fraction
Eulerian number
R-Whitney-Eulerian number

ASJC Scopus subject areas

Analysis
Discrete Mathematics and Combinatorics
Applied Mathematics

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10.2298/AADM180420012M

Cite this

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title = "Some combinatorial identities of the r-whitney-eulerian numbers",

abstract = "In this paper, we study further properties of a recently introduced generalized Eulerian number, denoted by Am;r(n; k), which reduces to the classical Eulerian number when m = 1 and r = 0. Among our results is a generalization of an earlier symmetric Eulerian number identity of Chung, Graham and Knuth. Using the row generating function for Am;r(n; k) for a fixed n, we introduce the r-Whitney-Euler-Frobenius fractions, which generalize the Euler-Frobenius fractions. Finally, we consider a further four-parameter combinatorial generalization of Am;r(n; k) and find a formula for its exponential generating function in terms of the Lambert-W function.",

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author = "Toufik Mansour and Ram{\'i}rez, \{Jos{\'e} L.\} and Mark Shattuck and Villamar{\'i}n, \{Sergio N.\}",

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year = "2019",

doi = "10.2298/AADM180420012M",

language = "English",

volume = "13",

pages = "378--398",

journal = "Applicable Analysis and Discrete Mathematics",

issn = "1452-8630",

publisher = "University of Belgrade",

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T1 - Some combinatorial identities of the r-whitney-eulerian numbers

AU - Mansour, Toufik

AU - Ramírez, José L.

AU - Shattuck, Mark

AU - Villamarín, Sergio N.

PY - 2019

Y1 - 2019

N2 - In this paper, we study further properties of a recently introduced generalized Eulerian number, denoted by Am;r(n; k), which reduces to the classical Eulerian number when m = 1 and r = 0. Among our results is a generalization of an earlier symmetric Eulerian number identity of Chung, Graham and Knuth. Using the row generating function for Am;r(n; k) for a fixed n, we introduce the r-Whitney-Euler-Frobenius fractions, which generalize the Euler-Frobenius fractions. Finally, we consider a further four-parameter combinatorial generalization of Am;r(n; k) and find a formula for its exponential generating function in terms of the Lambert-W function.

AB - In this paper, we study further properties of a recently introduced generalized Eulerian number, denoted by Am;r(n; k), which reduces to the classical Eulerian number when m = 1 and r = 0. Among our results is a generalization of an earlier symmetric Eulerian number identity of Chung, Graham and Knuth. Using the row generating function for Am;r(n; k) for a fixed n, we introduce the r-Whitney-Euler-Frobenius fractions, which generalize the Euler-Frobenius fractions. Finally, we consider a further four-parameter combinatorial generalization of Am;r(n; k) and find a formula for its exponential generating function in terms of the Lambert-W function.

KW - Combinatorial identity

KW - Euler-Frobenius fraction

KW - Eulerian number

KW - R-Whitney-Eulerian number

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M3 - Article

AN - SCOPUS:85076769676

SN - 1452-8630

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SP - 378

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JO - Applicable Analysis and Discrete Mathematics

JF - Applicable Analysis and Discrete Mathematics

IS - 2

ER -

Some combinatorial identities of the r-whitney-eulerian numbers

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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