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

University of Haifa

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	American 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

Keywords

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

All Science Journal Classification (ASJC) codes

Analysis
Discrete Mathematics and Combinatorics
Applied Mathematics

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10.2298/AADM180420012M

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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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doi = "10.2298/AADM180420012M",

language = "American English",

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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

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KW - R-Whitney-Eulerian number

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DO - 10.2298/AADM180420012M

M3 - Article

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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

Keywords

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