SOME COMBINATORIAL IDENTITIES OF THE $r$-WHITNEY-EULERIAN NUMBERS

Applicable Analysis and Discrete Mathematics

article

Toufik Mansour¹  Jose L. Ramirez²  Mark Shattuck³  Sergio N. Villamarin⁴ 

[1] Department of Mathematics, University of Haifa;Departamento de Matem´aticas, Universidad Nacional de Colombia;Institute for Computational Science & Faculty of Mathematics and Statistics, Ton Duc Thang University;Department of Mathematics, Tulane University

关键词: Euler-Frobenius fraction;    r-Whitney-Eulerian number;    Eulerian number;    combinatorial identity;   

DOI  :  10.2298/AADM180420012M

学科分类：社会科学、人文和艺术（综合）

来源: Univerzitet u Beogradu * Elektrotehnicki Fakultet / University of Belgrade, Faculty of Electrical Engineering

【 摘 要 】

In this paper, we study further properties of a recently introduced generalized Eulerian number, denoted by Am,r(n, k), which reduces to the classicalEulerian number when m = 1 and r = 0. Among our results is a generalization of an earlier symmetric Eulerian number identity of Chung, Grahamand 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 theEuler-Frobenius fractions. Finally, we consider a further four-parameter combinatorial generalization of Am,r(n, k) and find a formula for its exponentialgenerating function in terms of the Lambert-W function.

【 授权许可】

Unknown