1307.5624 (J. Fernando Barbero G. et al.)

Bivariate Generating Functions for a Class of Linear Recurrences. II.
Applications    [PDF]

J. Fernando Barbero G., Jesús Salas, Eduardo J. S. Villaseñor

In a previous paper, we classified and obtained the exponential generating functions for the large class of bivariate linear recurrences proposed by Graham, Knuth, and Patashnik. In this paper, we obtain general Rodrigues-like formulas for the corresponding univariate row generating polynomials. We make special emphasis on two-parameter generalizations of the Eulerian numbers and <>. In these cases, starting from the exponential generating function, we achieve a complete solution to the problem: i.e., closed formulas for these numbers. Finally, we briefly discuss some other applications of combinatorial interest.

View original: http://arxiv.org/abs/1307.5624