ABSTRACT
We define a generalized vector partition function and derive an identity for the generating series of such functions associated with solutions to basic recurrence relations of combinatorial analysis. As a consequence we obtain the generating function of the number of generalized lattice paths and a new version of the Chaundy-Bullard identity for the vector partition function.
Acknowledgments
The authors express their gratitude to E. K. Leinartas for guidance and permanent interest in the work. The authors thank W. M. Lawton for helpful comments which significantly improved this paper.
Disclosure statement
No potential conflict of interest was reported by the authors.