Generating functions for vector partition functions and a basic recurrence relation

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.

KEYWORDS:

• Generating function
• basic recurrence relation
• vector partition function
• Chaundy–Bullard identity

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.

Additional information

Funding

The second author was supported by the PhD SibFU (Siberian Federal University) grant for support of scientific research No: 14.