Generating Functions for P1r (n) and P2r (n)

Das, Sabuj and Mohajan, Haradhan (2014): Generating Functions for P1r (n) and P2r (n). Published in: Journal of Environmental Treatment Techniques , Vol. 2, No. 2 (30 June 2014): pp. 55-57.

Abstract

In 1970 George E. Andrews defined the generating functions for P1r (n) and P2r (n). In this article these generating functions are discussed elaborately. This paper shows how to prove the theorem P2r (n) = P3r (n) with a numerical example when n = 9 and r = 2. In 1966 Andrews defined the terms A/(n) and B/(n), but this paper proves the remark A/(n) = B/(n) with the help of an example when n = 10. In 1961, N. Bourbaki defined the term P(n, m). This paper shows how to prove a Remark in terms of P(n, m), where P(n, m) is the number of partitions of the type of enumerated by P3r (n ) with the further restrictions that b1< 2m.

• Item Type: MPRA Paper
• Language: English
• Keywords: Generating functions, number of partitions.
• Subjects: C - Mathematical and Quantitative Methods > C3 - Multiple or Simultaneous Equation Models ; Multiple Variables

References

1. Andrews, G.E. On Schur’s Second Partition Theorem, Glasgow Math. J.8, 1967. 127–132.

2. Andrews, G.E. Note on a Partition Theorem Glasgow Math. J. 11. 1970.108–109.

3. Andrews, GE, An Introduction to Ramanujan’s Lost Notebook, Amer. Math. Monthly, 86, 1979. 89–108.

4. Bourbaki,N. Algebree Commutative, Chapitres 1–2, Hermann, Paris 1961.

5. Hardy, G.H. and Wright, E.M. Introduction to the Theory of Numbers, 4th Edition, Oxford, Clarendon Press, 1965.