Partitions with unique largest part and their generating functions

Authors

DOI:

https://doi.org/10.13069/jacodesmath.v14i1.459

Keywords:

Generating functions, Integer partitions, $q$-series

Abstract

The paper introduces a new type of partition where the largest part appears only once, and the remaining parts together form a partition of that largest part. We also derive the generating function for these partitions, a variation of it.

Received: 10 June 2026 | Revised: 02 August 2026 | Accepted: 07 September 2026

Downloads

Download data is not yet available.

References

A. K. Agarwal, Padmavathamma, and M. V. Subbarao, Partition Theory, Atma Ram & Sons, Chandigarh (2005).

G. E. Andrews, The Theory of Partitions, Cambridge Mathematical Library, Cambridge University Press, Cambridge (1998).

W. Gleißssberg, Über einen Satz von Herrn I. Schur, Math. Z. 28 (1928) 372–382.

M. D. Hirschhorn and J. A. Sellers, Arithmetic properties of partitions with odd parts distinct, Ramanujan J. 22 (2010) 273–284.

M. Merca and A. J. Yee, On the sum of parts with multiplicity at least 2 in all the partitions of $n$, Int. J. Number Theory 17(3) (2021) 665–681.

I. Schur, Zur additiven Zahlentheorie, in: A. Brauer and H. Rohrbach, Gesammelte Abhandlungen. Band III, Springer-Verlag, Berlin (1973) 43–50.

Downloads

Published

2026-10-18

How to Cite

Kaur, H., & Rana, M. (2026). Partitions with unique largest part and their generating functions. Journal of Algebra Combinatorics Discrete Structures and Applications, 14(1), 147–153. https://doi.org/10.13069/jacodesmath.v14i1.459

Issue

Section

Articles