Some methods for finding the number of partitions of n with m−parts, P(n, m)

Authors

YUSUF SOYVURALFollow
ALİ BÜLENT EKİNFollow

Author ORCID Identifier

YUSUF SOYVURAL: 0000-0002-0880-9627

ALİ EKİN: 0000-0002-8191-3383

Abstract

P(n, m) denotes the number of partitions of n with m parts, while P_m(n) denotes the number of partitions of n with parts at most m. It is a well-known result that the number of partitions of n ≥ 0 into m or fewer parts is equal to P_m(n). In the literature, there are some results for P(n, m) and P_m(n) for some values of m. In this work, we give more compact results for P(n, m) for the values of m ≤ 12. Furthermore, we obtain a method for determining P(n, m) when we know the expression for P(n, m − 1).

DOI

10.55730/1300-0098.3633

Keywords

Partitions with m parts, Bernoulli polynomials, Faulhaber's formula

First Page

23

Last Page

39

Publisher

The Scientific and Technological Research Council of Türkiye (TÜBİTAK)

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Recommended Citation

SOYVURAL, Y, & EKİN, A. B (2026). Some methods for finding the number of partitions of n with m−parts, P(n, m). Turkish Journal of Mathematics 50 (1): 23-39. https://doi.org/10.55730/1300-0098.3633