Some methods for finding the number of partitions of n with m-parts, P(n,m)
Turkish Journal of Mathematics, vol.50, no.1, pp.23-39, 2026 (SCI-Expanded, Scopus, TRDizin)
- Publication Type: Article / Article
- Volume: 50 Issue: 1
- Publication Date: 2026
- Doi Number: 10.55730/1300-0098.3633
- Journal Name: Turkish Journal of Mathematics
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, TR DİZİN (ULAKBİM)
- Page Numbers: pp.23-39
- Keywords: Bernoulli polynomials, Faulhaber’s formula, Partitions with m parts
- Hakkari University Affiliated: Yes
Abstract
P(n, m) denotes the number of partitions of n with m parts, while Pm(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 Pm(n). In the literature, there are some results for P(n, m) and Pₘ(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).