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

SOYVURAL Y., EKİN A. B.

Turkish Journal of Mathematics, cilt.50, sa.1, ss.23-39, 2026 (SCI-Expanded, Scopus, TRDizin) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 50 Sayı: 1
  • Basım Tarihi: 2026
  • Doi Numarası: 10.55730/1300-0098.3633
  • Dergi Adı: Turkish Journal of Mathematics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.23-39
  • Anahtar Kelimeler: Bernoulli polynomials, Faulhaber’s formula, Partitions with m parts
  • Hakkari Üniversitesi Adresli: Evet

Özet

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).