A note on the number of partitions of $n$ into $k$ parts

Abstract

We prove new formulas and congruences for $p(n,k):=$ the number of partitions of $n$ into $k$ parts and $q(n,k):=$ the number of partitions of $n$ into $k$ distinct parts. Also, we give lower and upper bounds for the density of the set $\{n\in \mathbb{N}:p(n,k)\equiv i(\mathrm{mod}m)\}$, where $m\ge 2$ and $0\le i\le m-1$.

8 pages

References in corpus (1)

• On the restricted partition function via determinants with Bernoulli polynomials