Summary: A partition of a non-negative integer $n$ is a way of writing $n$ as a sum of a nondecreasing sequence of parts. The present paper provides the number of partitions of an integer $n$ into parts of a specified number of different sizes. We establish new formulas for such partitions with particular interest to the number of partitions of $n$ into parts of two sizes. A geometric application is given at the end of this paper.

05A17, 11P83

integer partitions, partitions into parts of different sizes, partitions into parts of two sizes, number of divisors