×

Enumeration of the partitions of an integer into parts of a specified number of different sizes and especially two sizes. (English) Zbl 1217.05035

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.

MSC:

05A17 Combinatorial aspects of partitions of integers
11P83 Partitions; congruences and congruential restrictions

Software:

OEIS
PDFBibTeX XMLCite
Full Text: EuDML EMIS