A.M. Legendre noted that Euler's pentagonal number theorem implies that the number of partitions of n into an even number of distinct parts almost always equals the number of partitions of n into an odd number of distinct parts (the exceptions occur when n is a pentagonal number). Subsequently other classes of partitions, including overpartitions, have yielded related Legendre theorems. In this paper, we examine four subclasses of overpartitions that have surprising Legendre theorems.
All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics