Finding the largest size of a partition under certain restrictions has been an interesting subject to study. For example, it is proved by Olsson and Stanton that for two coprime integers s and t, the largest size of an (s,t)-core partition is (s2 - 1)(t2 - 1)/24. Xiong found a formula for the largest size of a (t,mt + 1)-core partitions with distinct parts. In this paper, we find an explicit formula for the largest size of an (s,s + 1)-core partition such that all parts are odd (or even).
Bibliographical notePublisher Copyright:
© 2021 World Scientific Publishing Company.
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory