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 noteFunding Information:
We are grateful to Armin Straub for throwing an interesting question that led to this project. We thank the anonymous referee for comments to improve the exposition of this paper. The second author was supported by a KIAS Individual Grant (SP075201) via the Center for Mathematical Challenges at Korea Institute for Advanced Study.
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All Science Journal Classification (ASJC) codes
- Algebra and Number Theory