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TITLE The largest size of an (s, s+1)-core partition with parts of the same parity
KIAS AUTHORS Yu, Myungjun
JOURNAL INTERNATIONAL JOURNAL OF NUMBER THEORY, 2021
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ABSTRACT 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 (s(2) - 1)(t(2) - 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).
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