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).

中文翻译：

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具有相同奇偶校验部分的 (s,s + 1) 核心分区的最大大小

在某些限制下找到分区的最大大小一直是一个有趣的研究课题。例如，Olsson 和 Stanton 证明了对于两个互质整数s和吨, 的最大尺寸(s,吨)-核心分区是(s2 - 1)(吨2 - 1)/24. 熊找到了一个最大尺寸的公式(吨,米吨 + 1)-具有不同部分的核心分区。在本文中，我们找到了一个显式公式(s,s + 1)-core 分区，使得所有部分都是奇数（或偶数）。