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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… Click to show full 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 [Formula: see text] and [Formula: see text], the largest size of an [Formula: see text]-core partition is [Formula: see text]. Xiong found a formula for the largest size of a [Formula: see text]-core partitions with distinct parts. In this paper, we find an explicit formula for the largest size of an [Formula: see text]-core partition such that all parts are odd (or even).
Journal Title: International Journal of Number Theory
Year Published: 2020
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