The Largest Size of (t, t plus d, t+2d)-Core Partitions

Abstract

In 2007, Olsson and Stanton determined the largest size of (t1, t2)-core partitions. Inspired by their result, there have been considerable research on the largest size simultaneous core partitions. In this work, we compute the largest size of (t, t+d, 2d)-core partitions for any coprime positive integers t and d. This generalizes result of Yang, Zhong, and Zhou, who proved the largest size of (t, t + 1, t + 2)-core partitions.