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

Abstract

In 2007, Olsson and Stanton determined the largest size of $(t_1,t_2)$-core partitions. Inspired by their result, there have been considerable research on the largest size of simultaneous core partitions. In this work, we compute the largest size of $(t,t+d,t+2d)$-core partitions for any coprime positive integers $t$ and $d$. This generalizes the result by Yang, Zhong, and Zhou, who proved the largest size of $(t,t+1,t+2)$-core partitions.