Average size of a self-conjugate $(s,t)$-core partition
Average size of a self-conjugate $(s,t)$-core partition
Armstrong, Hanusa and Jones conjectured that if $s,t$ are coprime integers, then the average size of an $(s,t)$-core partition and the average size of a self-conjugate $(s,t)$-core partition are both equal to $\frac {(s+t+1)(s-1)(t-1)}{24}$. Stanley and Zanello showed that the average size of an $(s,s+1)$-core partition equals $\binom {s+1}{3}/2$. Based …