Abstract
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 (s+t+1)(s−1)(t−1) 24 . Stanley and Zanello showed that the average size of an (s, s + 1)-core partition equals ( s+1 3 ) /2. Based on a bijection of Ford, Mai and Sze between self-conjugate (s, t)-core partitions and lattice paths in b s 2c × b t 2c rectangle, we obtain the average size of a self-conjugate (s, t)-core partition as conjectured by Armstrong, Hanusa and Jones.
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