科研之友
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摘要
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 an left perpendiculars/2right perpendicular x left perpendiculart/2right perpendicular rectangle, we obtain the average size of a self-conjugate (s, t)-core partition as conjectured by Armstrong, Hanusa and Jones.
