Average Size of a Self-conjugate (s, t)-Core Partition

William Y.C. Chen, Harry H.Y. Huang and Larry X.W. Wang

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

  AMS Classification:  05A17, 05A15


  Keywords:
  (s, t)-core partition, self-conjugate partition, lattice path

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