On the size of the Durfee square of a random integer partition

  • Authors:

  • Ljuben R. Mutafchiev

  • Affiliations:

  • Institute of Mathematics and Informatics, Bulgarian Academy of Science, P.O. Box 373, 1090 Sofia, Bulgaria and American University in Bulgaria, Sofia, Bulgaria

  • Venue:
  • Journal of Computational and Applied Mathematics - Special issue: Probabilistic methods in combinatorics and combinatorial optimization
  • Year:
  • 2002

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Abstract

We prove a local limit theorem for the length of the side of the Durfee square in a random partition of a positive integer n as n → ∞. We rely our asymptotic analysis on the power series expansion of xm2 Π(1 -xj)-2 whose coefficient of xn equals the number of partitions of n in which the Durfee square is m2.