On the size of the Durfee square of a random integer partition |
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| Institution: | 1. Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, P.O. Box 373, 1090 Sofia, Bulgaria;2. American University in Bulgaria, Sofia, Bulgaria |
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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∏j=1m(1−xj)−2 whose coefficient of xn equals the number of partitions of n in which the Durfee square is m2. |
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