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

摘要

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 x~(m~2) ∏_(j=1)~m (1 = x~j)~(-2) whose coefficient of x~n equals the number of partitions of n in which the Durfee square is m~2.