On the size of the Durfee square of a random integer partition
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...
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| Veröffentlicht in: | Journal of computational and applied mathematics 2002-05, Vol.142 (1), p.173-184 |
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| Format: | Artikel |
| Sprache: | eng |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | 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. |
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| ISSN: | 0377-0427 1879-1778 |
| DOI: | 10.1016/S0377-0427(01)00467-8 |