限制分拆的GeorgeSzekeres公式
A George Szekeres Formula for Restricted Partitions
摘要：
我们推导出一个渐近公式$A(n,j,r)$的整数划分的$n$的数目至多$j$部分每个部分$\le r$。我们假设$j$和$r$接近它们的平均值。我们还调查了第二大部分，部分的数量$\ge 2$等，我们表明，分数的分区的一个偶数整数$n$的图形，即。其部分形成单图的度序列的图是$O(\ln^{-1/2} n)$。概率结果用于我们讨论的图形划分。乔治Szekeres圆方法是必不可少的，我们的渐近结果分区。我们确定的分布所定义的分区的连续的秩，推广的结果Erdos和Richmond的分区的秩。
英文摘要：
We derive an asymptotic formula for $A(n,j,r)$ the number of integer partitions of $n$ into at most $j$ parts each part $\le r$. We assume $j$ and $r$ are near their mean values. We also investigate the second largest part, the number of parts $\ge 2$, etc. We show that the fraction of the partitions of an even integer $n$ that are graphical, ie. whose parts form the degree sequence of a simple graph, is $O(\ln^{-1/2} n)$. Probabilistic results are used in our discussion of graphical partitions. The George Szekeres circle method is essential for our asymptotic results on partitions. We determine the distributions defined by the successive ranks of partitions, generalizing the result of Erdos and Richmond for the rank of a partition.
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