论文标题
将最大部分的不同部分划分为不同的部分
Partitions into distinct parts with bounded largest part
论文作者
论文摘要
我们证明了$ n $的分区数量到不同部分的渐近公式，其中最大的部分最多是$ t \ sqrt {n} $，用于固定的$ t \ in \ mathbb {r} $。我们的方法遵循Romik的一种概率方法，当Szekeres的渐近公式用于不同零件分区时，当零件的数量受$ t \ sqrt {n} $界定时。尽管等同于圆形方法/鞍点方法计算，但概率方法在某种程度上预测了渐近公式的形状。
We prove an asymptotic formula for the number of partitions of $n$ into distinct parts where the largest part is at most $t\sqrt{n}$ for fixed $t \in \mathbb{R}$. Our method follows a probabilistic approach of Romik, who gave a simpler proof of Szekeres' asymptotic formula for distinct parts partitions when instead the number of parts is bounded by $t\sqrt{n}$. Although equivalent to a circle method/saddle-point method calculation, the probabilistic approach predicts the shape of the asymptotic formula, to some degree.
