论文标题
限制单峰序列的形状
Limit Shapes for Unimodal Sequences
论文作者
论文摘要
我们证明了通过正整数的单峰序列图满足的渐近0-1定律。这些图由平面中的正方形列组成，上边界称为形状。对于各种类型，我们表明，由于正方形的数量趋于无穷大，因此$ 100 \％的形状靠近一定曲线，也就是说，有一个{\ it限制了形状}。类似的现象已经在整数分区进行了充分研究，因此目前的工作是自然的扩展。一个值得注意的推论是过度分区的转移极限形状。
We prove asymptotic 0-1 Laws satisfied by diagrams of unimodal sequences of positive integers. These diagrams consist of columns of squares in the plane, and the upper boundary is called the shape. For various types, we show that, as the number of squares tends to infinity, $100\%$ of shapes are near a certain curve---that is, there is a single {\it limit shape}. Similar phenomena have been well-studied for integer partitions, so the present work is a natural extension. One notable corollary is a transferred limit shape for overpartitions.
