论文标题
通过分区圈子的添加数理论的研究
Studies in Additive Number Theory by Circles of Partition
论文作者
论文摘要
在本文中，我们介绍并开发了圆圈嵌入方法。该方法基本上取决于我们选择调用分区圆的组合结构。我们在与确定将数字分配到某些类整数类别的可行性有关的问题的背景下提供的应用程序。特别是，我们的方法允许我们将任何足够大的$ n \ in \ mathbb {n} $划分为自然密度大于$ \ frac {1} {2} $的任何集合$ \ mathbb {h} $。这种可能性可以预示着类似风味的问题类别的前所未有的进步。该论文通过给出二元Goldbach的渐近证明和柠檬蛋白的猜想作为已开发方法的应用来结束。
In this paper we introduce and develop the circle embedding method. This method hinges essentially on a Combinatorial structure which we choose to call circles of partition. We provide applications in the context of problems relating to deciding on the feasibility of partitioning numbers into certain class of integers. In particular, our method allows us to partition any sufficiently large number $n\in\mathbb{N}$ into any set $\mathbb{H}$ with natural density greater than $\frac{1}{2}$. This possibility could herald an unprecedented progress on class of problems of similar flavour. The paper finishes by giving an asymptotic proof of the binary Goldbach and the Lemoine conjecture as application of the developed method..
