论文标题
两者的权力作为分区的总和
The powers of two as sums over partitions
论文作者
论文摘要
在本文中，我们研究了两种方法，以表达$ 2 $的自然权力，这是整数分区的总和。首先，我们将N. J. Fine的公式考虑一个公式，它使我们能够以多项式系数表示二项式系数作为分区的总和。第二种方法调用了中央二项式系数和其生成函数的对数分化。一些实验结果表明，存在其他方法的其他方法，将$ 2 $的功率作为分区的总和。
In this paper, we investigate two methods to express the natural powers of $2$ as sums over integer partitions. First we consider a formula by N. J. Fine that allows us to express a binomial coefficient in terms of multinomial coefficients as a sum over partitions. The second method invokes the central binomial coefficients and the logarithmic differentiation of their generating function. Some experimental results suggest the existence of other methods of decomposing the power of $2$ as sums over partitions.
