The powers of two as sums over partitions

被引：0
|
作者：
Merca, Mircea [1 ,2 ]
机构：
[1] Univ Craiova, Dept Math, Craiova 200585, Romania
[2] Acad Romanian Sci, Ilfov 3,Sect 5, Bucharest, Romania
来源：
QUAESTIONES MATHEMATICAE | 2021年 / 44卷 / 12期
关键词：
Binomial coeffcients; partitions;
D O I：
10.2989/16073606.2020.1825019
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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.
引用
收藏
页码：1745 / 1755
页数：11
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