摘要
n是正整数,P(n)表示n的加法分拆数,f(n)表示n的乘法分拆数。F_n是Fjbonacci数列的第n项。在本文中,我们有: 1.给出了计算f(n)的递推公式; 2.证明了:P(n)≤F_(n+1),f(n)≤(2/3)n和f(n)≤n/logn(n≠144),从而回答了Hughes和shallit关于f(n)≤n和f(n)≤n/logn(n≠144)的两个猜想。
Let n be a pasitive integer, p(n) (f(n)) denotes the number of additive (multiplicative) partitions of n. Fn denotes the n-th of Fibonacci Sequence. In this paper:(Ⅰ)We have obtained recursion formula of Caculating f(n)(Ⅱ) We proved: p(n)≤Fn+1, f(n)≤2/3n and f(n)≤n/(logn) (n≠144)Therefore, we have answered the conjectured of J. H. Hughes and J. O. Shallit for f(n)≤nand f(n)≤n/(logn)(n≠144).
关键词
加法分柝数
乘法分柝数
上界
数论
Number of additive Partitions, Number of multiplicative Partitionts, Set of multiplicative Partitions
