| 关于Hughues-Shallit猜想——自然数乘法分拆之个数的上界问题 |
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| 引用本文： | 杨富太.关于Hughues-Shallit猜想——自然数乘法分拆之个数的上界问题[J].河南师范大学学报(自然科学版),1990(3):11-15. |
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| 作者姓名： | 杨富太 |
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| 作者单位： | 河南师范大学数学系 |
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| 摘 要： | 以f(n)表自然数N的乘法分拆的个数。本文证明了:当n=p~a及n=p_1p_2…p_l时,Hughues-Shal-Lit的第一猜想:f(n)≤n/logn,(n≠144)成立。其中p为素数;p_1,p_2,…,p_1为互异素数。第二猜想:f(n)
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| 关 键 词： | 自然数的乘法分拆 Bell数 自然数的加法分拆 |
ON CONJECTURE OF HUGHUES--SHALLIT--THE UPPER BOUND OF NUMBER OF MULTIPLICATIVE PARTITION OF NATURAL NUMBER |
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| Yang Futai.ON CONJECTURE OF HUGHUES--SHALLIT--THE UPPER BOUND OF NUMBER OF MULTIPLICATIVE PARTITION OF NATURAL NUMBER[J].Journal of Henan Normal University(Natural Science),1990(3):11-15. |
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| Authors: | Yang Futai |
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| Institution: | Yang Futai Department of Mathematics |
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| Abstract: | In this paper the conditions under which the Hughues--Shallit conjectures hold were considered. Denoting byf(n) the number of multiplicative partitions of an integer n, we obtained that if n=p~o(a>0) or n=p_1p_2…p_i where pp_i, sarew primes and different, then the first conjecture f(n)≤N/logn(n≠4)holds and that for any integer n>1 the Second conjecture f(n)
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| Keywords: | multiplicative partition of natural number additive partition of natural number Bell number |
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