On the monotonicity properties of additive representation functions
On the monotonicity properties of additive representation functions
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DOI：
10.1017/s0004972700034912
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发表时间：
2005-08
影响因子：
0.7
通讯作者：
Yong-Gao Chen;A. Sárközy;V. Sós;M. Tang
中科院分区：
文献类型：
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作者：
Yong-Gao Chen;A. Sárközy;V. Sós;M. Tang
若A是一组正整数，设R1 (n)为A + A ‘ = n, A A ‘∈A的解的个数，设R2(n)和R3(n)分别为附加约束条件A < A ’和A≤A ’的解的个数。研究并比较了R1(n)、R2(n)、R3(n)三个函数的单调性。
If A is a set of positive integers, let R1 (n) be the number of solutions of a + a′ = n, a. a′ ∈ A, and let R2(n) and R3(n) denote the number of solutions with the additional restrictions a < a′, and a ≤ a′ respectively. The monotonicity properties of the three functions R1(n), R2(n), and R3(n) are studied and compared.