论文标题
具有相同表示功能的有限非负整数集的分区
Partitions of finite nonnegative integer sets with identical representation functions
论文作者
论文摘要
令$ \ mathbb {n} $为所有非负整数的集合。对于$ s \ subseteq \ mathbb {n} $和$ n \ in \ mathbb {n} $，让表示函数$ r_ {s}（s}（n）$表示等式$ n = s+s'$的解决方案的数量，s+s，s in s $ in s $ in s $ s $ s $ s $ s $ s <s <s'$。在本文中，我们确定$ c，d \ subseteq \ mathbb {n} $带有$ c \ cup d = [0，m] $和$ | c \ cap d | = 2 $的结构，以使任何非维持integer $ n $ nontegation integer integer $ n $ $ n $ n $。
Let $\mathbb{N}$ be the set of all nonnegative integers. For $S\subseteq \mathbb{N}$ and $n\in \mathbb{N}$, let the representation function $R_{S}(n)$ denote the number of solutions of the equation $n=s+s'$ with $s, s'\in S$ and $s<s'$. In this paper, we determine the structure of $C, D\subseteq \mathbb{N}$ with $C\cup D=[0, m]$ and $|C\cap D|=2$ such that $R_{C}(n)=R_{D}(n)$ for any nonnegative integer $n$.
