Report
On partitions of $\mathbb{Z}_{m}$ with the same representation function
| العنوان: | On partitions of $\mathbb{Z}_{m}$ with the same representation function |
|---|---|
| المؤلفون: | Sun, Cui-Fang, Xiong, Meng-Chi |
| سنة النشر: | 2020 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Number Theory |
| الوصف: | For any positive integer $m$, let $\mathbb{Z}_{m}$ be the set of residue classes modulo $m$. For $A\subseteq \mathbb{Z}_{m}$ and $\overline{n}\in \mathbb{Z}_{m}$, let $R_{A}(\overline{n})$ denote the number of solutions of $\overline{n}=\overline{a}+\overline{a'}$ with unordered pairs $(\overline{a}, \overline{a'})\in A \times A$. In this paper, we prove that if $m=2^{\alpha}$ with $\alpha\neq 2$, $A\cup B=\mathbb{Z}_{m}$ and $|A\cap B|=2$, then $R_{A}(\overline{n})=R_{A}(\overline{n})$ for all $\overline{n}\in \mathbb{Z}_{m}$ if and only if $B=A+\overline{\frac{m}{2}}$. Comment: 9 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2007.00414 |
| رقم الانضمام: | edsarx.2007.00414 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |