تقرير
On monotone increasing representation functions
| العنوان: | On monotone increasing representation functions |
|---|---|
| المؤلفون: | Kiss, Sándor Z., Sándor, Csaba, Yang, Quan-Hui |
| سنة النشر: | 2023 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Number Theory, Mathematics - Combinatorics, 11B34 |
| الوصف: | Let $k\ge 2$ be an integer and let $A$ be a set of nonnegative integers. The representation function $R_{A,k}(n)$ for the set $A$ is the number of representations of a nonnegative integer $n$ as the sum of $k$ terms from $A$. Let $A(n)$ denote the counting function of $A$.Bell and Shallit recently gave a counterexample for a conjecture of Dombi and proved that if $A(n)=o(n^{\frac{k-2}{k}-\epsilon})$ for some $\epsilon>0$, then $R_{\mathbb{N}\setminus A,k}(n)$ is eventually strictly increasing. In this paper, we improve this result to $A(n)=O(n^{\frac{k-2}{k-1}})$. We also give an example to show that this bound is best possible. Comment: 11 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2303.01314 |
| رقم الأكسشن: | edsarx.2303.01314 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |