Critical numbers of intervals

详细信息    查看全文

• 作者：Jin-Kai Li ^{962801813@qq.com" class="auth_mail" title="E-mail the corresponding author} ; Yong-Gao Chen ; ^{ygchen@njnu.edu.cn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：11B13 ; 11L07
• 刊名：Journal of Number Theory
• 出版年：2016
• 出版时间：September 2016
• 年：2016
• 卷：166
• 期：Complete
• 页码：400-405
• 全文大小：220 K

文摘

In 2014, Herzog, Kaplan and Lev introduced the critical numbers cr(r,n)$\mathit{cr}(r,n)$ of natural intervals [r,n]$[r,n]$ and determined the values of cr(1,n)$\mathit{cr}(1,n)$ and cr(2,n)$\mathit{cr}(2,n)$ for all n  , and for r≥3$r\ge 3$, they determined the values of cr(r,n)$\mathit{cr}(r,n)$ for n≤(3r²+3r)/2$n\le (3r^2+3r)/2$ and n≥(5r²+r)/2$n\ge (5r^2+r)/2$. In this note, we determine the remaining values of cr(r,n)$\mathit{cr}(r,n)$ for r≥3$r\ge 3$.

Video

For a video summary of this paper, please visit https://youtu.be/hZSI-Ul3K94.