| 一些与Dyck路有关的数的恒等式 |
| |
| 引用本文： | 孙怡东.一些与Dyck路有关的数的恒等式[J].数学研究及应用,2005,25(3):441-446. |
| |
| 作者姓名： | 孙怡东 |
| |
| 作者单位： | 南开大学组合数学研究中心,天津,300071 |
| |
| 基金项目： | the “973” Project on Mathematical Mechanization, the National Science Foundation, theMinistry of Education, and the Ministry of Science and Technology of China. |
| |
| 摘 要： | 本文通过Cauchy留数定理和算子方法导出了一些形如∑i=0n (-1)n-i(n i)Um+k+i, k+i =f(n) 和∑i=02n(-1 )i(2n i) Um+k+i, k+i = g(n)的差分恒等式,这里Un, κ表示Dyck路在不同条件下的计数公式,f(n),g(n)与m(n)只和n有关的函数.
|
| 关 键 词： | 恒等式 Dyck路 Catalan数 Motzkin数 |
| 文章编号： | 1000-341X(2005)03-0441-06 |
| 收稿时间： | 06 23 2003 12:00AM |
| 修稿时间： | 2003年6月23日 |
Identities Involoving Some Numbers Related to Dyck Paths |
| |
| SUN Yi-dong.Identities Involoving Some Numbers Related to Dyck Paths[J].Journal of Mathematical Research with Applications,2005,25(3):441-446. |
| |
| Authors: | SUN Yi-dong |
| |
| Institution: | Center of Combinatorics, LPMC, Nankai University, Tianjin 300071, China |
| |
| Abstract: | In the paper we derive many identities of forms ∑n i=0(-1)n-i (n i)Um+κ+i, κ+i =f(n) and ∑2n i=0(-1 )i (2n i) Um+κ+i, κ+i = g(n) by the Cauchy Residue Theorem and an operator method, where Un, κ are numbers of Dyck paths counted under different conditions, and f(n), g(n) and m are functions depending only on about n. |
| |
| Keywords: | Identities Dyck path Catalan numbers Motzkin numbers |
| 本文献已被 维普 万方数据 等数据库收录！ |
| 点击此处可从《数学研究及应用》浏览原始摘要信息 |
| 点击此处可从《数学研究及应用》下载免费的PDF全文 |
|
