An integrable semi-discrete equation and combinatorial numbers with their combinatorial interpretations
An integrable semi-discrete equation and combinatorial numbers with their combinatorial interpretations
复制标题
DOI：
10.1080/10236198.2012.719024
复制
发表时间：
2013-07
影响因子：
1.1
通讯作者：
Xiang-Ke Chang;Xing-Biao Hu;Guo-Fu Yu
中科院分区：
文献类型：
--
作者：
Xiang-Ke Chang;Xing-Biao Hu;Guo-Fu Yu
给出了一类可积半离散方程的Hankel型行列式解。作为应用，讨论了解与组合数之间的关系，得到了新的组合数。得到了所谓的Motzkin-like数，并给出了相应的组合解释。此外，还证明了某些格路与特解有联系。
A Hankel type determinant solution for an integrable semi-discrete equation is presented. As an application, the relations between the solution and combinatorial numbers are discussed, which lead to new combinatorial numbers. The so-called Motzkin-like numbers are obtained, and the corresponding combinatorial interpretation is given. Additionally, it is also shown that some lattice paths have connections with the special solution.