Colored-Motzkin数对数凸性研究

Study on the Log-convexity of Colored-Motzkin Numbers

通过构造Colored-Motzkin三角矩阵,验证了该矩阵为Aigner-Catalan-Riordan矩阵的特例。通过证明Colored-Motzkin数是Colored-Motzkin三角矩阵的第0列元素来研究其对数凸性。由于Catalan数、Motzkin数、Hexagonal数都是Colored-Motzkin数的特例,因此可以统一的推导出Catalan数、Motzkin数、Hexagonal数各自都构成对数凸序列。

In this paper,by means of constructing Colored- Motzkin triangles array,we verify that the array is the special case of Aigner- Catalan- Riordan arrays. We investigate the log-convexity of Colored- Motzkin numbers by proofing the fact that Colored- Motzkin numbers coincide with the first column of the Colored- Motzkin triangles. For the reason that Catalan numbers,Motzkin numbers and Hexagonal numbers are special cases of Colored- Motzkin numbers,we could get the log- convexity of Catalan numbers,Motzkin numbers and Hexagonal numbers,respectively.