广义Motzkin序列的Hankel行列式  

Hankel determinant of generalized Motzkin sequence

作　　者：杨胜良[1] 许艳雪 YANG Sheng-liang;XU Yan-xue(School of Science,Lanzhou Univ. of Tech.,Lanzhou 730050,China)

机构地区：[1]兰州理工大学理学院,甘肃兰州730050

出　　处：《兰州理工大学学报》2019年第1期149-154,共6页Journal of Lanzhou University of Technology

基　　金：国家自然科学基金(11561044)

摘　　要：基于经典的Motzkin路引入一类新的加权Motzkin路的定义.用这种路给出一类Riordan矩阵组合解释,并得到Riordan矩阵首列元素(广义Motzkin序列)的加法公式.利用此加法公式和Riordan矩阵的生成矩阵将广义Motzkin序列的Hankel矩阵进行分解,从而得到广义Motzkin序列的Hankel行列式的一般公式.通过将Motzkin路的权特殊化,得到一些组合序列的Hankel行列式.Based on the classical Motzkin paths,the definition of a new family of weighted Motzkin paths is introduced,the combinatorial interpretation of a class of Riordan arrays are given by using these paths,and the addition formula of elements in first column of Riordan arrays,i.e.generalized Motzkin sequence,is obtained.The decompositions of Hankel matrices of generalized Motzkin sequence is conducted by using this addition formula and produced matrix of the Riordan array,so that a general formula for the Hankel determinants of the generalized Motzkin sequences is obtained.Finally,by means of specialization of the weights of Motzkin path,the Hankel determinants of some combinatorial sequences are obtained.

关 键 词：加权Motzkin路 Riordan矩阵 Stieltjes矩阵 广义Motzkin序列 Hankel行列式 

分 类 号：O157.1[理学—数学]