加权Motzkin数的恒等式及其组合意义  

Identities of weighted Motzkin numbers and their combinatorial meaning

作　　者：辛华 杨胜良[1] Xin Hua;Yang Shengliang(School of Science,Lanzhou University of Technology,Lanzhou 710069,China)

机构地区：[1]兰州理工大学理学院,甘肃兰州730050

出　　处：《纯粹数学与应用数学》2018年第3期301-308,共8页Pure and Applied Mathematics

基　　金：国家自然科学基金(11561044)

摘　　要：利用Riordan矩阵的A序列和Z序列得到了水平步、上步和下步加权的Motzkin路和Riordan路的矩阵表达式,并利用拉格朗日反演公式计算得出其一般元.最后证明了水平步、上步和下步加权分别为α,β,γ的Motzkin数的递推关系式.We consider the Motzkin paths and Riordan paths that use the steps Level,Up,and Down with assigned weightedα;β;γ.The counting matrix of the weighted Motzkin paths and Riordan paths are obtained by using A-sequences and Z-sequences of the Riordan array.The entries of the matrix are computed by means of the Lagrange inversion formula.Finally,we give a algebraic proof of a three-term recursion identities for a weighted Motzkin sequence.

关 键 词：Motzkin路 Riordan路 生成函数 拉格朗日反演公式 

分 类 号：O157.1[理学—数学]