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加权Motzkin数的恒等式及其组合意义 被引量:1

Identities of weighted Motzkin numbers and their combinatorial meaning
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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.
作者 辛华 杨胜良 Xin Hua;Yang Shengliang(School of Science,Lanzhou University of Technology,Lanzhou 710069,China)
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)
关键词 Motzkin路 Riordan路 生成函数 拉格朗日反演公式 Motzkin paths Riordan paths generating function the Lagrange inversion formula
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