加权Motzkin数的恒等式及其组合意义Identities of weighted Motzkin numbers and their combinatorial meaning
辛华;杨胜良;
摘要(Abstract)：
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.
关键词(KeyWords)： Motzkin路;Riordan路;生成函数;拉格朗日反演公式
基金项目(Foundation): 国家自然科学基金(11561044)
作者(Authors): 辛华;杨胜良;
参考文献(References)：
- [1]Sapounakis A,Tsikouras P.On k-colored Motzkin words[J].J.Integer Seq.,2004(7):1-13.
- [2]Shapiro L W,Wang C J.A bijection between 3-Motzkin paths and Schr¨oder paths with no peak at odd height[J].J.Integer Seq.,2009(12):1-9.
- [3]Barrucci E,Lungo A Del,Pergola E,et al.A construction for enumerating k-coloured Motzkin paths.Proc.of the First Annual International Conference on Computing and Combinatorics[C].New York:Springer,1995:254-263.
- [4]Sapounakis A,Tsikouras P.Counting peaks and valleys in k-colored Motzkin words[J].Electron.J.Comb.,2005(12):1-20.
- [5]Luz′on A,Merlini D,Mor′on M,et al.Complementary Riordan arrays[J].Discrete Appl.Math.,2014(172):75-87.
- [6]Schork Matthias,Mansour Toufik,Sun Yidong.Motzkin Numbers of Higher Rank:Generating Function and Explict Expression[J].J.Integer Seq.,2007(7):1-9.
- [7]Deutsch E,Shapiro L W.A bijection between ordered trees and 2-Motzkin paths and its many consequences[J].Discrete Math.,2002(256):655-670.
- [8]Bernhart F.Catalan,Motzkin,and Riordan numbers[J].Discrete Math.,1999(204):73-112.
- [9]Merlini D,Sprugnoli R.Arithmetic into geometric progressions through Riordan arrays[J].Discrete Math.,2017(340):160-174.
- [10]Cheon Gi Sang,Kim Hana,Shapiro Louis W.Combinatorics of Riordan arrays with identical A and Zsequences[J].Discrete Math.,2012(312):2040-2049.
- [11]He T X,Sprugnoli R.Sequence characterization of Riordan arrays[J].Discrete Math.,2009(309):3962-3974.
- [12]Merlini D,Rogers D G,Sprugnoli R,et al.On some alterative characterizations of Riordan arrays[J].Can.J.Math.,1997(49):301-320.
- [13]Sprugnoli R.Riordan arrays and combinatorial sums[J].Discrete Math.,1994(132):267-290.
- [14]Woan W J.A recursive relation for weighted Motzkin sequences[J].J.Integer Seq.,2005(8):1-8.