Skew Motzkin Paths

发布时间：2018-08-10 19:30

【摘要】：In this paper, we study the class S of skew Motzkin paths, i.e., of those lattice paths that are in the first quadrat, which begin at the origin, end on the x-axis, consist of up steps U =(1, 1),down steps D =(1,-1), horizontal steps H =(1, 0), and left steps L =(-1,-1), and such that up steps never overlap with left steps. Let S_n be the set of all skew Motzkin paths of length n and let 8_n = |S_n|. Firstly we derive a counting formula, a recurrence and a convolution formula for sequence{8_n}n≥0. Then we present several involutions on S_n and consider the number of their fixed points.Finally we consider the enumeration of some statistics on S_n.
[Abstract]:In this paper, we study the class S of skew Motzkin paths, i.e., of those lattice paths that are in the first quadrat, which begin at the origin, end on the x-axis, consist of up steps U = (1,1) down steps D = (1), horizontal steps H = (1,0), and left steps L = (-1), and such that up steps never overlap with left steps.) Let Sn be the set of all skew Motzkin paths of length n and let 8n = StackSn. Firstly we derive a counting formula, a recurrence and a convolution formula for sequence {8n} n 鈮，

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