Skew Motzkin Paths  

作　　者：Qing Lin LU 

机构地区：[1]School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou 221116, P. R. China

出　　处：《Acta Mathematica Sinica,English Series》2017年第5期657-667,共11页数学学报（英文版）

基　　金：Supported by National Natural Science Foundation of China(Grant No.11571150)

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;be the set of all skew Motzkin paths of length n and let 8;= |S;|. Firstly we derive a counting formula, a recurrence and a convolution formula for sequence{8;}n≥0. Then we present several involutions on S;and consider the number of their fixed points.Finally we consider the enumeration of some statistics on S;.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.

关 键 词：Dyck path Motzkin path skew Motzkin path ENUMERATION 

分 类 号：O157[理学—数学]