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...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;.展开更多
基金Supported by National Natural Science Foundation of China(Grant No.11571150)
文摘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;.
