The Properties And Applications Of A Symmetric Lattice Path

This paper deals with a special symmetric lattice path. Based on the Dyck path, we define this kind of symmetric lattice path as the L-symmetric lattice path. Through study, we find several properties of it. Then we establish a bijection between the restricted permutation Sn(231,312,321) and the L-symmetric lattice path. Moreover, several related statistics are obtained via the bijection. The paper is organized as followsSection 1, introduction.Section 2, we give the preliminaries of this paper.Section 3, we present the definition and obtain several properties of the L-symmetric lattice path.Section 4, we establish a bijection between the L-symmetric lattice path and the Sn(231,312,321). Moreover, several important statistics are obtained via the bijection.Section 5, conclusion.