The Complete Central Delannoy Number And Enumeration Of Dyck Paths

In this paper,we introduce the concept of the complete central Delannoy number by using the Delannoy triangle matrix.We obtain the expression of a kind of Riordan matrix by the recurrence relation of lattice path and the -matrix of Riordan matrix,hence we give the combination interpretation of the complete central Delannoy number in terms of enumeration of lattice paths.In addition,we give a new lattice path and a new combinatorial interpretation of the complete central Delannoy number.We enumerate the number of protected points and the number of points nearing the leaves of the complete binary trees respectively and discuss the relation of the complete binary tree and the Dyck path.In chapter one,we introduce the concept of lattice,generating function and Riordan matrix in combinatorial mathematics.In chapter two,we discuss the complete central Delannoy number.Firstly,we define the concept of the complete central Delannoy number in the Delannoy triangle matrix.Secondly,we introduce a new lattice path to get two new Riordan matrices and prove the relation of these two matrices.Finally,we give the counting objects of 7 sets of the complete central Delannoy number.In chapter three,we compute the number of protected points and the number of points nearing the leaves in the complete binary trees,and discuss the connection between the complete binary tree and the Dyck path.