A Study On The Equivalence Class With Length Of Mold Structure Less Than 2 In Part Of Motzkin Paths

The lattice problem is one of the typical model problems of the combinatorial mathematics,which is the object of research and an important combination structure.The mature grid theory system has laid a solid foundation for the development and research of other disciplines such as bioinformatics,computer science,structural chemistry and so on.The promotion of the lattice problem also promotes that the combination of mathematics and other branches of mathematics has a very wide range of links,resulting in a lot of new interdisciplines,such as algebra combination,topology combination,which constitutes the theoretical basis of computer science and has been widely used in other areas of the natural sciences.Based on the importance of lattice problem research,this paper will study the equivalence class set and its generating function of modulo structure with no longer than two in the part of Motzkin paths.The main contents and methods are as follows:Chapter 1 introduces the research status of lattice problem and puts forward the definition of the part of Motzkin paths.Chapter 2 illustrates the corresponding equivalence relations and generating functions when mold structure equals 1 in Motzkin paths,or,U-equivalence class,D-equivalence class and F-equivalence class,through the methods of partition,symmetry and building function to obtain relevant equivalence class sets and generating functions.Chapter 3 demonstrates the corresponding equivalence relations and generating functions when mold structure equals 2 in Motzkin paths.The following all kinds of mold structure can be considered,or,UU-equivalence class,UD-equivalence class,UF-equivalence class,DD-equivalence class,DF-equivalence class,FU-equivalence class,FD-equivalence class,FF-equivalence class,with the methods of partition,symmetry and building function to obtain relevant equivalence class sets and generating functions.