Application Of The ECO Method To Combinatorial Sequence

This thesis mainly studies the application of the ECO method in somecombinatorial objects: plane trees, lattice paths and permutations. In particular,combinatorial objects we study in thesis can respectively by the correspondingcombinatorial number to count. The research method of this paper is ECO method, andspecific steps have two steps:1) Define operator, and use it to get all the elements of therecursive structure.2) By using the recursion structure enumerate the correspondingcombinatorial object, and gives combination object’s generating tree and generatingrule.The first chapter of the article mainly introduces the research situation, the basicidea and specific steps of the ECO method and some basic concepts. The second, third,and fourth chapters studies the application of ECO method to Ternary paths, Dyck pathswith no mountain, plane trees with no leaves on the first level and involution byintroducing the definitions and corresponding combinatorial objects about Ternarynumbers, Fine numbers and permutations.