Bijection between 20-Dyck path and ternary tree

In order to expand the basic theory of Dyck path and ternary tree, the bijection and counting problems between the 20-Dyck path and the ternary tree with n inliers were studied. Firstly, the bijection between the 20-Dyck path and the L-R-T sequence was established by constructing a novel combinatorial L-R-T sequence. Secondly, the transformation relationship between the L-R-T sequence and the ternary tree with n inliers was constructed by means of analysis and induction, thus providing a combined proof of its counting formula. Finally, the relationship between the peaks and valleys of the 20-Dyck Path and the L-R-T sequence and the ternary tree was studied. The results show that the bijection problem between two combined structures can be proved by the relationship with other structures. The research results enrich the related theories of Dyck path and ternary tree, and provide theoretical reference value for the application of these two structures in the field of combinatorics.