河北科技大学学报2025，Vol.46Issue(2)：161-166,6.DOI:10.7535/hbkd.2025yx02005
20-Dyck路与三元树之间的双射
Bijection between 20-Dyck path and ternary tree
摘要
Abstract
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.关键词
计数组合学/20-Dyck路/kt-Dyck路/三元树/Catalan数/L-R-T序列Key words
enumerative combinatorics/20-Dyck path/kt-Dyck path/ternary tree/Catalan number/the L-R-T sequence分类
数学引用本文复制引用
王佳合,窦裕杰,庞兴梅,吕仑..20-Dyck路与三元树之间的双射[J].河北科技大学学报,2025,46(2):161-166,6.基金项目
国家自然科学基金(11001073) （11001073）
河北省自然科学基金(A2023208006) （A2023208006）
河北省引进留学人员资助项目(C20230357) （C20230357）
