3 di-sk树的计数

兰州理工大学学报 ›› 2024, Vol. 50 ›› Issue (6): 144-149.

3 di-sk树的计数

田振际^*, 豆舒平

兰州理工大学理学院, 甘肃兰州 730050

收稿日期:2023-04-23 出版日期:2024-12-28 发布日期:2025-01-13
通讯作者: 田振际(1964-),男,甘肃会宁人,教授.Email:zjtian@lut.edu.cn
基金资助:
国家自然科学基金(12101280,11861045)

Enumerations of 3 di-sk trees

TIAN Zhen-ji, DOU Shu-ping

School of Science, Lanzhou Univ. of Tech., Lanzhou 730050, China

Received:2023-04-23 Online:2024-12-28 Published:2025-01-13

摘要/Abstract

摘要： 3 di-sk树是一种不存在标记为(2,2)左边的混合三元树. 研究3 di-sk树上的几类计数问题,并给出了有n个内点的3 di-sk树的集合与从(0,0)到(3n,0)的3-Schröder路的集合之间的双射.

关键词: 混合三元树, 3 di-sk树, 3-Schröder路, 双射

Abstract: The study investigates several counting problems related to 3 di-sk trees, which are characterized as a hybrid ternary tree without the left edge labeled (2,2). Obtaining several enumeration results with respect to certain statistics of 3 di-sk trees. A bijection between the set of all 3 di-sk trees with n internal nodes and the set of all 3-Schröder paths from (0,0) to (3n,0) is given.

Key words: hybrid ternary trees, 3 di-sk trees, 3-Schröder paths, bijection

中图分类号:

O157.1

田振际, 豆舒平. 3 di-sk树的计数[J]. 兰州理工大学学报, 2024, 50(6): 144-149.

TIAN Zhen-ji, DOU Shu-ping. Enumerations of 3 di-sk trees[J]. Journal of Lanzhou University of Technology, 2024, 50(6): 144-149.

参考文献

[1] DERSHOWITZ N,ZAKS S.Enumerations of ordered trees[J].Discrete Mathematics,1980,31(1):9-28.
[2] 耿素云,屈婉玲,张立昂.离散数学[M].5版.北京:清华大学出版社,2013.
[3] CHEON G S,SHAPIRO L W.Protected points in ordered trees[J].Applied Mathematics Letters,2008,21(5):516-520.
[4] PANHOLZER A,PRODINGER H.Bijections for ternary trees and non-crossing trees[J].Discrete Mathematics,2002,250(1/2/3):181-195.
[5] GU S S,LI Y,MANSOUR T.2-binary trees: bijections and related issues[J].Discrete Mathematics,2008,308(7):1209-1221.
[6] GU S S,PRODINGER H.Bijections for 2-plane trees and ternary trees[J].European Journal of Combinatorics,2009,30(4):969-985.
[7] YANG L,REN F Y,YANG S L.Some refined enumerations of hybrid binary trees[J].Indian Journal of Pure and Applied Mathematics,2024:55(1):94-104.
[8] PANHOLZER A,PRODINGER H.Bijections between certain families of labelled and unlabelled d-ary trees[J].Applicable Analysis and Discrete Mathematics,2009,3(1):123-136.
[9] HONG S,PARK S.Hybrid d-ary trees and their generalization[J].Bulletin of the Korean Mathematical Society,2014,51(1):229-235.
[10] YANG S L,JIANG M Y.The m-Schröder paths andm-Schröder numbers[J].Discrete Mathematics,2021,344(2):112209.
[11] 姜美杨.Schröder路与混合d-元树的计数[D].兰州:兰州理工大学,2022.
[12] FU S S,LIN Z C,ZENG J.On two unimodal descent polynomials[J].Discrete Mathematics,2018,341(9):2616-2626.
[13] FU S S,LIN Z C,WANG Y L.A combinatorial bijection on di-sk trees[J].Electronic Journal of Combinatorics,2021,28(4):1-23.
[14] MERLINI D,SPRUGNOLI R,VERRI M C.Lagrange inversion:when and how[J].Acta Applicandae Mathematicae,2006,94(3):233-249.
[15] GESSEL I M.Lagrange inversion[J].Journal of Combinatorial Theory,Series A,2016,144:212-249.
[16] SLOANE N J A.On-line encyclopedia of integer sequences (OEIS)[DB].[2023-04-01].https://oeis.org/.