信息工程大学学报2025，Vol.26Issue(4)：456-461,6.DOI:10.3969/j.issn.1671-0673.XXXX.XX.001
连分式在组合数中的相关性质
Exploration of Continued Fractions in the Application of Combinatorial Numbers
高冰 1郭晶晶 2王向宇 1王永娟1
作者信息
- 1. 信息工程大学,河南 郑州 450001
- 2. 武警士官学校,浙江 杭州 310000
- 折叠
摘要
Abstract
Using Flajolet's theory of combinatorial species,the study of the continued fraction expansion of the generating function for general combinatorial numbers naturally leads to the examination of other combinatorial numbers that have algebraic connections with Motzkin numbers.Based on the study of Motzkin and Catalan lattice paths,as well as the combinatorial models for Schröder numbers and Delannoy numbers,a transformation relationship between two different types of Catalan lattice paths is discovered.This leads to the idea of establishing appropriate lattice path transformations for other com-binatorial numbers.By utilizing the equivalence theorem between the generating functions of certain la-beled lattice paths on a plane and the Stieltjes-Jacobi type continued fractions,the continued fraction expressions for large Schröder paths,little Schröder paths are derived,and some algebraic conclusions related to Delannoy paths are obtained.关键词
连分式/格路径/Motzkin路/Schröder路Key words
continued fraction/lattice path/Motzkin path/Schröder path分类
数理科学引用本文复制引用
高冰,郭晶晶,王向宇,王永娟..连分式在组合数中的相关性质[J].信息工程大学学报,2025,26(4):456-461,6.
