摘要
通过Flajolet的连分式组合学理论,研究一般组合数母函数的连分式展开式,一种自然的想法是考察与Motzkin数有代数联系的其他组合数,基于Motzkin和Catalan格路的研究以及对Schröder数和Delannoy数组合模型的研究,发现Catalan格路两种不同格路径的转化关系,进而引出对其他组合数建立适当格路转化的思路,通过利用平面上某些带标签的格路径的母函数与Stieltjes-Jacobi型连分式等价定理,得出大Schröder路、小Schröder路的连分式表达式以及Delannoy路的连分式在代数方面的一些相关结论。
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.
作者
高冰
郭晶晶
王向宇
王永娟
GAO Bing;GUO Jingjing;WANG Xiangyu;WANG Yongjuan(Information Engineering University,Zhengzhou 450001,China;Noncommissioned Officer Academy of PAP,Hangzhou 310000,China)
出处
《信息工程大学学报》
2025年第4期456-461,共6页
Journal of Information Engineering University
