[1]肖杨,齐豪,叶永南.水平步或峰避免在给定集合的Motzkin路径[J].集美大学学报(自然科学版),2026,31(3):368-378.
XIAO Yang,QI Hao,YE Yongnan.Motzkin Path with Levels or Peaks Avoiding a Given Set[J].Journal of Jimei University,2026,31(3):368-378.
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水平步或峰避免在给定集合的Motzkin路径(PDF)
XIAO Yang,QI Hao,YE Yongnan.Motzkin Path with Levels or Peaks Avoiding a Given Set[J].Journal of Jimei University,2026,31(3):368-378.
《集美大学学报（自然科学版）》[ISSN:1007-7405/CN:35-1186/N]
- 卷:
- 第31卷
- 期数:
- 2026年第3期
- 页码:
- 368-378
- 栏目:
- 海洋信息与数理科学
- 出版日期:
- 2026-05-28
文章信息/Info
- Title:
- Motzkin Path with Levels or Peaks Avoiding a Given Set
- Author(s):
- XIAO Yang; QI Hao; YE Yongnan
- （School of Mathematics and Physics,Wenzhou University,Wenzhou 325005,China）
- Keywords:
- Motzkin path; avoiding levels; avoiding peaks; shift equivanlence
- 分类号:
- -
- DOI:
- -
- 文献标志码:
- A
- 摘要:
- 对于给定集合A，文中主要研究了水平步或峰避免在A的Motzkin路径（关于峰个数）的生成函数。首先，讨论了A为奇数集合或偶数集合时生成函数的显式表达式，然后给出了A为任意集合时，避免水平步在A的生成函数的递推关系及连分式，最后得出了水平步和峰分别避免在一对给定集合A和B的移位等价性。
- Abstract:
- In this paper,for a given set A,we study the generating functions with respect to the number of peaks in Motzkin paths in which the levels or peaks avoid A.We first consider the case Where A consists of odd or even integers,secondly,when A is any set,we give the recursive relations and continued fractions of the generating functions for Motzkin paths with levels avoiding A,finally,for any sets A and B,we also derive the shift equivanlence of Motzkin paths with levels and peaks avoiding a pair of given sets A and B,respectively.
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更新日期/Last Update:
2026-06-25