弱递增树的更多双射组合学

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Advances in Applied Mathematics Pub Date : 2024-08-20 DOI:10.1016/j.aam.2024.102755

Zhicong Lin , Jing Liu , Suijie Wang , Wenston J.T. Zang

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引用次数: 0

摘要

作为递增树和平面树的统一，林-马-周（2021）提出了多集标注的弱递增树。人们已经发现了弱递增树的各种有趣的联系和双射，本文的目的是在这个统一对象上提出更多的双射组合论。我们的两个主要贡献是--将 Eu-Seo-Shin (2017) 提出的平面树上关于节点等级和度的等分布结果扩展到弱递增树上；--用弱递增二叉树上的奇左链/奇右链解释多集谢特多项式。讨论了有趣的结果，包括雅可比椭圆函数和欧拉数的新树解释。此外，还介绍了涉及递推关系、指数生成函数和无上下文语法的相关枚举结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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More bijective combinatorics of weakly increasing trees

As a unification of increasing trees and plane trees, the weakly increasing trees labeled by a multiset was introduced by Lin–Ma–Ma–Zhou (2021). Various intriguing connections and bijections for weakly increasing trees have already been found and the purpose of this paper is to present yet more bijective combinatorics on this unified object. Two of our main contributions are

•
extension of an equidistribution result on plane trees due to Eu–Seo–Shin (2017), regarding levels and degrees of nodes, to weakly increasing trees;
•
a new interpretation of the multiset Schett polynomials in terms of odd left/right chains on weakly increasing binary trees.

Interesting consequences are discussed, including new tree interpretations for the Jacobi elliptic functions and Euler numbers. Relevant enumerative results are also presented, involving recurrence relations, exponential generating functions and context-free grammars.

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来源期刊

Advances in Applied Mathematics 数学-应用数学

CiteScore

2.00

自引率

9.10%

发文量

审稿时长

85 days

期刊介绍： Interdisciplinary in its coverage, Advances in Applied Mathematics is dedicated to the publication of original and survey articles on rigorous methods and results in applied mathematics. The journal features articles on discrete mathematics, discrete probability theory, theoretical statistics, mathematical biology and bioinformatics, applied commutative algebra and algebraic geometry, convexity theory, experimental mathematics, theoretical computer science, and other areas. Emphasizing papers that represent a substantial mathematical advance in their field, the journal is an excellent source of current information for mathematicians, computer scientists, applied mathematicians, physicists, statisticians, and biologists. Over the past ten years, Advances in Applied Mathematics has published research papers written by many of the foremost mathematicians of our time.