通过二叉树的弱递增树的对射

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics Pub Date : 2025-06-11 DOI:10.1016/j.disc.2025.114632

Yang Li, Zhicong Lin

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引用次数: 0

摘要

弱增长树作为增长树和平面树的统一，由Lin-Ma-Ma-Zhou于2021年引入了多集标记的弱增长树。利用董、杜、吉、张等人最近证明的平面树的一些对称性，我们通过交换相应二叉树中某些特定节点的左子和右子的角色，在相同风格的弱递增树上构造了四个双凸。因此，本文提供了Dong等人发现的上述对称性的双射证明，以及Deutsch平面树上双射的非递归构造。本文还讨论了弱递增树的一些对称性在排列模式和统计中的应用。

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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Bijections in weakly increasing trees via binary 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 in 2021. Motived by some symmetries in plane trees proved recently by Dong, Du, Ji and Zhang, we construct four bijections on weakly increasing trees in the same flavor via switching the role of left child and right child of some specified nodes in their corresponding binary trees. Consequently, bijective proofs of the aforementioned symmetries found by Dong et al. and a non-recursive construction of a bijection on plane trees of Deutsch are provided. Applications of some symmetries in weakly increasing trees to permutation patterns and statistics will also be discussed.

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来源期刊

Discrete Mathematics 数学-数学

CiteScore

1.50

自引率

12.50%

发文量

424

审稿时长

6 months

期刊介绍： Discrete Mathematics provides a common forum for significant research in many areas of discrete mathematics and combinatorics. Among the fields covered by Discrete Mathematics are graph and hypergraph theory, enumeration, coding theory, block designs, the combinatorics of partially ordered sets, extremal set theory, matroid theory, algebraic combinatorics, discrete geometry, matrices, and discrete probability theory. Items in the journal include research articles (Contributions or Notes, depending on length) and survey/expository articles (Perspectives). Efforts are made to process the submission of Notes (short articles) quickly. The Perspectives section features expository articles accessible to a broad audience that cast new light or present unifying points of view on well-known or insufficiently-known topics.