Work

Bijections in weakly increasing trees via binary trees

Year: 2025

Type: article

Abstract: 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.

Source: Discrete Mathematics

DOI: 10.1016/j.disc.2025.114632

Authors: Yang Li, Zhicong Lin

Institution: Shandong University

Language: English

Topic: Advanced Combinatorial Mathematics

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,320

Funders: National Natural Science Foundation of China, Fundamental Research Funds for the Central Universities