報 告 人：林志聰 教授

報告題目：Bijections in weakly increasing trees via binary trees

報告時間：2024年12月14日（周六）上午9：00

報告地點：靜遠樓1506學術(shù)報告廳

主辦單位：數(shù)學與統(tǒng)計學院、數(shù)學研究院、科學技術(shù)研究院

報告人簡介：

        林志聰，山東大學數(shù)學與交叉科學研究中心教授，國家優(yōu)青獲得者。主要從事計數(shù)組合學的研究，在《J. Combin. Theory Ser. A》、《Combinatorica》、《European J. Combin.》、《Proc. Amer. Math. Soc.》等權(quán)威期刊發(fā)表SCI學術(shù)論文50余篇。任中國數(shù)學會計算機數(shù)學專業(yè)委員會委員和中國運籌學會圖論組合分會青年理事。近期的研究興趣主要集中在排列統(tǒng)計量及其相關(guān)組合結(jié)構(gòu)上的雙射和同分布問題。

報告摘要：

        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.