報(bào) 告 人：林志聰 教授

報(bào)告題目：Bijections in weakly increasing trees via binary trees

報(bào)告時(shí)間：2024年12月14日（周六）上午9：00

報(bào)告地點(diǎn)：靜遠(yuǎn)樓1506學(xué)術(shù)報(bào)告廳

主辦單位：數(shù)學(xué)與統(tǒng)計(jì)學(xué)院、數(shù)學(xué)研究院、科學(xué)技術(shù)研究院

報(bào)告人簡(jiǎn)介：

        林志聰，山東大學(xué)數(shù)學(xué)與交叉科學(xué)研究中心教授，國(guó)家優(yōu)青獲得者。主要從事計(jì)數(shù)組合學(xué)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(xué)術(shù)論文50余篇。任中國(guó)數(shù)學(xué)會(huì)計(jì)算機(jī)數(shù)學(xué)專(zhuān)業(yè)委員會(huì)委員和中國(guó)運(yùn)籌學(xué)會(huì)圖論組合分會(huì)青年理事。近期的研究興趣主要集中在排列統(tǒng)計(jì)量及其相關(guān)組合結(jié)構(gòu)上的雙射和同分布問(wèn)題。

報(bào)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.