Equidistributions on planar maps via involutions on description trees
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：Sergey Kitaev（英国思克莱德大学）
：2022-09-01 16:00
：腾讯会议ID：947-841-4036（密码：260172）
报告人：Sergey Kitaev（英国思克莱德大学）
时 间：9月1日下午16:00
地 点：腾讯会议ID：947-841-4036（密码：260172）
内容摘要:
Description trees were introduced by Cori, Jacquard and Schaeffer in 1997 to give a general framework for the recursive decompositions of several families of planar maps studied by Tutte in a series of papers in the 1960s. We are interested in two classes of planar maps which can be thought of as connected planar graphs embedded in the plane or the sphere with a directed edge distinguished as the root. These classes are rooted non-separable (or, 2-connected) and bicubic planar maps, and the corresponding to them trees are called, respectively, $\beta(1,0)$-trees and $\beta(0,1)$-trees.
Using different ways to generate these trees we define two maps on them that turned out to be involutions. These involutions are not only interesting in their own right, in particular, from counting fixed points point of view, but also they were used to obtain non-trivial equidistribution results on planar maps, certain pattern avoiding permutations, and objects counted by the Catalan numbers.
The results to be presented in this talk are obtained in a series of papers in collaboration with several researchers.
个人简介：
Sergey Kitaev，英国思克莱德大学理学院副院长、教授。2003年博士毕业于瑞典哥德堡大学。主要研究组合计数问题，完成了置换与词和图的两本著作，在J. Combin. Theory Ser. A，Adv in Appl. Math., European J. Combin.等杂志上发表多篇文章。先后主持过冰岛和英国国家基金委的项目，并多次被邀请在重要组合数学会议上做大会报告。
联系人：靳宇
