题目：The (a,b,c)-Generalized Motzkin Paths with Vertical Steps: Bijections and Statistic Enumerations
报告人：孙怡东 教授 （大连海事大学）
时间：2023年11月13日 （星期一） 下午3:00-4:30
地点：致远楼103室
摘要：A generalized Motzkin path, called G-Motzkin path for short, of length n is a lattice path from (0, 0) to (n, 0) in the first quadrant of the xoy-plane that consists of up steps u=(1, 1), down steps d=(1, -1), horizontal steps h=(1, 0) and vertical steps v=(0, -1). An (a, b, c)-G-Motzkin path is a weighted G-Motzkin path such that the u-steps, h-steps, v-steps and d-steps are weighted respectively by 1, a, b and c. In this talk, we first focus on the enumeration of statistics “number of z-steps” for z ∈ {u, h, v, d}, “number of z1z2-steps” for z1, z2 ∈ {u, h, v, d} and “number of z-steps” at given level in G-Motzkin paths. Secondly, we give bijections between the set of uvu-avoiding (a, b, b^2)-G-Motzkin paths of length n and the set of (a, b)-Schroder paths as well as the set of (a+b, b)-Dyck paths of length 2n, between the set of {uvu, uu}-avoiding (a,b,b^2)-G-Motzkin paths of length n and the set of (a+b, ab)-Motzkin paths of length n, between the set of {uvu, uu}-avoiding (a, b, b^2)-G-Motzkin paths of length n+1 beginning with an h-step weighted by a and the set of (a, b)-Dyck paths of length 2n+2.
报告人简介：孙怡东，教授，现任大连海事大学理学院院长。先后在《European Journal of Combinatorics》、《Electronic Journal of Combinatorics》、《Discrete Mathematics》等组合数学国际知名杂志发表学术论文40余篇。主持完成国家自然科学基金项目2项，主持省部级项目多项。指导研究生荣获辽宁省优秀硕士论文2人次。2009年入选辽宁省“百千万人才工程”千层人选；2018年09月至今担任大连市数学学会副理事长，2023年10月至今担任辽宁省数学会副理事长。
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