报告题目：Improper Edges of Rooted Trees and Plane Trees Revisited

报 告 人：季青 教授（天津大学应用数学中心）

报告时间：2026年10月9日（星期五）15:00—16:00

报告地点：线上报告            会议ID：腾讯会议327 765 867

校内联系人：陈曦 副教授         联系方式：84708351-8504

报告摘要：Improper edges were introduced independently by Shor and by Dumont and Ramamonjisoa to refine Cayley’s formula for rooted labeled trees. Zeng later established a connection between Shor’s polynomials and the Ramanujan polynomials. Guo and Zeng extended the notion to labeled plane trees, providing a combinatorial interpretation of Chapoton’s generalized Ramanujan polynomials.

In this talk, I will revisit improper edges in rooted labeled trees and labeled plane trees. For rooted labeled trees, we prove that the number of improper edges in a uniformly random tree is asymptotically normal. For labeled plane trees, we construct commuting involutions that yield a polynomial refinement of a classical counting identity and symmetry properties of refined leaf statistics.

This talk is based on joint work with Lora R. Du (杜睿), Wennie W. J. Ma (马文婧), and Dax T. X. Zhang (张添星).

报告人简介：季青，天津大学应用数学中心教授，副主任。主要从事组合数学的研究，解决了沃尔夫奖获得者和多位美国科学院院士提出的猜想和公开问题, 相关成果发表在包括J. Reine Angew. Math., Adv. Math. (3篇), Trans. Amer. Math. Soc. (2篇), J. Combin. Theory A (3篇)等期刊上，并被多位著名学者在包括权威杂志Notice AMS上正面引用。 先后主持国家自然科学基金项目优秀青年基金项目和面上基金项目，参与创新群体项目和重点项目。