报告题目：Equidistribution of set-valued statistics on standardYoung tableaux and transversals

报告人： 周大跑博士（绍兴文理学院）

报告时间：2023年6月2日15：30-16: 30

报告地点：20-306

报告摘要： As a natural generalization of permutations, transversals of Young diagrams play an important role in the study of pattern avoiding permutations. Let  and  denote the set of τ-avoiding transversals and τ-avoiding symmetric transversals of a Young diagram λ, respectively. In this paper, we are mainly concerned with the distribution of the peak set and the valley set on standard Young tableaux and pattern avoiding transversals. In particular, by introducing Knuth transformations on standard Young tableaux, we prove that the peak set and the valley set are equidistributed on the standard Young tableaux of shape λ/μ for any skew diagram λ/μ. The equidistribution enables us to show that the peak set is equidistributed over  (resp. ) and  (resp. ) for any Young diagram λ and any permutation τ of {k+1, k+2, …, k + m} with k, m≥1. Our results are refinements of the result of Backelin-West-Xin which states that  and the result of Bousquet-Mélou and Steingrímsson which states that . As applications, we are able to　　

（1）confirm a recent conjecture posed by Yan-Wang-Zhou which asserts that the peak set is equidistributed over 12…k τ-avoiding involutions and k…21τ-avoiding involutions;　

（2）prove that alternating involutions avoiding the pattern 12…kτ are equinumerous with alternating involutions avoiding the pattern k…21τ, paralleling the result of Backelin-West-Xin for permutations, the result of Bousquet-Mélou and Steingrímsson for involutions, and the result of Yan for alternating permutations.

报告人简介：周大跑，2015年获南开大学理学博士学位。主要研究组合计数、组合双射以及一些组合结构统计量的相关问题，与人合作撰写论文10余篇，分别发表在J. Combin. Theory Ser. A，  Advances in Applied Mathematics，  European Journal of Combinatorics，Journal of Algebraic Combinatorics等组合数学领域权威刊物上。主持国家自然科学基金青年基金一项，国家自然科学数学天元基金一项，浙江省自然科学青年基金一项。现任职于绍兴文理学院。