一、报告题目：On determinants of tournaments
二、报告人：尤利华 教授
三、时 间：2025年10月26日(周日)19:30---21:30
四、腾讯会议：390-534-555
报告摘要：The determinant of a tournament T is the determinant of the skew-adjacency of T. It is well-known that the determinant of a tournament T with n vertices is 0 if n is odd, and the square of an odd integer if n is even. For odd k>0, the tournament set $\mathcal{D}_k$ consists of tournaments whose all subtournaments have determinant at most k^2.
In 2000, Babai and Cameron [L. Babai, P.J. Cameron, Automorphisms and enumeration of switching classes of tournaments, The electronic journal of combinatorics, 7 (1) (2000) R38] proved that a tournament is switching equivalent to a transitive tournament if and only if it contains no diamonds, which implies $T\in \mathcal{D}_1$ if and only if T is switching equivalent to a transitive tournament. In 2023, Boussaïri et al. [A. Boussaïri, S. Ezzahir, S. Lakhlifi, S. Mahzoum, Skew-adjacency matrices of tournaments with bounded principal minors, Discrete Mathematics, 346 (10) (2023) 113552] characterized $\mathcal{D}_3$ as follows: $T\in \mathcal{D}_3$ if and only if $T$ is switching equivalent to a transitive tournament or a transitive blowup of a diamond.
In this talk, we study $\mathcal{D}_k$ and further questions.
报告人简介：尤利华，博士，教授，博士生导师，先后从事组合矩阵论、图谱理论、张量与超图谱理论、极值图论和结构图论等问题的研究，发表SCI科研论文70余篇，先后主持5项国家自然科学基金，3项广东省自然科学基金和1项广州市科信局基金，2011年入选广州市首批珠江科技新星。
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