Report time: 14:00-16:00, April 7, 2021 (Wednesday)

Report location: Tencent Conference, ID: 680 745 150, password: 357159

Speaker: Professor Yang Libo

Employer: Nankai University

Organized by: School of Mathematics

Introduction to the Report:

Stern's triangle was introduced by Stanley, which is analogous to Pascal's triangle and naturally encodes a poset structure, called Stern's poset. Let $\{b_n(q)\}_{n\geq 1}$ be a sequence of polynomials which appear as the Eulerian polynomials associated to Stern's poset. Stanley further studied the following polynomials

L_n(q)=2 (\sum_{k=1}^{2^n-1}b_k(q) + b_{{2^n}}(q), n\geq 1.

Stanley conjectured that $L_n(q)$ has only real zeros and $L_{4n+1}(q)$ is divisible by $L_{2n}(q)$. In this talk, I will show how to prove these two conjectures.

Brief Introduction of speaker:

Yang Libo, professor, doctoral supervisor, Nankai University. He is now the deputy director of combinatorial Mathematics Center of Nankai University. He graduated from Nankai University with a ph. D. degree in 2004. In 2011, he was selected as new Century Excellent Talents of the Ministry of Education. Supported by national Natural Science Foundation of China for Outstanding Youth in 2015. Currently, he is the editorial board member of Progress in Mathematics, member of combinatorial Mathematics and Graph Theory Committee of Chinese Mathematical Society, standing member of Graph Theory Combination and Application Committee of Chinese Industrial and Applied Mathematics Society, and standing member of Graph Theory Combination Branch of Chinese Operations Research Society. He is mainly engaged in the research of combinatorial mathematics, and has made many important achievements in the theory of symmetric function and the theory of single modal. In trans.amer. Math. Soc., Intern. Math.res. Notice, Proc. Amer. Math. Soc., J. Combinatorial Theory Series, A, adv. Appl. Math., SIAM Discrete Math.