Academic Report
Title: γ-positivity and partial γ-positivity of descent-type polynomials
Reporter: YE Yongnan (research fellow) (Institute of Mathematics, Taipei Academy of Central Studies)
Time: May 30, 2019 (Thursday) PM 14:00-15:00
Location: A1101# room, Innovation Park Building
Contact: Prof. WANG Yi (tel:84708351-8099)
Abstract: In this talk, we study γ-positivity of descent-type polynomials by introducing the change of context-free grammars method. We first present a unified grammatical proof of the γ-positivity of Eulerian polynomials, type γ Eulerian polynomials, derangement polynomials, Narayana polynomials and type γ Narayana polynomials. We then provide partial -positive expansions for several multivariate polynomials associated to Stirling permutations, Legendre-Stirling permutations, Jacobi-Stirling permutations and type derangements, and the recurrence relations for the partial γ-coefficients of these expansions are also obtained. Moreover, by introducing variants of the Foata-Strehl group action, we give combinatorial interpretations for the coefficients of most of these partial -positive expansions.
The brief introduction to the reporter: Ye Yongnan graduated from the Department of Mathematics of Taiwan University in 1978 with a bachelor's degree. He received his master's and doctorate degrees in mathematics from Buffalo City, New York State University in 1983 and 1985, respectively. From 1985 to 1987, he worked for two years in the Department of Information and Mathematics, Montreal Branch, University of Quebec, Canada. He returned to Taiwan in July 1987 as an associate researcher at the Institute of Mathematics, Academia Sinica. Since 1991, he has been promoted as a researcher, and has served as a part-time professor in the Information Department of Taiwan Normal University, the Information Department of Taiwan University, the Mathematics Department of Jiaotong University, the Mathematics Department of Successful University, the Mathematics Department of Changsha Normal University, the Mathematics Department of Taiwan Normal University and the Mathematics Department of Taiwan University. From 1991 to 1992, he was a visiting scholar at the Mathematics Institute of MIT; in the summer of 1995, he was a visiting scholar at the Economics Institute of Monash University in Australia; and in the summer of 1999, he was a visiting scholar at the Statistical Institute of Berkeley University. In 1992 and 1994, he was awarded the Academic Research Excellence Award of the National Science Association (2 years for one time); from 2002 to 2005, he was awarded the first prize of the Academic Research of the National Science Association. 2009-2012 National Science Association Outstanding Program Research Award; 2011-2015 Academic Outstanding Award of Academia Sinica. At present, Ye Yongnan's research mainly focuses on Tutta polynomials of graphs and their related combinatorial structures and computational combinations of uniform partitions. More than 100 papers have been published.
