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Creative Telescoping: Theory and Algorithms


Academic Report

Title: Creative Telescoping: Theory and Algorithms

Reporter: Associate Research Fellow CHEN Shaoshi (Chinese Academy of Sciences)

Time: October 10, 2018 (Wednesday) PM 14:00-15:00

Location: A1101# room, Innovation Park Building

Contact: Lecturer CHEN Xi (tel: 84708351-8025)


Abstract: The method of creative telescoping is the core of Wilf-Zeilberger's theory for computer-generated proofs of identities in combinatorics and special functions. The key concept in this method is telescoper, which is a linear differential or recurrence operator. For a specific function, when does a telescoper of certain type exist? And how can one construct telescopers? These are two basic problems related to the method of creative telescoping. In this talk, I will give a survey on recent progress related to these two problems. One of the interesting aspects of Eulerian polynomials is the characterization as the moments of orthogonal Meixner polynomials. Motivated by the problems of total positivity and gamma-positivity of combinatorial polynomial sequences, I will present two recent generalizations from this perspective. Firstly we show a q-exponential generating function for Carlitz Scoville’s polynomials using inversion numbers of permutations. Secondly we find Stieltjes-type and Jacobi-type continued fractions for some master Eulerian polynomials that enumerate permutations. Our results contain many previously obtained identities as special cases.


The brief introduction to the reporter: Chen Shaoshi, who mainly studies symbolic computation, computational differential algebra and algebraic combinatorics (Wilf-Zeilberger method, formal power series theory, etc.), is now an associate researcher and doctoral supervisor at the Institute of Mathematics and Systems Sciences, Chinese Academy of Sciences. In 2011, he graduated from the Chinese Academy of Sciences and the Paris Polytechnic School in France. He worked as a postdoctoral fellow at the Institute of Symbolic Computing, Linz University, North Carolina State University, Fields Institute of Mathematics, Canada and Waterloo Symbolic Computing Research Group. He returned to China in 2013 and worked in the Institute of Systems, Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, and was promoted to associate research fellow in 2017. He has presided over the National Natural Science Youth Foundation, the Research Startup Fund for Returnees from the Ministry of Education, and the National Natural Science Foundation. He published more than 20 papers in "Journal of Symbolic Computation", "Journal of Algebra", "Advances in Applied Mathematics", and "Journal of Combinatorial Theory, Series A". He was awarded "the ISSAC2014 Outstanding Poster Award" at the International Symbolic and Algebraic Computing Annual Meeting and "the Outstanding Scientific Research Academy of Mathematics and Systems Science" of the Chinese Academy of Sciences in 2014. He was selected as a member of the 7th "Chen Jingrun Future Star" Talent Program of the Chinese Academy of Sciences and the Youth Innovation Promotion Association of the Chinese Academy of Sciences in 2018.