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Asymptotic Log-convexity



Academic Report

TitleAsymptotic Log-convexity

Reporter: Prof. HOU Qinghu

Time: 16 December, 2016 (Friday) AM 10:00-11:00

Location: A1045#room, Innovation Park Building

Contact: Prof. WANG Yi (tel: 84708351-8128)


Abstract: A sequence {a_n}_{n>=0} is said to be asymptotically r-log-convex if it is r-log-convex for n sufficiently large. We present a criterion on the asymptotical r-log-convexity based on the asymptotic behavior of a_n*a_{n+2}/a_{n+1}^2. As an application, we show that most P-recursive sequences are asymptotic r-log-convexity for any integer r once they are log-convex. Moreover, for a concrete integer r, we present a systematic method to fine the explicit integer N such that a P-recursive sequence {a_n}_{n>=N} is r-log-convex. This enable us to prove the r-log-convexity of some combinatorial sequences.


Brief introduction to the reporter: Prof. HOU Qinghu, received his PhD degree at Nankai University (2001). In the same year, he worked at the combined math center, Nankai University. Then he turned to Institute of Applied Mathematics, Tianjin University (2015). His main research direction is using machine to prove the combinatorial identity. He acquired the National Science Foundation for Distinguished Young Scholars (2012).