Abstract
It is known that the concept of ratio monotonicity is closely related to log-convexity and log-concavity. In this paper, by exploring the log-behavior properties of a new combinatorial sequence defined by Z.-W. Sun, we completely solve a conjecture on ratio monotonicity by him.
Highlights
To be self-contained in this paper, let us first review some necessary and important concepts.Let {zn}n≥0 be a number-theoretic or combinatorial sequence of positive numbers
Sun [2] posed a conjecture on ratio monotonicity of the sequence n n n+k 1
The ratio monotonicity conjecture on the sequence {Rn}∞ n=0 can not be attacked with the methods of Sun et al [7] since there exists no three-term recurrence for Rn
Summary
To be self-contained in this paper, let us first review some necessary and important concepts.Let {zn}n≥0 be a number-theoretic or combinatorial sequence of positive numbers. A sequence {zn}∞ n=0 is called log-convex If the inequality in (1.1) is strict, we call the sequence {zn}∞ n=0 strictly log-convex A sequence {zn}∞ n=0 is (strictly) log-convex
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callSimilar Papers
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
