Some Ratio Monotonic Properties of a New Kind of Numbers introduced by Z.-W. Sun

2015/12/03 by Sun, Brian Y.
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1512.01010

Abstract

Recently, Z. W. Sun introduced a new kind of numbers S_n and also posed a conjecture on ratio monotonicity of combinatorial sequences related to S_n. In this paper, by investigating some arithmetic properties of S_n, we give an affirmative answer to his conjecture. Our methods are based on a newly established criterion and interlacing method for log-convexity, and also the criterion for ratio log-concavity of a sequence due to Chen, Guo and Wang.

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