新疆大学数学与系统科学学院
纸质出版:2018
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[1]孙毅.一类广义斐波那契二项式系数序列的对数凹性研究(英文)[J],2018,35(04):416-420.
[1]孙毅.一类广义斐波那契二项式系数序列的对数凹性研究(英文)[J],2018,35(04):416-420. DOI: 10.13568/j.cnki.651094.2018.04.005.
DOI:10.13568/j.cnki.651094.2018.04.005.
近年来
在组合数学领域
组合序列的对数凸凹性引起了很多学者的兴趣和关注.文章研究了一类组合序列
称为s-Fibonomial序列
记作(nk)Fs.我们证明了(nk)Fs序列对于变量k是对数凹的
而对于变量n不是对数凹的也不是对数凸的;然而
当s是偶数的时候
(nk)Fs序列对变量n却是对数凹的.此外
通过考虑n-k的奇偶性
建立了两个关于s-Fibonomial序列的组合不等式.
In recent years
log-concavity and log-convexity of combinatorial sequences have aroused great interest of many scholars in the field of combinatorics. We consider in this note that log-concavity of a combinatorial sequence called s-Fibonomial sequence (nk)Fs. We confirm that the sequence is log-concave with respect to k and also demonstrate that it is neither log-concave nor log-convex with respect to n. However
when s is even we prove that the s-Fibonomial sequence is log-concave with respect to n. Moreover
by considering the parity of n-k
we also establish two inequalities on s-Fibonomial sequence.
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