一类广义斐波那契二项式系数序列的对数凹性研究（英文）  

On Log-concavity of a Generalized Fibonomials Sequence

作　　者：孙毅[1] SUN Yi(College of Mathematics and System Sciences,Xinjiang University,Urumqi Xinjiang 830046,China)

机构地区：[1]新疆大学数学与系统科学学院,新疆乌鲁木齐830046

出　　处：《新疆大学学报（自然科学版）》2018年第4期416-420,共5页Journal of Xinjiang University(Natural Science Edition)

基　　金：supported by the National Science Foundation of Xinjiang Uygur Autonomous Region(2017D01C084)

摘　　要：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.

关 键 词：斐波那契数列 s—Fibonomial序列 对数凹性 对数凸性 

分 类 号：O177.2[理学—数学]