与Pell数相关的三角矩阵的一些组合性质
Some Combinatorial Properties of Triangu-lar Matrices Related to Pell Numbers
摘要: Pell数，记，本文主要研究由v(n,k)构成的三角矩阵以及其伴随三角矩阵的组合性质，包括：行多项式的实根性和稠密性，矩阵的渐近正态性以及全正性。
Abstract: Pell number , denote . This article studies the combina-torial proprieties of two triangular matrices, one is formed by v(n,k) and the other is the adjoin-ing triangular matrices . More precisely we study the real rootedness and density of the row polynomials, and the asymptotic normality and total positivity of the matrices.
文章引用：尚宇, 刘相芯. 与Pell数相关的三角矩阵的一些组合性质[J]. 应用数学进展, 2022, 11(8): 6007-6014. https://doi.org/10.12677/AAM.2022.118633

参考文献

[1] Ivie, J. (1970) Problem B-161. Fibonacci Quarterly, 8, 107-108.
[2] 杨胜良, 高晓. Riordan矩阵与Pell数[J]. 兰州理工大学学报, 2017(43): 148-151.
[3] 裴毅, 王毅. Morgan-Voyce多项式的一些新性质[J]. 数学研究及应用: 中文版, 2019(39): 6.
[4] Liu, L.L. and Wang, Y. (2007) A Unified Approach to Polynomial Sequences with Only Real Zeros. Advances in Applied Mathematics, 38, 542-560. [Google Scholar] [CrossRef] 
[5] Brualdi, R.A. (1992) Introductory Combinatorics. 2nd Edition, North-Holland, Amsterdam.
[6] Beraha, S., Kahane, J. and Weiss, N.J. (1978) Limits of Zeros of Recursively Defined Families of Polynomials. Studies in Foundations and Com-binatorics, 1, 213-232.
[7] Barnard, S. and Child, J.F. (1955) Higher Algebra. Macmillan, London.
[8] Bender, E.A. (1973) Central and Local Limit Theorems Applied to Asymptotic Enumeration. Journal of Combinatorial Theory, Series A, 15, 91-111. [Google Scholar] [CrossRef] 
[9] Chen, X. and Wang, Y. (2019) Notes on the Total Positivity of Riordan Arrays. Linear Algebra and Its Applications, 569, 156-161. [Google Scholar] [CrossRef] 

为你推荐