论文标题
带有Tribonacci编号条目的Toeplitz-Hessenberg矩阵的决定性身份
Determinant Identities for Toeplitz-Hessenberg Matrices with Tribonacci Number Entries
论文作者
论文摘要
在本文中，我们评估了一些具有Tribonacci数字条目的Toeplitz-Hessenberg矩阵的决定因素。这些决定因素公式也可以等效地表示为涉及多项式系数和TribonAcci数量产物总和的身份。特别是，我们通过Toeplitz-Hessenberg的决定因素建立了Tribonacci和fibonacci和Padovan序列之间的联系。然后，我们通过组合参数获得了决定性公式的扩展，该公式的扩展是按照满足更通用形式的r-ther阶序列的序列，并具有适当的初始条件，其中r> 2是任意的。
In this paper, we evaluate determinants of some families of Toeplitz-Hessenberg matrices having tribonacci number entries. These determinant formulas may also be expressed equivalently as identities that involve sums of products of multinomial coefficients and tribonacci numbers. In particular, we establish a connection between the tribonacci and the Fibonacci and Padovan sequences via Toeplitz-Hessenberg determinants. We then obtain, by combinatorial arguments, extensions of our determinant formulas in terms of generalized tribonacci sequences satisfying an r-th order recurrence of a more general form with the appropriate initial conditions, where r>2 is arbitrary.
