Tribonacci数为n的Toeplitz-Hessenberg矩阵的行列式恒等式
Determinant Identities for Toeplitz-Hessenberg Matrices with Tribonacci Number Entries
摘要：
本文研究了一类含有tribonacci数的Toeplitz-Hessenberg矩阵族的行列式。这些行列式公式也可以等价地表示为涉及多项式系数和特里波那奇数的乘积之和的恒等式。特别是，我们通过Toeplitz-Hessenberg行列式建立了tribonacci和Fibonacci和Padovan序列之间的联系。然后，我们得到，通过组合参数，我们的行列式公式的推广广义tribonacci序列满足r阶递归的更一般的形式与适当的初始条件，其中r>2是任意的。
英文摘要：
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.
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