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Title: Determinant identities for Toeplitz-Hessenberg matrices with tribonacci number entries
Authors: Гой, Тарас Петрович
Keywords: tribonacci numbers
Toeplitz-Hessenberg matrix
multinomial coefficient
Issue Date: 2020
Citation: Goy, T. Determinant identities for Toeplitz-Hessenberg matrices with tribonacci number entries / T. Goy, M. Shattuck // Transactions on Combinatorics, 2020. − 9 (2). − P. 89-109.
Abstract: 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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