Determinant identities for toeplitz-hessenberg matrices with tribonacci entries
| Autor: | Taras Goy, Mark Shattuck |
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| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: | |
| Zdroj: | Transactions on Combinatorics, Vol 9, Iss 2, Pp 89-109 (2020) |
| Druh dokumentu: | article |
| ISSN: | 2251-8657 2251-8665 |
| DOI: | 10.22108/toc.2020.116257.1631 |
| Popis: | 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 a recurrence of the form $T_n^{(r)}=T_{n-1}^{(r)}+T_{n-2}^{(r)}+T_{n-r}^{(r)}$ for $n \geq r$, with the appropriate initial conditions, where $r \geq 3$ is arbitrary. |
| Databáze: | Directory of Open Access Journals |
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