Please use this identifier to cite or link to this item:
http://hdl.handle.net/123456789/2028
Full metadata record
DC Field | Value | Language |
---|---|---|
dc.contributor.author | Гой, Тарас Петрович | - |
dc.date.accessioned | 2020-03-24T15:00:21Z | - |
dc.date.available | 2020-03-24T15:00:21Z | - |
dc.date.issued | 2019 | - |
dc.identifier.citation | Goy, T. Fibonacci and Lucas identities using Toeplitz-Hessenberg matrices / T. Goy, M. Shattuck // Applications and Applied Mathematics. – 2019. – 14(2). – P. 699-715 | uk_UA |
dc.identifier.uri | http://hdl.handle.net/123456789/2028 | - |
dc.description.abstract | In this paper, we consider determinants for some families of Toeplitz–Hessenberg matrices having various translates of the Fibonacci and Lucas numbers for the nonzero entries. These determinant formulas may also be rewritten as identities involving sums of products of Fibonacci and Lucas numbers and multinomial coefficients. Combinatorial proofs are provided of several of the determinants which make use of sign-changing involutions and the definition of the determinant as a signed sum over the symmetric group. This leads to a common generalization of the Fibonacci and Lucas determinant formulas in terms of the so-called Gibonacci numbers. | uk_UA |
dc.language.iso | en | uk_UA |
dc.subject | Fibonacci sequence | uk_UA |
dc.subject | Lucas sequence | uk_UA |
dc.subject | Toeplitz-Hessenberg matrix | uk_UA |
dc.subject | Trudi’s formula | uk_UA |
dc.subject | multinomial coefficient | uk_UA |
dc.title | Fibonacci and Lucas identities using Toeplitz–Hessenberg matrices | uk_UA |
dc.type | Article | uk_UA |
Appears in Collections: | Статті та тези (ФМІ) |
Files in This Item:
File | Description | Size | Format | |
---|---|---|---|---|
05-R1320_AAM_Goy Shattuck.pdf | 249.7 kB | Adobe PDF | View/Open |
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.