Please use this identifier to cite or link to this item: http://hdl.handle.net/123456789/2028
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dc.contributor.authorГой, Тарас Петрович-
dc.date.accessioned2020-03-24T15:00:21Z-
dc.date.available2020-03-24T15:00:21Z-
dc.date.issued2019-
dc.identifier.citationGoy, T. Fibonacci and Lucas identities using Toeplitz-Hessenberg matrices / T. Goy, M. Shattuck // Applications and Applied Mathematics. – 2019. – 14(2). – P. 699-715uk_UA
dc.identifier.urihttp://hdl.handle.net/123456789/2028-
dc.description.abstractIn 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.isoenuk_UA
dc.subjectFibonacci sequenceuk_UA
dc.subjectLucas sequenceuk_UA
dc.subjectToeplitz-Hessenberg matrixuk_UA
dc.subjectTrudi’s formulauk_UA
dc.subjectmultinomial coefficientuk_UA
dc.titleFibonacci and Lucas identities using Toeplitz–Hessenberg matricesuk_UA
dc.typeArticleuk_UA
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