Please use this identifier to cite or link to this item: http://hdl.handle.net/123456789/8081
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dc.contributor.authorГой, Тарас Петрович-
dc.contributor.authorShattuck, Mark-
dc.date.accessioned2020-09-28T07:30:15Z-
dc.date.available2020-09-28T07:30:15Z-
dc.date.issued2020-
dc.identifier.citationGoy, T. Fibonacci–Lucas identities and the generalized Trudi formula / T. Goy, M. Shattuck // Notes on Number Theory and Discrete Mathematics. – 2020. – 26 (3). – P. 203-217.uk_UA
dc.identifier.urihttp://hdl.handle.net/123456789/8081-
dc.description.abstractIn this paper, we evaluate determinants of several families of Hessenberg matrices having Fibonacci numbers as their nonzero entries. By the generalized Trudi formula, these determinant identities may be written equivalently as formulas for the Lucas numbers in terms of the Fibonacci. We provide both algebraic and combinatorial proofs of our determinant results. The former makes use of expansion along columns and induction, while the latter draws upon the definition of the determinant as a signed sum over the symmetric group and uses parity-changing involutions.uk_UA
dc.language.isoenuk_UA
dc.subjectHessenberg matrixuk_UA
dc.subjectFibonacci numbersuk_UA
dc.subjectDeterminantuk_UA
dc.subjectTrudi formulauk_UA
dc.subjectLucas numbersuk_UA
dc.titleFibonacci–Lucas identities and the generalized Trudi formulauk_UA
dc.typeArticleuk_UA
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