Results 11 to 20 of about 1,028,977 (179)
Binet – Type Formula For The Sequence of Tetranacci Numbers by Alternate Methods
Mathematical Journal of Interdisciplinary Sciences, 2019 The sequence {Tn} of Tetranacci numbers is defined by recurrence relation Tn= Tn-1 + Tn-2 + Tn-3 + Tn-4; n≥4 with initial condition T0=T1=T2=0 and T3=1. In this Paper, we obtain the explicit formulla-Binet-type formula for Tn by two different methods. We
Gautam S. Hathiwala, Devbhadra V. Shah
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A generalized Cauchy-Binet formula and applications to total positivity and majorization
Journal of Multivariate Analysis, 1988 Publisher Summary This chapter discusses a generalized Cauchy–Binet formula and applications to total positivity and majorization. The identification and analysis of multivariate totally positive kernels, log concave densities, Schur-concave functions, and symmetric unimodal functions relies heavily on their conservation under convolution operators ...
Samuel Karlin, Yosef Rinott
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Multiparameter Quantum Cauchy-Binet Formulas [PDF]
Algebras and Representation Theory, 2020 The quantum Cayley-Hamilton theorem for the generator of the reflection equation algebra has been proven by Pyatov and Saponov, with explicit formulas for the coefficients in the Cayley-Hamilton formula. However, these formulas do not give an \emph{easy} way to compute these coefficients.
Matthias Floré
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Binet's second formula, Hermite's generalization, and two related identities
Open Mathematics, 2023 Legendre was the first to evaluate two well-known integrals involving sines and exponentials. One of these integrals can be used to prove Binet’s second formula for the logarithm of the gamma function.
R. Boyack
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A multilinear algebra proof of the Cauchy–Binet formula and a multilinear version of Parsevalʼs identity [PDF]
Linear Algebra and its Applications, 2013 9 pages, 2 ...
Takis Konstantopoulos
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A generalization of the Binet-Minc formula for the evaluation of permanents
Linear Algebra and its Applications, 1988 AbstractA formula for the sum of the coefficients of monomials of the form xl1j1⋯xlpjP is given, where j1,…,jp are given positive integers, in the polynomial ∏i=1n∑j=1maijxj. When p=n and j1 = ⋯jn = 1, this formula coincides with the Binet-Minc formula for the evaluation of the permanent of the matrix (aij).
Akihiro Nishi
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A simplified Binet formula for k-generalized Fibonacci numbers
, 2009 We present a particularly nice Binet-style formula that can be used to produce the k-generalized Fibonacci numbers (that is, the Tribonaccis, Tetranaccis, etc). Furthermore, we show that in fact one needs only take the integer closest to the first term of this Binet-style formula to generate the desired sequence.
Gregory P. Dresden
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A combined approach to Perrin and Padovan hybrid sequences [PDF]
Heliyon, 2021 Recently, there has been huge interest to a new numeric set, which brings together three numerical systems: complex, hyperbolic and dual numbers, called as hybrid number.
Seyyed H. Jafari Petroudi +3 more
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New results for the Fibonacci sequence using Binet's formula [PDF]
International Mathematical Forum, 2018 Let k ≥ 1 and h = 0, . . . , k − 1. In this note we study the monotonicity of the sequences (Fkn+h) , where Fn denotes the n-th Fibonacci number. In particular, we prove that the sequences (F2n) 1/n and (F2n+1) 1/n are strictly increasing for n ≥ 1.
Reza Farhadian, R. Jakimczuk
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Noncommutative determinants, Cauchy–Binet formulae, and Capelli-type identities I. Generalizations of the Capelli and Turnbull identities [PDF]
The Electronic Journal of Combinatorics, 2009 We prove, by simple manipulation of commutators, two noncommutative generalizations of the Cauchy–Binet formula for the determinant of a product. As special cases we obtain elementary proofs of the Capelli identity from classical invariant theory and of Turnbull's Capelli-type identities for symmetric and antisymmetric matrices.
S. Caracciolo +2 more
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