Title | Applications of Fibonacci Numbers [electronic resource] : Volume 3 Proceedings of 'The Third International Conference on Fibonacci Numbers and Their Applications', Pisa, Italy, July 25-29, 1988 / edited by G. E. Bergum, A. N. Philippou, A. F. Horadam |
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Imprint | Dordrecht : Springer Netherlands, 1990 |
Connect to | http://dx.doi.org/10.1007/978-94-009-1910-5 |
Descript | XXIV, 366 p. online resource |
The Role of the Fibonacci Sequence in the Isolation of the Real Roots of Polynomial Equations -- A GCD Property on Pascal's Pyramid and the Corresponding LCM Property of the Modified Pascal Pyramid -- Translatable and Rotatable Configurations Which Give Equal Product, Equal GCD and Equal LCM Properties Simultaneously -- Fibonacci Length of Generating Pairs in Groups -- A Generalization of Fibonacci Trees -- Generalized Fibonacci Numbers are Rounded Powers -- On Generalized Fibonacci Numbers of Graphs -- An Investigation of Sequences Derived from Hoggatt Sums and Hoggatt Triangles -- Representation of Natural Numbers as Sums of Fibonacci Numbers: An Application to Modern Cryptography -- A Note on Ramifications Concerning the Construction of Pythagorean Triples from Recursive Sequences -- On the Representation of {Fkn/Fn}, {Fkn/Ln }, {Lkn/Ln} and {Lkn/Fn} as Zeckendorf Sums -- Functional Recurrences -- Concentric Cycles in Mosaic Graphs -- Fibonacci Triangles -- Mosaic Numbers of Fibonacci Trees -- Falling Factorial Polynomials of Generalized Fibonacci Type -- Some Notes on Fibonacci Binary Sequences -- Congruences for Weighted and Degenerate Stirling Numbers -- An Inverse Theorem on Fibonacci Numbers -- Some Results on Divisibility Sequences -- On Mental Calculation of Repeating Decimals, Finding Fibonacci Numbers and a Connection to Pascal's Triangle -- Diophantine Representation of Fibonacci Numbers Over Natural Numbers -- On Prime Divisors of the Terms of Second Order Linear Recurrence Sequences -- An Alternating Product Representation for Real Numbers -- Maximum Length of the Euclidean Algorithm and Continued Fractions in F(X) -- Recurrence Relations in Sinusoids and Their Applications to Spectral Analysis and to the Resolution of Algebraic Equations -- A Recurrence Relation for Gaussian Multinomial Coefficients -- Some Binomial Fibonacci Identities -- A Survey of Properties of Third Order Pell Diagonal Functions -- Multivariate Fibonacci Polynomials of Order K and the Multiparameter Negative Binomial Distribution of the Same Order -- Longest Circular Runs with an Application in Reliability Via the Fibonacci-Type Polynomials of Order K -- Fibonacci Numbers and an Algorithm of Lemoine and Kรกtai -- Generalizations of Sequences of Lucas and Bell -- Distribution of Residues of Certain Second-Order Linear Recurrences Modulo P -- The Fibonacci Tree, Hofstadter and the Golden String -- Three Number Trees โ Their Growth Rules and Related Number Properties