Higher Order Bernoulli Polynomials and Newton Polygons; A. Adelberg. The Fibonacci Shuffle Tree; P.G. Anderson. On the Period of Sequences Modulo a Prime Satisfying a Second Order Recurrence; S. Ando. Generalizations to Large Hexagons of the Star of David Theorem with Respect to GCD; S. Ando, et al. Longest Success and Failure Runs and New Polynomials Related to the Fibonacci-Type Polynomials of Order K; D.L. Antzoulakos, A.N. Philippou. A Note on a Representation Conjecture by Hoggatt; M. Bicknell-Johnson. Some Remarks on the Distribution of Subsequences of Second Order Linear Recurrences; J.R. Burke. A Criterion for Stability of Two-Term Recurrence Sequences Modulo Odd Primes; W. Carlip, et al. A Problem of Diophantus and Pell Numbers; A. Dujella. On the Exceptional Set in the Problem of Diophantus and Davenport; A. Dujella. Substitutive Numeration Systems and a Combinatorial Problem; J.-M. Dumont. A Note on Derived Linear Recurring Sequences; M. Elia. Observations from Computer Experiments on an Integer Equation; D.C. Fielder, C.O. Alford. Some Probabilistic Aspects of the Zeckendorf Decomposition of Integers; P. Filipponi, H.T. Freitag. First Derivative Sequences of Extended Fibonacci and Lucas Polynomials; P. Filipponi, A.F. Horadam. Elements of Zeckendorf Arithmetic; H.T. Freitag, G.M. Phillips. Binomial Coefficients Generalized with Respect to a Discrete Valuation; S. Frisch. The Dying Fibonacci Tree; B. Gittenberger. Smallest Integral Combinatorial Box; H. Harborth, M. Moller. New Aspects of Morgan-Voyce Polynomials; A.F. Horadam. Growing a Self-Similar Tree; Y. Horibe. Lacunary Sums of Binomial Coefficients; F.T. Howard, R. Witt. Some Reciprocal Summation Identities with Applications to the Fibonacci and Lucas Numbers; D. Jennings. A Relative Rank Function on Sets of Continued Fractions Having Bounded Partial Quotients; C. Kimberling. On Sums of the Reciprocals of Prime Divisors of Terms of a Linear Recurrence; P. Kiss. A Fibonacci-Fractal: A Bicolored Self-Similar Multifractal; W. Lang. A Generalisation of Ratios of Fibonacci Numbers with Application to Numerical Quadrature; T.N. Langtry. The Fibonacci Pyramid; T.G. Lavers. On a Three Dimensional Approximation Problem; K. Liptai. Analysis of the Euclidean and Related Algorithms; C.T. Long, W.A. Webb. Fundamental Solutions of u2-5v2 = -4r2; C.T. Long, W.A. Webb. Probable Prime Tests Using Lucas Sequences; W. More. On a Functional Equation Associated with the Fibonacci Numbers; K. Ozeki. Diophantine Properties of Linear Recursive Sequences I; A. Petho. The Cantor-Fibonacci Distribution; H. Prodinger. On the Parity of Certain Partition Functions; N. Robbins. There are Infinitely Many Arithmetical Progressions Formed by Three Different Fibonacci Pseudoprimes; A. Rotkiewicz. On Mikolas' Summation Formula Involving Farey Fractions; K. Sato. Second Order Linear Recurring Sequences in Hypercomplex Numbers; K. Scheicher. The Bell Differential Polynomials; R. Schimming, S.Z. Rida. On Lucas d-Pseudoprimes; L. Somer. Asymmetric Cell Division: Binomial Identities for Age Analysis of Mortal Vs Immortal Trees; C.P. Spears, M. Bicknell-Johnson. The Golden Section and Modern Harmony Mathematics; A.P. Stakhov. Lucas Factors and a Fibonomial Generating Function; I. Strazdins. Elementary Properties of Canonical Number Systems in Quadratic Fields; J.M. Thuswaldner. Three Examples of Triangular Arrays with Optimal Discrepancy and Linear Recurrences; R.F. Tichy. A Multivariate Inverse Polya Distribution of Order K Arising in the Case of Overlapping Success Runs; G.A. Tripsiannis, A.N. Philippou. Introduction to a Fibonacci Geometry; J.C. Turner, A.G. Shannon. Taylor Functionals and the Solution of Linear Difference Equations; L. Verde-Star. Section-Invariant Numbers and Generalised Golden Section Optimization Algorithms; A.A. Zhigljavsky, et al. Subject Index
Author(s): Bergum, G. E.; Philippou, Andreas N.; Horadam, Alwyn F (eds.)
Series: Applications of Fibonacci numbers, vol.7
Publisher: Springer
Year: 1998
Language: English
Pages: 497
Tags: Математика;Теория чисел;
Cover......Page 1
Front matter......Page 2
1. Higher Order Bernoulli Polynomials and Newton Polygons......Page 32
2. The Fibonacci Shuffle Tree......Page 40
3. On The Period of Sequences Modulo a Prime Satisfying A Second order Recurrence......Page 48
4. Generalizations to Large Hexagons of The Star of David Theorem with Respect to Gcd......Page 54
5. Longest Success and Failure Runs and New Polynomials Related to The Fibonacci-Type Polynomials of Order k......Page 60
6. A Note on a Representation Conjecture By Hoggatt......Page 70
7. Some Remarks on The Distribution of Subsequences of Second Order Linear Recurrences......Page 74
8. A Criterion For Stability of Two-Term Recurrence Sequences Modulo Odd Primes......Page 79
9. A Problem of Diophantus and Pell Numbers......Page 91
10. On the Exceptional Set in the Problem of Diophantus and Davenport......Page 99
11. Substitutive Numeration Systems and A Combinatorial Problem......Page 107
12. A Note on Derived Linear Recurring Sequences*......Page 113
13. Observations from Computer Experiments on An Integer Equation......Page 123
14. Some Probabilistic Aspects of the Zeckendorf Decomposition of Integers......Page 134
15. First Derivative Sequences of Extended Fibonacci and Lucas Polynomials......Page 144
16. Elements of Zeckendorf Arithmetic......Page 158
17. Binomial Coefficients Generalized with Respect to a Discrete Valuation......Page 162
18. The Dying Fibonacci Tree......Page 174
19. Smallest Integral Combinatorial Box......Page 182
20. New Aspects of Morgan-Voyce Polynomials......Page 189
21. Growing a Self-Similar Tree......Page 205
22. Lacunary Sums of Binomial Coefficients......Page 213
23. Some Reciprocal Summation Identities with Applications to the Fibonacci and Lucas Numbers......Page 224
24. A Relative Rank Function on Sets of Continued Fractions Having Bounded Partial Quotients......Page 228
25. On Sums of the Reciprocals of Prime Divisors of Terms of a Linear Recurrence......Page 241
26. A Fibonacci-Fractal: A Bicolored Self-Similar Multifractal......Page 247
27. A Generalisation of Ratios of Fibonacci Numbers with Application to Numerical Quadrature......Page 264
28. The Fibonacci Pyramid......Page 279
29. On a Three Dimensional Approximation Problem......Page 288
30. Analysis of the Euclidean and Related Algorithms......Page 294
31. Fundamental Solutions of......Page 302
32. Probable Prime Tests Using Lucas Sequences......Page 306
33. On a Functional Equation Associated with the Fibonacci Numbers......Page 313
34. Diophantine Properties of Linear Recursive Sequences I......Page 317
35. The Cantor-Fibonacci Distribution......Page 332
36. On the Parity of Certain Partition Functions......Page 340
37. There Are Infinitely Many Arithmetical Progressions Formed By Three Different Fibonacci Pseudoprimes......Page 347
38. On MikolÃsâ Summation Formula Involving Farey Fractions......Page 353
39. Second Order Linear Recurring Sequences in Hypercomplex Numbers......Page 357
40. The Bell Differential Polynomials......Page 372
41. On Lucas d-Pseudoprimes......Page 387
42. Asymmetric Cell Division: Binomial Identities for Age Analysis of Mortal vs. Immortal Trees......Page 394
43. The Golden Section and Modern Harmony Mathematics......Page 409
44. Lucas Factors and a Fibonomial Generating Function......Page 416
45. Elementary Properties of Canonical Number Systems in Quadratic Fields......Page 420
46. Three Examples of Triangular Arrays with Optimal Discrepancy and Linear Recurrences......Page 430
47. A Multivariate Inverse Polya Distribution of Order k Arising in the Case of Overlapping Success Runs......Page 439
48. Introduction to a Fibonacci Geometry......Page 449
49. Taylor Functionals and the Solution of Linear Difference Equations......Page 463
50. Section â Invariant Numbers and Generalised Golden Section Optimization Algorithms*......Page 477
Back matter......Page 492
