THIRTEENTH INTERNATIONAL CONFERENCE ON FIBONACCI NUMBERS AND THEIR APPLICATIONS
|
|
|
- Julia Reed
- 5 years ago
- Views:
Transcription
1 Monday, July 7 First Day of the Conference 8:30 9:30 Pick up packets and say hello Mathematics and Biology Building, Room 62 9:30 9:50 Welcome and Announcements Monday Morning Session moderated by William Webb Session Time Title Authors 9:50 10:10 Combinatorial Trigonometry through Chebyshev Polynomials Arthur Benjamin, Larry Ericksen, Pallavi Jayawant, Mark Shattuck 10:10 10:30 New Variation on the Tower of Hanoi Paul K. Stockmeyer, Fred Lunnon, Victor Mascolo 10:30 10:50 Counting i paths R. L. Ollerton 10:50 11:20 Refreshment Break 11:20 11:40 Board Tiling of the Second Kind Peter G. Anderson, Ryan H. Lewis 11:40 12:00 Triangles with coordinates of vertices from Pell and Pell Lucas numbers Zvonko Čerin, Gian Mario Gianella 12:00 1:30 Lunch Break Monday Afternoon Session moderated by Peter Anderson 1:30 1:50 Spectral Properties of Some Combinatorial Matrices Pante Stănică 1:50 2:10 Fibonacci Phyllotaxis by Asymmetric Cell Division: Zeckendorf and Wythoff Trees Colin Paul Spears, Marjorie Bicknell Johnson, John J. Yan 2:10 2:30 About (a,b) Type Balancing Numbers Péter Olajos 2:30 2:50 A Style of Music Characterized by Fibonacci Numbers and the Golden Ratio Casey Mongoven 2:50 3:20 Refreshment Break 3:20 3:40 Beatty Sequences Generated Several Ways Clark Kimberling 3:40 4:00 Word Recurrences, with Word Reversals Radex and J. C. Turner APFP Integer Word Sequences 4:00 4:20 Generalized Fibonacci Dynamical Systems Adriano Fagiolini, Aldo Balestrino, Giancarlo Zini 4:20 4:40 Generalized Alternating Subsets with Permutations Augustine O. Munagi 7:00 10:00 Wine & Cheese Reception University Conference Center
2 Tuesday, July 8 Second Day of the Conference Tuesday Morning Session moderated by Clark Kimberling 9:00 9:20 Independent Chess Pieces on Fibonacci Boards Heiko Harborth 9:20 9:40 A p adic formula for the Norlund numbers and for Paul Young Bernoulli numbers of the second kind 9:40 10:00 Operators acting on sequences Stefano Barbero 10:00 10:20 Hadamard Circulants and Recurrences Moon Ho Lee, Veselin Vl. Vavrek 10:20 10:50 Refreshment Break 10:50 11:10 φ F n =F m Florian Luca, F. Nicolae 11:10 11:30 On Recurrences over Algebraic Number Fields Lawrence Somer Containing a d th Root of Unity 11:30 11:50 Fibonacci Complementary Duality in Optimization Akifumi Kira, Seiichi Iwamoto 11:50 1:30 Lunch Break Tuesday Afternoon Session moderated by Marjorie Bicknell Johnson 1:30 1:50 Proving Identities Involving Products of Recurrence William Webb Sequences and Binomial Coefficients 1:50 2:10 Some Properties of Generalized Third Order Pell A.G.Shannon, C.K. Wong Numbers 2:10 2:30 On Melham s Sum Kiyota Ozeki 2:30 2:50 On some new Fibonacci identities Hideyuki Ohtsuka, Shigeru Nakamura 2:50 3:20 Refreshment Break 3:20 3:40 Restricted Occupancy of s Kinds of Cells and Generalized Pascal Triangles Spiros D. Dafnis, Frosso S. Makri, Andreas N. Philippou 3:40 4:00 Fibonacci Representations and Wythoff Arrays Larry Ericksen 4:00 4:20 An Entry Point Algorithm for High Speed Factorization Ramón Glez Regueral 4:20 4:40 Fibonacci Jacket Conference Matrices Moon Ho Lee, Veselin Vl. Vavrek 4:40 5:00 A Canonical formulation to applied physics problems Karem Ben Mahmoud with exogenous boundary conditions using Fibonacci Boubaker sequence like Boubaker polynomials
3
4 9:00 12:00 Tour of Patras Wednesday, July 9 Third Day of the Conference Wednesday Morning 12:00 1:30 Lunch Break Wednesday Afternoon Session Moderated by Art Benjamin 1:30 1:50 Complementary Equations and Zeckendorf Arrays Clark Kimberling, Peter Moses 1:50 2:10 Triangular Number Patterns in the Coefficients and Diagonal Sequences of Zernike and Related Polynomials Rebecca A. Hillman, Michael R. Bacon, Charles K. Cook 2:10 2:30 On Products of Fibonacci Numbers and Their Recurrence Relations Charles K. Cook, Rebecca Hillman 2:30 2:50 The 1/3 2/3 prime proportion in α n α n. Christian Ballot 2:50 3:30 Refreshment Break 3:30 4:30 Edouard Lucas Invited Lecture Primality testing variations on a theme of Lucas Carl Pomerance
5 Thursday, July 10 Fourth Day of the Conference Thursday Morning Session moderated by Florian Luca 9:00 9:20 Knapsack Cryptography Using Recurrence Sequences William Webb, Bala Krishnamoorthy, Nathan Moyer 9:20 9:40 On The Ljunggren Equation y 2 =2x 4 1 Konstantinos A. Draziotis 9:40 10:00 Mixed succession rules: the commutative case Silvia Bacchelli, Luca Ferrari, Renzo Pinzani 10:00 10:20 Generalizations of the Bramhagupta Polynomials Medha Bodas, Samih Obaid 10:20 10:50 Refreshment Break 10:50 11:10 Convolutions Associated with Tilings of the Second Kind Peter G. Anderson, Ryan H. Lewis 11:10 11:30 Diophantine equations and balancing numbers Liptai Kálmán 11:30 11:50 On the generalization of the Fibonacci coefficient polynomials Ferenc Mátyás 11:50 1:30 Lunch Break Thursday Afternoon Session moderated by Karl Dilcher 1:30 1:50 Lucas a 1, a 2,, a k =1 Sequences and Curtis Cooper Pseudoprimes 1:50 2:10 Lucas Quotient Lemmas Marjorie Bicknell Johnson, Colin Paul Spears 2:10 2:30 Central Trinomial Coefficients and Convolution Type Roman Witula, Damian Identities Stota 2:30 2:50 Quasi Fibonacci Numbers of Order 13 Roman Witula, Damian Stota 2:50 3:20 Refreshment Break 3:20 3:40 Fibonacci Sequence and its Extensions through S.P. Pethe Differential Equations 3:40 4:00 The (p,q) Fibonacci Hyperbolic Functions and Their Properties Gülfer Tatar, Neşe Ömür, Yücel Türker Ulutaş 4:00 4:20 On Fibonacci k Vectors and Their Applications Neşe Ömür, Yücel Türker
6 Ulutaş 4:20 4:40 Fundamental Theorem For Generalized Quaternions Marco Abrate 4:40 5:00 Title TBA Bennett Stancil
7 Friday, July 11 Fifth Day of the Conference Friday Morning Session moderated by Curtis Cooper 9:00 9:20 Stern polynomials and continued fractions Karl Dilcher 9:20 9:40 On Compositeness in Multicompositions Temba Shonhiwa 9:40 10:00 Digital Roots, Vedic Multiplications and Fibonacci Osman Yürekli Numbers 10:00 10:20 Log concavity and unimodality in Pascal triangles László Szalay, H. Belbachir, F. Bencherif 10:20 10:50 Refreshment Break 10:50 11:30 Problem Session 11:30 11:50 Business Meeting 12:00 1:30 Lunch Break 1:30 5:00 Fibonacci Board of Directors Meeting
ABSTRACTS. 13th International Conference on Fibonacci Numbers and Their Applications
ABSTRACTS 13th International Conference on Fibonacci Numbers and Their Applications The Edouard Lucas Invited Lecture: Carl Pomerance Primality testing variations on a theme of Lucas One of the earliest
Monday, July 5 First Day of the Conference. Monday Morning Session moderated by William A. Webb
FOURTEENTH INTERNATIONAL CONFERENCE ON FIBONACCI NUMBERS AND THEIR APPLICATIONS Mathematical Institute UNAM, Morelia, Mexico July 5 9, 2010 Monday, July 5 First Day of the Conference 8:30 9:15 Pick up
Conference program. Sunday, June 24 Arrival Day. Monday, June 25 First Day of the Conference
Conference program Sunday, June 24 Arrival Day 16:0020:00 Conference registration at Hotel Eger (Szálloda str. 1) Monday, June 25 First Day of the Conference 8:309:15 9:159:30 Conference registration,
Fibonacci-18 Conference Schedule
Fibonacci-18 Conference Schedule Monday, July 2 8:15 Registration opens 8:45 Opening Remarks 9:00 9:25 Christian Ballot: Variations on Catalan Lucasnomials 9:30 9:55 Heiko Harborth: A Conjecture for Pascal
FOURTEENTH INTERNATIONAL CONFERENCE ON FIBONACCI NUMBERS AND THEIR APPLICATIONS. ABSTRACTS OF TALKS in the order in which they are presented
FOURTEENTH INTERNATIONAL CONFERENCE ON FIBONACCI NUMBERS AND THEIR APPLICATIONS Mathematical Institute UNAM, Morelia, Mexico July 5 9, 2010 ABSTRACTS OF TALKS in the order in which they are presented MONDAY,
Two Identities Involving Generalized Fibonacci Numbers
Two Identities Involving Generalized Fibonacci Numbers Curtis Cooper Dept. of Math. & Comp. Sci. University of Central Missouri Warrensburg, MO 64093 U.S.A. email: cooper@ucmo.edu Abstract. Let r 2 be
Counting on Chebyshev Polynomials
DRAFT VOL. 8, NO., APRIL 009 1 Counting on Chebyshev Polynomials Arthur T. Benjamin Harvey Mudd College Claremont, CA 91711 benjamin@hmc.edu Daniel Walton UCLA Los Angeles, CA 90095555 waltond@ucla.edu
A MATRIX GENERALIZATION OF A THEOREM OF FINE
A MATRIX GENERALIZATION OF A THEOREM OF FINE ERIC ROWLAND To Jeff Shallit on his 60th birthday! Abstract. In 1947 Nathan Fine gave a beautiful product for the number of binomial coefficients ( n, for m
Named numbres. Ngày 25 tháng 11 năm () Named numbres Ngày 25 tháng 11 năm / 7
Named numbres Ngày 25 tháng 11 năm 2011 () Named numbres Ngày 25 tháng 11 năm 2011 1 / 7 Fibonacci, Catalan, Stirling, Euler, Bernoulli Many sequences are famous. 1 1, 2, 3, 4,... the integers. () Named
Generalized Lucas Sequences Part II
Introduction Generalized Lucas Sequences Part II Daryl DeFord Washington State University February 4, 2013 Introduction Èdouard Lucas: The theory of recurrent sequences is an inexhaustible mine which contains
TILING PROOFS OF SOME FORMULAS FOR THE PELL NUMBERS OF ODD INDEX
#A05 INTEGERS 9 (2009), 53-64 TILING PROOFS OF SOME FORMULAS FOR THE PELL NUMBERS OF ODD INDEX Mark Shattuck Department of Mathematics, University of Tennessee, Knoxville, TN 37996-1300 shattuck@math.utk.edu
arxiv: v1 [math.co] 11 Aug 2015
![arxiv: v1 [math.co] 11 Aug 2015](/thumbs/86/93497673.jpg "arxiv: v1 [math.co] 11 Aug 2015")
arxiv:1508.02762v1 [math.co] 11 Aug 2015 A Family of the Zeckendorf Theorem Related Identities Ivica Martinjak Faculty of Science, University of Zagreb Bijenička cesta 32, HR-10000 Zagreb, Croatia Abstract
EVERY POSITIVE K-BONACCI-LIKE SEQUENCE EVENTUALLY AGREES WITH A ROW OF THE K-ZECKENDORF ARRAY
EVERY POSITIVE K-BONACCI-LIKE SEQUENCE EVENTUALLY AGREES WITH A ROW OF THE K-ZECKENDORF ARRAY PETER G. ANDERSON AND CURTIS COOPER Abstract. For k 2, a fixed integer, we work with the k-bonacci sequence,
Binomial coefficients and k-regular sequences
Binomial coefficients and k-regular sequences Eric Rowland Hofstra University New York Combinatorics Seminar CUNY Graduate Center, 2017 12 22 Eric Rowland Binomial coefficients and k-regular sequences
The solutions to the two examples above are the same.
One-to-one correspondences A function f : A B is one-to-one if f(x) = f(y) implies that x = y. A function f : A B is onto if for any element b in B there is an element a in A such that f(a) = b. A function
UNIT 9 (Chapter 7 BI) Polynomials and Factoring Name:
UNIT 9 (Chapter 7 BI) Polynomials and Factoring Name: The calendar and all assignments are subject to change. Students will be notified of any changes during class, so it is their responsibility to pay
Binomial Coefficient Identities/Complements
Binomial Coefficient Identities/Complements CSE21 Fall 2017, Day 4 Oct 6, 2017 https://sites.google.com/a/eng.ucsd.edu/cse21-fall-2017-miles-jones/ permutation P(n,r) = n(n-1) (n-2) (n-r+1) = Terminology
ADVANCED PROBLEMS AND SOLUTIONS
Edited by RAYMOND E. WHITNEY Please send all communications concerning ADVANCED PROBLEMS AND SOLUTIONS to RAYMOND E. WHITNEY, MATHEMATICS DEPARTMENT, LOCK HAVEN UNIVERSITY, LOCK HA PA 17745, This department
Applications. More Counting Problems. Complexity of Algorithms
Recurrences Applications More Counting Problems Complexity of Algorithms Part I Recurrences and Binomial Coefficients Paths in a Triangle P(0, 0) P(1, 0) P(1,1) P(2, 0) P(2,1) P(2, 2) P(3, 0) P(3,1) P(3,
From Simplest Recursion to the Recursion of Generalizations of Cross Polytope Numbers
Kennesaw State University DigitalCommons@Kennesaw State University Honors College Capstones and Theses Honors College Spring 5-6-2017 From Simplest Recursion to the Recursion of Generalizations of Cross
Some Determinantal Identities Involving Pell Polynomials
International Journal of Scientific and Innovative Mathematical Research (IJSIMR) Volume, Issue 5, May 4, PP 48-488 ISSN 47-7X (Print) & ISSN 47-4 (Online) www.arcjournals.org Some Determinantal Identities
MATRICES AND LINEAR RECURRENCES IN FINITE FIELDS
Owen J. Brison Departamento de Matemática, Faculdade de Ciências da Universidade de Lisboa, Bloco C6, Piso 2, Campo Grande, 1749-016 LISBOA, PORTUGAL e-mail: brison@ptmat.fc.ul.pt J. Eurico Nogueira Departamento
In Search of Combinatorial Fibonacci Identities
Summer Research 2010 Duncan McGregor Mike Rowell Department of Mathematics and Computer Science Pacific University, Oregon NUMS, April 9, 2011 Outline 1 2 Fibonacci Sequence Defined Recursively: f 0 =
ON SUMS OF SQUARES OF PELL-LUCAS NUMBERS. Gian Mario Gianella University of Torino, Torino, Italy, Europe.
INTEGERS: ELECTRONIC JOURNAL OF COMBINATORIAL NUMBER THEORY 6 (2006), #A15 ON SUMS OF SQUARES OF PELL-LUCAS NUMBERS Zvonko Čerin University of Zagreb, Zagreb, Croatia, Europe cerin@math.hr Gian Mario Gianella
Notes Friday, September 09, 2016
Notes Friday, September 09, 2016 Day 1 - Polynomials Page 1 Notes Friday, September 09, 2016 Day 1 - Polynomials Page 2 Notes Friday, September 09, 2016 Day 1 - Polynomials Page 3 Notes Friday, September
Unit D Student Success Sheet (SSS) Factoring (section 2.1)
Unit D Student Success Sheet (SSS) Factoring (section 2.1) Standards: Alg 1 14.0, Alg 1 11.0, Alg 2 4.0 Mr. Werdel Segerstrom High School Math Analysis Honors 2011-2012 Name: Period: Mr. Werdel: Monday
Cryptography. Number Theory with AN INTRODUCTION TO. James S. Kraft. Lawrence C. Washington. CRC Press
AN INTRODUCTION TO Number Theory with Cryptography James S Kraft Gilman School Baltimore, Maryland, USA Lawrence C Washington University of Maryland College Park, Maryland, USA CRC Press Taylor & Francis
On Some Properties of Bivariate Fibonacci and Lucas Polynomials
1 2 3 47 6 23 11 Journal of Integer Sequences, Vol. 11 (2008), Article 08.2.6 On Some Properties of Bivariate Fibonacci and Lucas Polynomials Hacène Belbachir 1 and Farid Bencherif 2 USTHB/Faculty of Mathematics
Chapter 3: Section 3.1: Factors & Multiples of Whole Numbers
Chapter 3: Section 3.1: Factors & Multiples of Whole Numbers Prime Factor: a prime number that is a factor of a number. The first 15 prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43,
Algebra 1 Unit 6B Factoring
Algebra 1 Unit 6B Factoring Monday Tuesday Wednesday Thursday Friday 9 A Day 10 B Day 11 A Day 12 B Day 13 A Day Test Exponents and Polynomials Factor GCF and Trinomials box method Factoring Trinomials
ADVANCED PROBLEMS AND SOLUTIONS
Edited by RAYMOND E. WHITNEY Please send all communications concerning to RAYMOND E. WHITNEY, MATHEMATICS DEPARTMENT, LOCK HAVEN UNIVERSITY, LOCK HAVEN, PA 17745. This department especially welcomes problems
Series Editor KENNETH H. ROSEN INDUCTION THEORY AND APPLICATIONS. of Manitoba. University. Winnipeg, Canada. CRC Press. Taylor StFrancis Group
DISCIIETE MATHEMATICS AND ITS APPLICATIONS Series Editor KENNETH H. ROSEN HANDBOOK OF MATHEMATICAL INDUCTION THEORY AND APPLICATIONS David S. Gunderson University of Manitoba Winnipeg, Canada CRC Press
Ron Paul Curriculum Mathematics 8 Lesson List
Ron Paul Curriculum Mathematics 8 Lesson List 1 Introduction 2 Algebraic Addition 3 Algebraic Subtraction 4 Algebraic Multiplication 5 Week 1 Review 6 Algebraic Division 7 Powers and Exponents 8 Order
q-binomial coefficient congruences
CARMA Analysis and Number Theory Seminar University of Newcastle August 23, 2011 Tulane University, New Orleans 1 / 35 Our first -analogs The natural number n has the -analog: [n] = n 1 1 = 1 + +... n
On Sums of Products of Horadam Numbers
KYUNGPOOK Math J 49(009), 483-49 On Sums of Products of Horadam Numbers Zvonko ƒerin Kopernikova 7, 10010 Zagreb, Croatia, Europe e-mail : cerin@mathhr Abstract In this paper we give formulae for sums
Formulas for sums of squares and products of Pell numbers
Formulas for sums of squares and products of Pell numbers TEORIA DEI NUMERI Nota di Zvonko ČERIN e Gian Mario GIANELLA presentata dal socio Corrispondente Marius I. STOKA nell adunanza del 1 Giugno 2006.
CS311H. Prof: Peter Stone. Department of Computer Science The University of Texas at Austin
CS311H Prof: Department of Computer Science The University of Texas at Austin Recurrences In how many ways can a 2 n rectangular checkerboard be tiled using 1 2 and 2 2 pieces? Good Morning, Colleagues
1 Sequences and Summation
1 Sequences and Summation A sequence is a function whose domain is either all the integers between two given integers or all the integers greater than or equal to a given integer. For example, a m, a m+1,...,
MATH 122 SYLLBAUS HARVARD UNIVERSITY MATH DEPARTMENT, FALL 2014
MATH 122 SYLLBAUS HARVARD UNIVERSITY MATH DEPARTMENT, FALL 2014 INSTRUCTOR: HIRO LEE TANAKA UPDATED THURSDAY, SEPTEMBER 4, 2014 Location: Harvard Hall 102 E-mail: hirohirohiro@gmail.com Class Meeting Time:
All numbered readings are from Beck and Geoghegan s The art of proof.
MATH 301. Assigned readings and homework All numbered readings are from Beck and Geoghegan s The art of proof. Reading Jan 30, Feb 1: Chapters 1.1 1.2 Feb 6, 8: Chapters 1.3 2.1 Feb 13, 15: Chapters 2.2
F. T. HOWARD AND CURTIS COOPER
SOME IDENTITIES FOR r-fibonacci NUMBERS F. T. HOWARD AND CURTIS COOPER Abstract. Let r 1 be an integer. The r-generalized Fibonacci sequence {G n} is defined as 0, if 0 n < r 1; G n = 1, if n = r 1; G
CLASSES OF IDENTITIES FOR THE GENERALIZED FIBONACCI NUMBERS G n = G n _ t + G n _ c FROM MATRICES WITH CONSTANT VALUED DETERMINANTS
CLASSES OF IDENTITIES FOR THE GENERALIZED FIBONACCI NUMBERS G n = G n _ t + G n _ c FROM MATRICES WITH CONSTANT VALUED DETERMINANTS Marjorle Bicknell-Johnson 665 Fairlane Avenue, Santa Clara, CA 955 Colin
Announcements. CSE 321 Discrete Structures. Counting. Counting Rules. Important cases of the Product Rule. Counting examples.
Announcements CSE 321 Discrete Structures Winter 2008 Lecture 16 Counting Readings Friday, Wednesday: Counting 6 th edition: 5.1, 5.2, 5.3, 5 th edition: 4.1, 4.2. 4.3 Lecture 16 video will be posted on
A Note on the Determinant of Five-Diagonal Matrices with Fibonacci Numbers
Int. J. Contemp. Math. Sciences, Vol. 3, 2008, no. 9, 419-424 A Note on the Determinant of Five-Diagonal Matrices with Fibonacci Numbers Hacı Civciv Department of Mathematics Faculty of Art and Science
Combinatorial Diophantine Equations
Combinatorial Diophantine Equations Szabolcs Tengely Arctic Number Theory School, Helsinki May 21, 2011 Integer sequences Problem: find intersection of integer sequences Some well-known sequences: perfect
L U C A S SEQUENCES AND FUNCTIONS O F A 3-BY-3 M A T R I X
L U C A S SEQUENCES AND FUNCTIONS O F A 3-BY-3 M A T R I X R. S. Melham School of Mathematical Sciences, University of Technology, Sydney PO Box 123, Broadway, NSW 2007 Australia {SubmittedMay 1997-Final
11. THE IAUX XXVIII GENERAL ASSEMBLY DAY BY DAY
11. THE IAUX XXVIII GENERAL ASSEMBLY DAY BY DAY PROGRAMME and EVENT SCHEDULE DAY BY DAY Week 1 Sunday 19 August 9:30-17:30 Executive Committee Meeting EC91-1 plus Division Presidents NAOC Monday 20 August
Number Theory, Algebra and Analysis. William Yslas Vélez Department of Mathematics University of Arizona
Number Theory, Algebra and Analysis William Yslas Vélez Department of Mathematics University of Arizona O F denotes the ring of integers in the field F, it mimics Z in Q How do primes factor as you consider
NEW IDENTITIES FOR THE COMMON FACTORS OF BALANCING AND LUCAS-BALANCING NUMBERS
International Journal of Pure and Applied Mathematics Volume 85 No. 3 013, 487-494 ISSN: 1311-8080 (printed version); ISSN: 1314-3395 (on-line version) url: http://www.ijpam.eu doi: http://dx.doi.org/10.173/ijpam.v85i3.5
Problem 1, posed by Curtis Cooper: Find a linear recurrence relation Let a, b, c and d 0 be integers, and let
PROBLEM PROPOSALS CLARK KIMBERLING These fourteen problems were posed by participants of the Seventeenth International Conference on Fibonacci Numbers and Their Applications, Université de Caen Normandie,
P.1: Algebraic Expressions, Mathematical Models, and Real Numbers
Chapter P Prerequisites: Fundamental Concepts of Algebra Pre-calculus notes Date: P.1: Algebraic Expressions, Mathematical Models, and Real Numbers Algebraic expression: a combination of variables and
EXTENDING FREITAG S FIBONACCI LIKE MAGIC SQUARE TO OTHER DIMENSIONS
EXTENDING FREITAG S FIBONACCI LIKE MAGIC SQUARE TO OTHER DIMENSIONS MICHAEL R. BACON, CHARLES K. COOK, AND RUSSELL JAY HENDEL Abstract. The Fibonacci like 4 4 magic square of Herta Freitag is analyzed
BIJECTIVE PROOFS FOR FIBONACCI IDENTITIES RELATED TO ZECKENDORF S THEOREM
BIJECTIVE PROOFS FOR FIBONACCI IDENTITIES RELATED TO ZECKENDORF S THEOREM Philip Matchett Wood Department of Mathematics, Rutgers University, Piscataway, NJ 08854 e-mail: matchett@math.rutgers.edu (Submitted
ELEMENTARY PROBLEMS AND SOLUTIONS. Edited by A. P. Hillman
Edited by A. P. Hillman Please send all material for to Dr. A. P. HILLMAN; 709 SOLANO DR., S.E.; ALBUQUERQUE, NM 87108. Each solution should he on a separate sheet (or sheets) and must be received within
Florian Luca Instituto de Matemáticas, Universidad Nacional Autonoma de México, C.P , Morelia, Michoacán, México
Florian Luca Instituto de Matemáticas, Universidad Nacional Autonoma de México, C.P. 8180, Morelia, Michoacán, México e-mail: fluca@matmor.unam.mx Laszlo Szalay Department of Mathematics and Statistics,
IRIS Undergraduate Internship Orientation Week May 26 June 1, 2013 New Mexico Tech
IRIS Undergraduate Internship Orientation Week May 26 June 1, 2013 New Mexico Tech Staff: Rick Aster (NMT) Greg Chavez (PIC) Gary Axen (NMT) Katie Foster (U. of Wyoming & Program Alumnus) Michael Hubenthal
Bijective proofs for Fibonacci identities related to Zeckendorf s Theorem
Bijective proofs for Fibonacci identities related to Zeckendorf s Theorem Philip Matchett Wood Department of Mathematics, Rutgers University, Hill Center Busch Campus, 0 Frelinghuysen Rd, Piscataway, NJ
Titles and abstracts
Titles and abstracts Workshop Effective Methods for Diophantine Problems *** Mike Bennett (University of British Columbia) An old and new approach to Goormaghtigh s equation This is joint work with Adela
Pascal triangle variation and its properties
Pascal triangle variation and its properties Mathieu Parizeau-Hamel 18 february 2013 Abstract The goal of this work was to explore the possibilities harnessed in the the possible variations of the famous
TILING PROOFS OF SOME FIBONACCI-LUCAS RELATIONS. Mark Shattuck Department of Mathematics, University of Tennessee, Knoxville, TN , USA
INTEGERS: ELECTRONIC JOURNAL OF COMBINATORIAL NUMBER THEORY 8 (008), #A18 TILING PROOFS OF SOME FIBONACCI-LUCAS RELATIONS Mark Shattuck Department of Mathematics, University of Tennessee, Knoxville, TN
At-A-Glance SIAM Events Mobile App
At-A-Glance SIAM Events Mobile App Scan the QR code with any QR reader and download the TripBuilder EventMobile app to your iphone, ipad, itouch or Android mobile device.you can also visit www.tripbuildermedia.com/apps/siamevents
1. Introduction Definition 1.1. Let r 1 be an integer. The r-generalized Fibonacci sequence {G n } is defined as
SOME IDENTITIES FOR r-fibonacci NUMBERS F. T. HOWARD AND CURTIS COOPER Abstract. Let r 1 be an integer. The r-generalized Fibonacci sequence {G n} is defined as 8 >< 0, if 0 n < r 1; G n = 1, if n = r
In memoriam Péter Kiss
Kálmán Liptai Eszterházy Károly Collage, Leányka út 4, 3300 Eger, Hungary e-mail: liptaik@gemini.ektf.hu (Submitted March 2002-Final Revision October 2003) In memoriam Péter Kiss ABSTRACT A positive integer
THE ZECKENDORF ARRAY EQUALS THE WYTHOFF ARRAY
Clark Kimberllng University of Evansville, Evansville, IN 47722 (Submitted February 1993) 1. INTRODUCTION It is well known that every n in the set N of positive integers is uniquely a sum of nonconsecutive
Catholic Central High School
Catholic Central High School Course: Basic Algebra 2 Department: Mathematics Length: One year Credit: 1 Prerequisite: Completion of Basic Algebra 1 or Algebra 1, Basic Plane Geometry or Plane Geometry,
Industrial Strength Factorization. Lawren Smithline Cornell University
Industrial Strength Factorization Lawren Smithline Cornell University lawren@math.cornell.edu http://www.math.cornell.edu/~lawren Industrial Strength Factorization Given an integer N, determine the prime
Balancing sequences of matrices with application to algebra of balancing numbers
Notes on Number Theory and Discrete Mathematics ISSN 1310 5132 Vol 20 2014 No 1 49 58 Balancing sequences of matrices with application to algebra of balancing numbers Prasanta Kumar Ray International Institute
A hyperfactorial divisibility Darij Grinberg *long version*
A hyperfactorial divisibility Darij Grinberg *long version* Let us define a function H : N N by n H n k! for every n N Our goal is to prove the following theorem: Theorem 0 MacMahon We have H b + c H c
Exercises MAT2200 spring 2014 Ark 4 Homomorphisms and factor groups
Exercises MAT2200 spring 2014 Ark 4 Homomorphisms and factor groups This Ark concerns the weeks No. (Mar ) and No. (Mar ). It is not very logical to have lectures on Fridays and problem solving in plenum
On the Sum of Corresponding Factorials and Triangular Numbers: Some Preliminary Results
Asia Pacific Journal of Multidisciplinary Research, Vol 3, No 4, November 05 Part I On the Sum of Corresponding Factorials and Triangular Numbers: Some Preliminary Results Romer C Castillo, MSc Batangas
Announcements. CS243: Discrete Structures. Sequences, Summations, and Cardinality of Infinite Sets. More on Midterm. Midterm.
Announcements CS43: Discrete Structures Sequences, Summations, and Cardinality of Infinite Sets Işıl Dillig Homework is graded, scores on Blackboard Graded HW and sample solutions given at end of this
The Édouard Lucas Memorial Lecture
Abstracts The Édouard Lucas Memorial Lecture Hugh C. Williams, University of Calgary, Calgary, AB, Canada Mersenne, Fibonacci and Lucas: The Mersenne Prime Story and Beyond On Dec. 26 of last year, it
Pre-Calculus Assignment Sheet Unit 8-3rd term January 20 th to February 6 th 2015 Polynomials
Pre-Calculus Assignment Sheet Unit 8- rd term January 0 th to February 6 th 01 Polynomials Date Topic Assignment Calculator Did it Tuesday Multiplicity of zeroes of 1/0/1 a function TI-nspire activity
Improving the Accuracy of Primality Tests by Enhancing the Miller-Rabin Theorem
Improving the Accuracy of Primality Tests by Enhancing the Miller-Rabin Theorem Shyam Narayanan Fourth Annual MIT-PRIMES Conference Mentor: David Corwin Project Proposed by Stefan Wehmeier and Ben Hinkle
UNCORRECTED SAMPLE PAGES. Extension 1. The binomial expansion and. Digital resources for this chapter
15 Pascal s In Chapter 10 we discussed the factoring of a polynomial into irreducible factors, so that it could be written in a form such as P(x) = (x 4) 2 (x + 1) 3 (x 2 + x + 1). In this chapter we will
Algorithm Analysis Recurrence Relation. Chung-Ang University, Jaesung Lee
Algorithm Analysis Recurrence Relation Chung-Ang University, Jaesung Lee Recursion 2 Recursion 3 Recursion in Real-world Fibonacci sequence = + Initial conditions: = 0 and = 1. = + = + = + 0, 1, 1, 2,
Fermat s Little Theorem. Fermat s little theorem is a statement about primes that nearly characterizes them.
Fermat s Little Theorem Fermat s little theorem is a statement about primes that nearly characterizes them. Theorem: Let p be prime and a be an integer that is not a multiple of p. Then a p 1 1 (mod p).
27 Wyner Math 2 Spring 2019
27 Wyner Math 2 Spring 2019 CHAPTER SIX: POLYNOMIALS Review January 25 Test February 8 Thorough understanding and fluency of the concepts and methods in this chapter is a cornerstone to success in the
CBMS Conference on Higher Representation Theory. Schedule of Talks. July 6, 2014, Sunday. July 7, 2014, Monday. (all talks are held in SAS 1102, NCSU)
CBMS Conference on Higher Representation Theory Schedule of Talks (all talks are held in SAS 1102, NCSU) July 6, 2014, Sunday 8:30-9:00 Registration, Coffee and Refreshments, 4th floor lounge 9:00-9:15
1 Solution of a Large-Scale Traveling-Salesman Problem... 7 George B. Dantzig, Delbert R. Fulkerson, and Selmer M. Johnson
Part I The Early Years 1 Solution of a Large-Scale Traveling-Salesman Problem............ 7 George B. Dantzig, Delbert R. Fulkerson, and Selmer M. Johnson 2 The Hungarian Method for the Assignment Problem..............
On arithmetic functions of balancing and Lucas-balancing numbers
MATHEMATICAL COMMUNICATIONS 77 Math. Commun. 24(2019), 77 1 On arithmetic functions of balancing and Lucas-balancing numbers Utkal Keshari Dutta and Prasanta Kumar Ray Department of Mathematics, Sambalpur
Sunday, June 10 Monday, June 11 Tuesday, June 12
At-A-Glance Society for Industrial and Applied Mathematics 3600 Market Street, 6th Floor Philadelphia, PA 19104-2688 USA Telephone: +1-215-382-9800 Fax: +1-215-386-7999 Conference E-mail: meetings@siam.org
College Prep Math Final Exam Review Packet
College Prep Math Final Exam Review Packet Name: Date of Exam: In Class 1 Directions: Complete each assignment using the due dates given by the calendar below. If you are absent from school, you are still
4. Write the multiplication sentence that is represented by the diagram at right. 6. Use the distributive property to determine each product.
Polynomials Practice Questions Complete the following on a separate piece of paper.. Write the prime factorization of 0.. Given the numbers, 5, and 7, determine the: GCF LCM. Use algebra tiles or a diagram
Enumerating Distinct Chessboard Tilings and Generalized Lucas Sequences Part I
Enumerating Distinct Chessboard Tilings and Generalized Lucas Sequences Part I Daryl DeFord Washington State University January 28, 2013 Roadmap 1 Problem 2 Symmetry 3 LHCCRR as Vector Spaces 4 Generalized
I-2 Index. Coterminal Angles, 738 Counting numbers, 8 Cramer, Gabriel, 309 Cramer s rule, 306 Cube root, 427, 434 Cylinder, right circular, 117
Index Absolute value, 18 equations, 154, 162 inequalities, 159, 162 Absolute error, 158 Addition, 4 associative property, 19 commutative property, 18 of complex numbers, 481 of fractions, 21 of functions,
1.2 Inductive Reasoning
1.2 Inductive Reasoning Goal Use inductive reasoning to make conjectures. Key Words conjecture inductive reasoning counterexample Scientists and mathematicians look for patterns and try to draw conclusions
Unit 4 Day 8 Symmetry & Compositions
Unit 4 Day 8 Symmetry & Compositions Warm Up Day 8 1. f ( ) 4 3. g( ) 4 a. f(-1)= a. -g()= b. f(3)= b. g(+y)= c. f(-y)= c. g(-)= 3. Write and graph an equation that has the following: -Nonremovable discontinuity
Notice: Individual students, nonprofit libraries, or schools are permitted to make fair use of the papers and its solutions.
Notice: Individual students, nonprofit libraries, or schools are permitted to make fair use of the papers and its solutions. Republication, systematic copying, or multiple reproduction of any part of this
The Huxley Meeting On Analytic Number Theory September School of Mathematics Cardiff University
The Huxley Meeting On Analytic Number Theory 17 19 September 2014 School of Mathematics Cardiff University Location: The workshop will take place at the following address: School of Mathematics Cardiff
Lucas Polynomials and Power Sums
Lucas Polynomials and Power Sums Ulrich Tamm Abstract The three term recurrence x n + y n = (x + y (x n + y n xy (x n + y n allows to express x n + y n as a polynomial in the two variables x + y and xy.
COMPLEMENTARY FAMILIES OF THE FIBONACCI-LUCAS RELATIONS. Ivica Martinjak Faculty of Science, University of Zagreb, Zagreb, Croatia
#A2 INTEGERS 9 (209) COMPLEMENTARY FAMILIES OF THE FIBONACCI-LUCAS RELATIONS Ivica Martinjak Faculty of Science, University of Zagreb, Zagreb, Croatia imartinjak@phy.hr Helmut Prodinger Department of Mathematics,
Advanced Engineering Mathematics Prof. Pratima Panigrahi Department of Mathematics Indian Institute of Technology, Kharagpur
Advanced Engineering Mathematics Prof. Pratima Panigrahi Department of Mathematics Indian Institute of Technology, Kharagpur Lecture No. # 02 Vector Spaces, Subspaces, linearly Dependent/Independent of
Definitions. Notations. Injective, Surjective and Bijective. Divides. Cartesian Product. Relations. Equivalence Relations
Page 1 Definitions Tuesday, May 8, 2018 12:23 AM Notations " " means "equals, by definition" the set of all real numbers the set of integers Denote a function from a set to a set by Denote the image of
Advanced Counting Techniques
. All rights reserved. Authorized only for instructor use in the classroom. No reproduction or further distribution permitted without the prior written consent of McGraw-Hill Education. Advanced Counting
A CONGRUENTIAL IDENTITY AND THE 2-ADIC ORDER OF LACUNARY SUMS OF BINOMIAL COEFFICIENTS
A CONGRUENTIAL IDENTITY AND THE 2-ADIC ORDER OF LACUNARY SUMS OF BINOMIAL COEFFICIENTS Gregory Tollisen Department of Mathematics, Occidental College, 1600 Campus Road, Los Angeles, USA tollisen@oxy.edu
Algebra III and Trigonometry Summer Assignment
Algebra III and Trigonometry Summer Assignment Welcome to Algebra III and Trigonometry! This summer assignment is a review of the skills you learned in Algebra II. Please bring this assignment with you
USACIL TRAINING. Training Agenda. Presented by Trial Counsel Assistance Program (TCAP) FORT GILLEM, GA JAN Admin. Breaks.
USACIL TRAINING Training Agenda Presented by Trial Counsel Assistance Program (TCAP) FORT GILLEM, GA 13 17 JAN 2014 Admin Breaks Lecture 1 DAY 1: M ONDAY, January 13 0 9 0 0-0 9 5 0 Welcome and Laboratory
Probability & Combinatorics Test and Solutions February 18, 2012
1. A standard 12-hour clock has hour, minute, and second hands. How many times do two hands cross between 1:00 and 2:00 (not including 1:00 and 2:00 themselves)? Answer: 119 Solution: We know that the
SOME MORE PATTERNS FROM PASCAL^ TRIANGLE
SOME MORE PATTERNS FROM PASCAL^ TRIANGLE. D. ANDERSON Civil Service College, London SWlV RB. INTRODUCTION Over the years, much use has been made of Pascal's triangle, part of which is shown in Table..