Proofs that Really Count: The Art of Combinatorial Proof at Meripustak

Proofs that Really Count: The Art of Combinatorial Proof

Books from same Author: T. Benjamin and Jennifer J. Quinn

Books from same Publisher: Universities Press

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  • General Information  
    Author(s)T. Benjamin and Jennifer J. Quinn
    PublisherUniversities Press
    Edition2022
    ISBN9789393330116
    Pages208
    BindingPaperback
    LanguageEnglish
    Publish YearJanuary 2022

    Description

    Universities Press Proofs that Really Count: The Art of Combinatorial Proof by T. Benjamin and Jennifer J. Quinn

    Foreword
    1 Fibonacci Identities
    1.1 Combinatorial Interpretation of Fibonacci Numbers
    1.2 Identities
    1.3 A Fun Application
    1.4 Notes
    1.5 Exercises

    2 Gibonacci and Lucas Identities
    2.1 Combinatorial Interpretation of Lucas Numbers
    2.2 Lucas Identities
    2.3 Combinatorial Interpretation of Gibonacci Numbers
    2.4 Gibonacci Identities
    2.5 Notes
    2.6 Exercises

    3 Linear Recurrences
    3.1 Combinatorial Interpretations of Linear Recurrences
    3.2 Identities for Second-Order Recurrences
    3.3 Identities for Third-Order Recurrences
    3.4 Identities for kth Order Recurrences
    3.5 Get Real! Arbitrary Weights and Initial Conditions
    3.6 Notes
    3.7 Exercises

    4 Continued Fractions
    4.1 Combinatorial Interpretation of Continued Fractions
    4.2 Identities
    4.3 NonsimpleContinued Fractions
    4.4 Get Real Again!
    4.5 Notes
    4.6 Exercises

    5 Binomial Identities
    5.1 Combinatorial Interpretations of Binomial Coefficients
    5.2 Elementary Identities
    5.3 More Binomial Coefficient Identities
    5.4 Multichoosing
    5.5 Odd Numbers in Pascal’s Triangle
    5.6 Notes
    5.7 Exercises

    6 Alternating Sign Binomial Identities
    6.1 ParityArguments and Inclusion-Exclusion
    6.2 Alternating Binomial Coefficient Identities
    6.3 Notes
    6.4 Exercises

    7 Harmonic and Stirling Number Identities
    7.1 HarmonicNumbers and Permutations
    7.2 StirlingNumbers of the First Kind
    7.3 Combinatorial Interpretation of Harmonic Numbers
    7.4 Recounting Harmonic Identities
    7.5 StirlingNumbers of the Second Kind
    7.6 Notes
    7.7 Exercises

    8 Number Theory
    8.1 Arithmetic Identities
    8.2 Algebra and Number Theory
    8.3 GCDs Revisited
    8.4 Lucas’ Theorem
    8.5 Notes
    8.6 Exercises

    9 Advanced Fibonacci & Lucas Identities
    9.1 More Fibonacci and Lucas Identities
    9.2 Colorful Identities
    9.3 Some “Random” Identities and the Golden Ratio
    9.4 Fibonacci and Lucas Polynomials
    9.5 NegativeNumbers
    9.6 Open Problems and Vajda Data

    Some Hints and Solutions for Chapter Exercises
    Appendix of Combinatorial Theorems
    Appendix of Identities
    Bibliography
    Index