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    Introduction to Enumerative and Analytic Combinatorics

    Introduction to Enumerative and Analytic Combinatorics by Bona, Miklos;

    Sorozatcím: Discrete Mathematics and Its Applications;

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    A termék adatai:

    • Kiadás sorszáma 3
    • Kiadó Chapman and Hall
    • Megjelenés dátuma 2025. március 11.

    • ISBN 9781032302706
    • Kötéstípus Keménykötés
    • Terjedelem566 oldal
    • Méret 234x156 mm
    • Súly 1210 g
    • Nyelv angol
    • 694

    Kategóriák

    Rövid leírás:

    These award-winning textbook targets the gap between introductory texts in discrete mathematics and advanced graduate texts in enumerative combinatorics. The author?s goal is to make combinatorics more accessible to encourage student interest and to expand the number of students studying this rapidly expanding field. 

    Több

    Hosszú leírás:

    This award-winning textbook targets the gap between introductory texts in discrete mathematics and advanced graduate texts in enumerative combinatorics. The author?s goal is to make combinatorics more accessible to encourage student interest and to expand the number of students studying this rapidly expanding field.


    The book first deals with basic counting principles, compositions and partitions, and generating functions. It then focuses on the structure of permutations, graph enumeration, and extremal combinatorics. Lastly, the text discusses supplemental topics, including error-correcting codes, properties of sequences, and magic squares.


    Updates to the Third Edition include:



    • Quick Check exercises at the end of each section, which are typically easier than the regular exercises at the end of each chapter.

    • A new section discussing the Lagrange Inversion Formula and its applications, strengthening the analytic flavor of the book.

    • An extended section on multivariate generating functions.

    Numerous exercises contain material not discussed in the text allowing instructors to extend the time they spend on a given topic. A chapter on analytic combinatorics and sections on advanced applications of generating functions, demonstrating powerful techniques that do not require the residue theorem or complex integration, and extending coverage of the given topics are highlights of the presentation.


    The second edition was recognized as an Outstanding Academic Title of the Year by Choice Magazine, published by the American Library Association.

    Több

    Tartalomjegyzék:

    Basic methods
    When we add and when we subtract
    When we multiply
    When we divide
    Applications of basic counting principles
    The pigeonhole principle
    Notes
    Chapter review
    Exercises
    Solutions to exercises
    Supplementary exercises


    Applications of basic methods
    Multisets and compositions
    Set partitions
    Partitions of integers
    The inclusion-exclusion principle
    The twelvefold way
    Notes
    Chapter review
    Exercises
    Solutions to exercises
    Supplementary exercises


    Generating functions
    Power series
    Warming up: Solving recurrence relations
    Products of generating functions
    Compositions of generating functions
    A different type of generating functions
    Notes
    Chapter review
    Exercises
    Solutions to exercises
    Supplementary exercises



    TOPICS



    Counting permutations
    Eulerian numbers
    The cycle structure of permutations
    Cycle structure and exponential generating functions
    Inversions
    Advanced applications of generating functions to permutation enumeration
    Notes
    Chapter review
    Exercises
    Solutions to exercises
    Supplementary exercises


    Counting graphs
    Trees and forests
    Graphs and functions
    When the vertices are not freely labeled
    Graphs on colored vertices
    Graphs and generating functions
    Notes
    Chapter review
    Exercises
    Solutions to exercises
    Supplementary exercises


    Extremal combinatorics
    Extremal graph theory
    Hypergraphs
    Something is more than nothing: Existence proofs
    Notes
    Chapter review
    Exercises
    Solutions to exercises
    Supplementary exercises



    AN ADVANCED METHOD



    Analytic combinatorics
    Exponential growth rates
    Polynomial precision
    More precise asymptotics
    Notes
    Chapter review
    Exercises
    Solutions to exercises
    Supplementary exercises



    SPECIAL TOPICS



    Symmetric structures
    Designs
    Finite projective planes
    Error-correcting codes
    Counting symmetric structures
    Notes
    Chapter review
    Exercises
    Solutions to exercises
    Supplementary exercises


    Sequences in combinatorics
    Unimodality
    Log-concavity
    The real zeros property
    Notes
    Chapter review
    Exercises
    Solutions to exercises
    Supplementary exercises


    Counting magic squares and magic cubes
    A distribution problem
    Magic squares of fixed size
    Magic squares of fixed line sum
    Why magic cubes are different
    Notes
    Chapter review
    Exercises
    Solutions to exercises
    Supplementary exercises


    Appendix: The method of mathematical induction
    Weak induction
    Strong induction

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