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    How to count : an introduction to combinatorics / R.B.J.T. Allenby, Alan Slomson.

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    • Title:How to count : an introduction to combinatorics / R.B.J.T. Allenby, Alan Slomson.
    •    
    • Author/Creator:Allenby, R. B. J. T.
    • Other Contributors/Collections:Slomson, A. B.
      Slomson, A. B. Introduction to combinatorics.
    • Published/Created:Boca Raton, FL : CRC Press, ©2011.

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    • Library of Congress Subjects:Combinatorial analysis.
    • Edition:2nd ed.
    • Description:xv, 430 p. : ill ; 27 cm.
    • Series:Discrete mathematics and its applications.
    • Notes:First published as: an introduction to combinatorics, 1991.
      Includes bibliographical references and index.
    • ISBN:9781420082609 (hardcover : alk. paper)
      1420082604 (hardcover : alk. paper)
    • Contents:Chapter 1. What's It All About?
      1.1. What is Combinatorics?
      1.2. Classic Problems
      1.3. What You Need To Know
      1.4. Are You Sitting Comfortably?
      Chapter 2. Permutations and Combinations
      2.1. Combinatorial Approach
      2.2. Permutations
      2.3. Combinations
      2.4. Applications To Probability Problems
      2.5. Multinomial Theorem
      2.6. Permutations And Cycles
      Chapter 3. Occupancy Problems
      3.1. Counting The Solutions Of Equations
      3.2. New Problems From Old
      3.3. "Reduction" Theorem For The Stirling Numbers
      Chapter 4. Inclusion-Exclusion Principle
      4.1. Double Counting
      4.2. Derangements
      4.3. Formula For The Stirling Numbers
      Chapter 5. Stirling and Catalan Numbers
      5.1. Stirling Numbers
      5.2. Permutations And Stirling Numbers
      5.3. Catalan Numbers
      Chapter 6. Partitions and Dot Diagrams
      6.1. Partitions
      6.2. Dot Diagrams
      6.3. Bit Of Speculation
      6.4. More Proofs Using Dot Diagrams
      Chapter 7. Generating Functions and Recurrence Relations
      7.1. Functions And Power Series
      7.2. Generating Functions
      7.3. What Is A Recurrence Relation?
      7.4. Fibonacci Numbers
      7.5. Solving Homogeneous Linear Recurrence Relations
      7.6. Nonhomogeneous Linear Recurrence Relations
      7.7. Theory Of Linear Recurrence Relations
      7.8. Some Nonlinear Recurrence Relations
      Chapter 8. Partitions and Generating Functions
      8.1. Generating Function For The Partition Numbers
      8.2. Quick(ISH) Way of Finding p(n)
      8.3. Upper Bound For The Partition Numbers
      8.4. Hardy-Ramanujan Formula
      8.5. Story Of Hardy And Ramanujan
      Chapter 9. Introduction to Graphs
      9.1. Graphs And Pictures
      9.2. Graphs: A Picture-Free Definition
      9.3. Isomorphism Of Graphs
      9.4. Paths And Connected Graphs
      9.5. Planar Graphs
      9.6. Eulerian Graphs
      9.7. Hamiltonian Graphs
      9.8. Four-Color Theorem
      Chapter 10. Trees
      10.1. What Is A Tree?
      10.2. Labeled Trees
      10.3. Spanning Trees And Minimal Connectors
      10.4. Shortest-Path Problem
      Chapter 11. Groups of Permutations
      11.1. Permutations As Groups
      11.2. Symmetry Groups
      11.3. Subgroups And Lagrange's Theorem
      11.4. Orders Of Group Elements
      11.5. Orders Of Permutations
      Chapter 12. Group Actions
      12.1. Colorings
      12.2. Axioms For Group Actions
      12.3. Orbits
      12.4. Stabilizers
      Chapter 13. Counting Patterns
      13.1. Frobenius's Counting Theorem
      13.2. Applications Of Frobenius's Counting Theorem
      Chapter 14. Polya Counting
      14.1. Colorings And Group Actions
      14.2. Pattern Inventories
      14.3. Cycle Index Of A Group
      14.4. Polya's Counting Theorem: Statement And Examples
      14.5. Polya's Counting Theorem: The Proof
      14.6. Counting Simple Graphs
      Chapter 15. Dirichlet's Pigeonhole Principle
      15.1. Origin Of The Principle
      15.2. Pigeonhole Principle
      15.3. More Applications Of The Pigeonhole Principle
      Chapter 16. Ramsey Theory
      16.1. What Is Ramsey's Theorem?
      16.2. Three Lovely Theorems
      16.3. Graphs Of Many Colors
      16.4. Euclidean Ramsey Theory
      Chapter 17. Rook Polynomials and Matchings
      17.1. How Rook Polynomials Are Defined
      17.2. Matchings And Marriages.
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