Introduction to Enumerative Combinatorics
Book 1
Book 2
Book 3
Book 1
Book 2
Book 3
Book 1
Book 2
Book 3
Book 1
Book 2
Book 3
Home > Mathematics and Science Textbooks > Mathematics > Combinatorics and graph theory > Introduction to Enumerative Combinatorics
Introduction to Enumerative Combinatorics

Introduction to Enumerative Combinatorics


     0     
5
4
3
2
1



Out of Stock


Notify me when this book is in stock
X
About the Book

Written by one of the leading authors and researchers in the field, this comprehensive modern text offers a strong focus on enumeration, a vitally important area in introductory combinatorics crucial for further study in the field. Miklós Bóna's text fills the gap between introductory textbooks in discrete mathematics and advanced graduate textbooks in enumerative combinatorics, and is one of the very first intermediate-level books to focus on enumerative combinatorics. The text can be used for an advanced undergraduate course by thoroughly covering the chapters in Part I on basic enumeration and by selecting a few special topics, or for an introductory graduate course by concentrating on the main areas of enumeration discussed in Part II. The special topics of Part III make the book suitable for a reading course.This text is part of the Walter Rudin Student Series in Advanced Mathematics.

Table of Contents:
ForewordPrefaceAcknowledgmentsI How: Methods1 Basic Methods1.1 When We Add and When We Subtract1.1.1 When We Add1.1.2 When We Subtract1.2 When We Multiply1.2.1 The Product Principle1.2.2 Using Several Counting Principles1.2.3 When Repetitions Are Not Allowed1.3 When We Divide1.3.1 The Division Principle1.3.2 Subsets1.4 Applications of Basic Counting Principles1.4.1 Bijective Proofs1.4.2 Properties of Binomial Coefficients1.4.3 Permutations With Repetition1.5 The Pigeonhole Principle1.6 Notes1.7 Chapter Review1.8 Exercises1.9 Solutions to Exercises1.10 Supplementary Exercises2 Direct Applications of Basic Methods2.1 Multisets and Compositions2.1.1 Weak Compositions2.1.2 Compositions2.2 Set Partitions2.2.1 Stirling Numbers of the Second Kind2.2.2 Recurrence Relations for Stirling Numbers of the Second Kind2.2.3 When the Number of Blocks Is Not Fixed2.3 Partitions of Integers2.3.1 Nonincreasing Finite Sequences of Integers2.3.2 Ferrers Shapes and Their Applications2.3.3 Excursion: Euler’s Pentagonal Number Theorem2.4 The Inclusion-Exclusion Principle2.4.1 Two Intersecting Sets2.4.2 Three Intersecting Sets2.4.3 Any Number of Intersecting Sets2.5 The Twelvefold Way2.6 Notes2.7 Chapter Review2.8 Exercises2.9 Solutions to Exercises2.10 Supplementary Exercises3 Generating Functions3.1 Power Series3.1.1 Generalized Binomial Coefficients3.1.2 Formal Power Series3.2 Warming Up: Solving Recursions3.2.1 Ordinary Generating Functions3.2.2 Exponential Generating Functions3.3 Products of Generating Functions3.3.1 Ordinary Generating Functions3.3.2 Exponential Generating Functions3.4 Excursion: Composition of Two Generating Functions3.4.1 Ordinary Generating Functions3.4.2 Exponential Generating Functions3.5 Excursion: A Different Type of Generating Function3.6 Notes3.7 Chapter Review3.8 Exercises3.9 Solutions to Exercises3.10 Supplementary ExercisesII What: Topics4 Counting Permutations4.1 Eulerian Numbers4.2 The Cycle Structure of Permutations4.2.1 Stirling Numbers of the First Kind4.2.2 Permutations of a Given Type4.3 Cycle Structure and Exponential Generating Functions4.4 Inversions4.4.1 Counting Permutations with Respect to Inversions4.5 Notes4.6 Chapter Review4.7 Exercises4.8 Solutions to Exercises4.9 Supplementary Exercises5 Counting Graphs5.1 Counting Trees and Forests5.1.1 Counting Trees5.2 The Notion of Graph Isomorphisms5.3 Counting Trees on Labeled Vertices5.3.1 Counting Forests5.4 Graphs and Functions5.4.1 Acyclic Functions5.4.2 Parking Functions5.5 When the Vertices Are Not Freely Labeled5.5.1 Rooted Plane Trees5.5.2 Binary Plane Trees5.6 Excursion: Graphs on Colored Vertices5.6.1 Chromatic Polynomials5.6.2 Counting k-colored Graphs5.7 Graphs and Generating Functions5.7.1 Generating Functions of Trees5.7.2 Counting Connected Graphs5.7.3 Counting Eulerian Graphs5.8 Notes5.9 Chapter Review5.10 Exercises5.11 Solutions to Exercises5.12 Supplementary Exercises6 Extremal Combinatorics6.1 Extremal Graph Theory6.1.1 Bipartite Graphs6.1.2 Tur´an’s Theorem6.1.3 Graphs Excluding Cycles6.1.4 Graphs Excluding Complete Bipartite Graphs6.2 Hypergraphs6.2.1 Hypergraphs with Pairwise Intersecting Edges6.2.2 Hypergraphs with Pairwise Incomparable Edges6.3 Something Is More Than Nothing: Existence Proofs6.3.1 Property B6.3.2 Excluding Monochromatic Arithmetic Progressions6.3.3 Codes Over Finite Alphabets6.4 Notes6.5 Chapter Review6.6 Exercises6.7 Solutions to Exercises6.8 Supplementary ExercisesIII What Else: Special Topics7 Symmetric Structures7.1 Hypergraphs with Symmetries7.2 Finite Projective Planes7.2.1 Excursion: Finite Projective Planes of Prime Power Order7.3 Error-Correcting Codes7.3.1 Words Far Apart7.3.2 Codes from Hypergraphs7.3.3 Perfect Codes7.4 Counting Symmetric Structures7.5 Notes7.6 Chapter Review7.7 Exercises7.8 Solutions to Exercises7.9 Supplementary Exercises8 Sequences in Combinatorics8.1 Unimodality8.2 Log-Concavity8.2.1 Log-Concavity Implies Unimodality8.2.2 The Product Property8.2.3 Injective Proofs8.3 The Real Zeros Property8.4 Notes8.5 Chapter Review8.6 Exercises8.7 Solutions to Exercises8.8 Supplementary Exercises9 Counting Magic Squares and Magic Cubes9.1 An Interesting Distribution Problem9.2 Magic Squares of Fixed Size9.2.1 The Case of n = 39.2.2 The Function Hn(r) for Fixed n9.3 Magic Squares of Fixed Line Sum9.4 Why Magic Cubes Are Different9.5 Notes9.6 Chapter Review9.7 Exercises9.8 Supplementary ExercisesA The Method of Mathematical InductionA.1 Weak InductionA.2 Strong InductionBibliographyIndexFrequently Used Notation


Best Sellers


Product Details
  • ISBN-13: 9780073125619
  • Publisher: McGraw-Hill Education - Europe
  • Publisher Imprint: McGraw-Hill Professional
  • Height: 244 mm
  • Returnable: N
  • Weight: 853 gr
  • ISBN-10: 007312561X
  • Publisher Date: 16 Oct 2005
  • Binding: Hardback
  • Language: English
  • Spine Width: 30 mm
  • Width: 165 mm


Similar Products

Add Photo
Add Photo

Customer Reviews

REVIEWS      0     
Click Here To Be The First to Review this Product
Introduction to Enumerative Combinatorics
McGraw-Hill Education - Europe -
Introduction to Enumerative Combinatorics
Writing guidlines
We want to publish your review, so please:
  • keep your review on the product. Review's that defame author's character will be rejected.
  • Keep your review focused on the product.
  • Avoid writing about customer service. contact us instead if you have issue requiring immediate attention.
  • Refrain from mentioning competitors or the specific price you paid for the product.
  • Do not include any personally identifiable information, such as full names.

Introduction to Enumerative Combinatorics

Required fields are marked with *

Review Title*
Review
    Add Photo Add up to 6 photos
    Would you recommend this product to a friend?
    Tag this Book Read more
    Does your review contain spoilers?
    What type of reader best describes you?
    I agree to the terms & conditions
    You may receive emails regarding this submission. Any emails will include the ability to opt-out of future communications.

    CUSTOMER RATINGS AND REVIEWS AND QUESTIONS AND ANSWERS TERMS OF USE

    These Terms of Use govern your conduct associated with the Customer Ratings and Reviews and/or Questions and Answers service offered by Bookswagon (the "CRR Service").


    By submitting any content to Bookswagon, you guarantee that:
    • You are the sole author and owner of the intellectual property rights in the content;
    • All "moral rights" that you may have in such content have been voluntarily waived by you;
    • All content that you post is accurate;
    • You are at least 13 years old;
    • Use of the content you supply does not violate these Terms of Use and will not cause injury to any person or entity.
    You further agree that you may not submit any content:
    • That is known by you to be false, inaccurate or misleading;
    • That infringes any third party's copyright, patent, trademark, trade secret or other proprietary rights or rights of publicity or privacy;
    • That violates any law, statute, ordinance or regulation (including, but not limited to, those governing, consumer protection, unfair competition, anti-discrimination or false advertising);
    • That is, or may reasonably be considered to be, defamatory, libelous, hateful, racially or religiously biased or offensive, unlawfully threatening or unlawfully harassing to any individual, partnership or corporation;
    • For which you were compensated or granted any consideration by any unapproved third party;
    • That includes any information that references other websites, addresses, email addresses, contact information or phone numbers;
    • That contains any computer viruses, worms or other potentially damaging computer programs or files.
    You agree to indemnify and hold Bookswagon (and its officers, directors, agents, subsidiaries, joint ventures, employees and third-party service providers, including but not limited to Bazaarvoice, Inc.), harmless from all claims, demands, and damages (actual and consequential) of every kind and nature, known and unknown including reasonable attorneys' fees, arising out of a breach of your representations and warranties set forth above, or your violation of any law or the rights of a third party.


    For any content that you submit, you grant Bookswagon a perpetual, irrevocable, royalty-free, transferable right and license to use, copy, modify, delete in its entirety, adapt, publish, translate, create derivative works from and/or sell, transfer, and/or distribute such content and/or incorporate such content into any form, medium or technology throughout the world without compensation to you. Additionally,  Bookswagon may transfer or share any personal information that you submit with its third-party service providers, including but not limited to Bazaarvoice, Inc. in accordance with  Privacy Policy


    All content that you submit may be used at Bookswagon's sole discretion. Bookswagon reserves the right to change, condense, withhold publication, remove or delete any content on Bookswagon's website that Bookswagon deems, in its sole discretion, to violate the content guidelines or any other provision of these Terms of Use.  Bookswagon does not guarantee that you will have any recourse through Bookswagon to edit or delete any content you have submitted. Ratings and written comments are generally posted within two to four business days. However, Bookswagon reserves the right to remove or to refuse to post any submission to the extent authorized by law. You acknowledge that you, not Bookswagon, are responsible for the contents of your submission. None of the content that you submit shall be subject to any obligation of confidence on the part of Bookswagon, its agents, subsidiaries, affiliates, partners or third party service providers (including but not limited to Bazaarvoice, Inc.)and their respective directors, officers and employees.

    Accept

    Fresh on the Shelf


    Inspired by your browsing history


    Your review has been submitted!

    You've already reviewed this product!