Problem-Solving Methods in Combinatorics

1. Front Matter

   Pages I-IX

   PDF

2. First Concepts

   • Pablo Soberón

   Pages 1-16

3. The Pigeonhole Principle

   • Pablo Soberón

   Pages 17-26

4. Invariants

   • Pablo Soberón

   Pages 27-41

5. Graph Theory

   • Pablo Soberón

   Pages 43-57

6. Functions

   • Pablo Soberón

   Pages 59-76

7. Generating Functions

   • Pablo Soberón

   Pages 77-92

8. Partitions

   • Pablo Soberón

   Pages 93-99

9. Hints for the Problems

   • Pablo Soberón

   Pages 101-112

10. Solutions to the Problems

    • Pablo Soberón

    Pages 113-167

11. Back Matter

    Pages 169-174

    PDF

Every year there is at least one combinatorics problem in each of the major international mathematical olympiads. These problems can only be solved with a very high level of wit and creativity. This book explains all the problem-solving techniques necessary to tackle these problems, with clear examples from recent contests.  It also includes a large problem section for each topic, including hints and full solutions so that the reader can practice the material covered in the book.​ The material will be useful not only to participants in the olympiads and their coaches but also in university courses on combinatorics.

• functions
• graph theory
• invariants
• olympiad
• partitions
• pigeonhole principle
• combinatorics

From the reviews:

 “Soberón (Univ. College London, UK) presents tools, techniques, and some tricks to tackle problems of varying difficulty in combinatorial mathematics in this well-written book. … Salient features include the wealth of examples, exercises, and problems and two additional chapters with hints and solutions to the problems. Valuable for all readers interested in combinatorics and useful as a course resource on the subject. Summing Up: Highly recommended. Upper-division undergraduate through professional mathematics collections.” (D. V. Chopra, Choice, Vol. 51 (4), December, 2013)

• Department of Mathematics, University College London, London, United Kingdom

  Pablo Soberón

Pablo Soberón (born 1988) is the first Mexican to obtain a gold medal in the International Mathematical Olympiad. After participating in mathematical olympiads, he has also trained Mexican teams for various international mathematical contests. He currently does research in discrete geometry at University College London and enjoys olympiad problem-solving in his free time.

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