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I am very weak in combinatorics and I have not got my understanding clear to think a problem in combinatorics and come up with a logic/analysis.I want to develop both the interest and the understanding so that I can proceed further and solve questions.Are there books on combinatorics that are both interesting and has good problems(problems of all difficulties)

anotherhyooman
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  • My go-to book is Grimaldi's Discrete and Combinatorial Mathematics. It's not all-encompassing, but it's enough to cover most of the bases and to spark the reader's interest. – Matti P. Nov 05 '20 at 12:52
  • thanks a lot for your suggestion!.. – anotherhyooman Nov 05 '20 at 12:53
  • David Patrick -- Intermediate Counting and Probability (2007). Wonderful book; great selection of problems at varying levels of difficulty. – quasi Nov 05 '20 at 12:55
  • @quasi I actually found that book to be lacking good problems. The challenge problems at the end of the chapters are sparse. I prefer Introductory Combinatorics by Brualdi. – Favst Nov 05 '20 at 21:56
  • I think the Grimaldi & Brualdi books are excellent. Also, Basic Techniques of Combinatorial Theory by D I A Cohen, https://www.maa.org/press/maa-reviews/basic-techniques-of-combinatorial-theory although it's probably long out-of-print and hard to find. – Gerry Myerson Nov 05 '20 at 22:52

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Two suggestions:

Schaum's Outline of Theory and Problems of Combinatorics by V.K. Balakrishnan has lots of worked problems and extensive coverage. Inexpensive, too.

A Walk Through Combinatorics: An Introduction to Enumeration and Graph Theory, Second Edition by Miklos Bona. "The strong points of this book are in particular a very inviting style of exposition, in which developments are always well motivated and well illustrated by numerous examples, and the long list of problems at the end of each chapter, with detailed solutions..." (Zentralblatt MATH, quoted on the back cover of the book). Of the combinatorics books on my shelf, I think this is the one most likely to get the reader hooked on combinatorics.

awkward
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Here are three books that I like:

  1. Introductory Combinatorics by Brualdi. It covers theory well, though not in an encylopaedic way, and has lots of examples.
  2. A Path to Combinatorics for Undergraduates by Andreescu. This books pretends to be for undergraduates, but like most of Andreescu's works, it is for olympiad or contest preparation. There is nothing "undergraduate" about it and can be approached by a motivated school student.
  3. Combinatorics: A Problem-Based Approach by Mladenović. There is a huge selection of problems in this book and it is fairly comprehensive.
Favst
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I second awkward’s recommendation of Bóna.

Kenneth P. Bogart’s Combinatorics Through Guided Discovery is freely available online and is a copious source of problems, many of which have hints at the back of the book.

Brian M. Scott
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