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I've been studying combinatorics for some time from a contest-prep perspective. The books I have more-or-less gone through are Principles and Techniques in Combinatorics and A Walk Through in Combinatorics (very slightly read). What I'd like to know is that are there more books on Combinatorics with numerous problems and proper, clear explanations. I went through a book on Combinatorics by Mladenovic--Its coverage of topics was great, with Burnside Lemma, Graph Theory, etc. However, the book escalated very quickly with complex explanations for even simple solutions that I knew.

So, tl;dr: please suggest books on Combinatorics that are informal in their tone, that delve into Combinatorics deeply with a hell lotta practice problems of ALL difficulties.

I don't want to be stuck on an impossible problem, but rather learn concepts nice and easy. Also, some difficult problems every now and then would be good too.

Thanks a ton!

P.S.: I read Combinatorics by Vilenkin and I liked the approach through real life examples. Would like something like it. Or is it good enough for contests?

Edit: I've already checked AoPS recommendations, previously as well. All I want are your personal opinions, kindly. (Any Math Olympians here? And enthusiasts?)

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    $\begingroup$ I don't know, sir, I got the English Translation, I think... $\endgroup$
    – Sen47
    Dec 15, 2019 at 12:15

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Have a look here.

In this aops-link you'll find some of the best books regarding Olympiad-training categorized into Theory, Problems and Both books and into Algebra, Number Theory, Geometry and Combinatorics (which are the basic olympiad disciplines).

I personally haven't read all of them, however, I would recommend you to read two of the books that helped me the most when I participated in math-olympiads:

  • A Course in Combinatorics - Lint and Wilson

  • A Path to Combinatorics for Undergraduates - Andreescu, Feng

Hope it helps ;)

Remark: Besides, I recommend you to practice as much as you can, i.e. solve as many Combinatorics problems as possible. I used to believe that reading Theory-Books would be enough, but it turned out that it wasn not...

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  • $\begingroup$ I think so too, about solving problems. The thing is, if I could have a book with relevant theory+problems. However, thanks a lot for your advice(+1). I'll wait for some more answers! $\endgroup$
    – Sen47
    Dec 15, 2019 at 13:12
  • $\begingroup$ I think I'll use Path to Combinatorics, seems really good. Do you know any problem books on Combinatorics? $\endgroup$
    – Sen47
    Dec 16, 2019 at 11:23
  • $\begingroup$ Well, there's this excellent pdf by Amir Hossein Parvardi $\endgroup$
    – Dr. Mathva
    Dec 17, 2019 at 16:51
  • $\begingroup$ You can also work with the IMO shortlisted Combinatorics problems. These might be difficult though $\endgroup$
    – Dr. Mathva
    Dec 17, 2019 at 16:52

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