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?)
Best Answer
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...