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I have been trying to improve my combinatorics for Math Olympiad. I am already familiar with like mid - AIME level, ie. essentially I only know short answer combo, and I wanted to improve to like USA(J)MO level and stuff.

But the problem is that there is no good book for olympiad combo (as pranav sriram's book is too $pr0$ for me right now.) And I know that a lot of people say that there is no theory required for Oly combo but I think that's completely false as one needs to know a lot of graph theory, group theory, ramsey theory and many more things I don't even know the name of.

So, I bought a college textbook, How to count by Slomson and I have started to read it.

But one problem I face with college books is that compared to Oly books, the problems are much much tamer and not instructive. What I mean is say if I read a topic from the book, after that when I start to do the exercises, the problems are not such that would cause me (or anyone for that matter) any problems, that is they are usually "textbook problems". So when I learn something, I am not sure how to apply it.

For example, I just read the cycle notation for permutations but I don't understand what/ where it is used.

So my question is, what should I do? Should I continue with this book, learn the basic theory like graph theory/ group theory and so on and then move onto more advanced books/questions, or try something else. Also, is solving this book going to even help me for Olympiads?

Thanks!

Aditya_math
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  • You need an easier book like Principles and Techniques in Combinatorics by Chen Chuan-Chong. Googling "combinatorics olympiad handouts" gives several resources. Googling "combinatorics olympiad book mse" returns more posts like yours. – cosmo5 Feb 21 '21 at 09:22
  • Have you seen AoPS's Intermediate Counting and Probability? See if you can do the diagnostic problems under 'do you need this?' to check up on your progress so far. – Toby Mak Feb 21 '21 at 09:23

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