Book recommendation : Olympiad Combinatorics book

Question

Can anyone recommend me an olympiad style combinatorics book which is suitable for a high schooler ? I know only some basics like Pigeon hole principle and stars and bars . I hope to find a book which contains problems which purely test our originality ( the problems with beautiful constructions like USAMO 2017 -TSTST P2: Which words can Ana pick?, Nim problems, games,tillings, etc ) . More specifically problems which doesn't require theory but requires out of the box thinking .

I don't know much about recurrence relations, generating functions or graph theory, so I would also love to see a book which introduces these topics .

Answer 1

One possibility is Problem-Solving Methods in Combinatorics: An Approach to Olympiad Problems by Pablo Soberon. As the title says, it's intended to prepare the student for Olympiad problems, and the author won a gold medal in the International Mathematical Olympiad. Some of the exercises in the book are drawn from recent Olympiads.

Coverage includes the pigeonhole principle, graph theory, generating functions, and partitions.

Answer 2

I think Olympiad combinatorics book, by Pranav A. Sriram will help you much

https://artofproblemsolving.com/community/c6h601134

Answer 3

Here is a list of books for perfect olympiad combinatorics preparation.

For general study:

(1) A Path to Combinatorics for Undergraduates

(2) Principles and Techniques in Combinatorics

(3) Problem-Solving Methods in Combinatorics: An Approach to Olympiad Problems

For practising problem-solving:

(1) 102 Combinatorial Problems

(2) Combinatorics: A Problem-Based Approach

(3) The IMO Compendium: A Collection of Problems Suggested for The International Mathematical Olympiads: 1959-2009 Second Edition

For Olympiad Graph theory:

Olympiad uses of graph theory is a bit different from formal graph theory taught in university courses. The best book for this is

(1) Graph Theory: In Mathematical Olympiad And Competitions

(2) IMO Training 2008: Graph Theory

For probabilistic methods in olympiad combinatorics:

(1) Expected uses of probability

(2) Unexpected uses of probability

For generating functions and recurrence relations:

Generatingfunctionology

For combinatorial inequality type problems:

Combinatorial Extremization

For various advanced techniques:

Extremal Combinatorics

For elementary combinatorial problems with geometric flavour:

Elementary Combinatorial Geometry

For ultimate problem solving (hard):

Problems from the Book

Pranav A. Sriram's book contains more than enough higher combinatorics contents which are only needed to tackle notoriously difficult (but not so elegant) Chinese TST problems. But what I have listed is enough for achieving success in EGMO or even in IMO!

Happy Problem Solving!