Any good resources/reference books about bijective proofs (Combinatorics)? I am currently taking a Combinatorics course in this sem,however, my prof hasn't talked much about how to construct a bijection between two sets we want to count.
I have searched online but I still couldn't find any precise/concrete examples or problems (with solutions) on how to proceed a bijective proof regarding combinatorics.
 A: I highly recommend the book Bijective Combinatorics by Nicholas A. Loehr.

From the Amazon description:

Bijective proofs are some of the most elegant and powerful techniques in all of mathematics. Suitable for readers without prior background in algebra or combinatorics, Bijective Combinatorics presents a general introduction to enumerative and algebraic combinatorics that emphasizes bijective methods.
The text systematically develops the mathematical tools, such as basic counting rules, recursions, inclusion-exclusion techniques, generating functions, bijective proofs, and linear-algebraic methods, needed to solve enumeration problems. These tools are used to analyze many combinatorial structures, including words, permutations, subsets, functions, compositions, integer partitions, graphs, trees, lattice paths, multisets, rook placements, set partitions, Eulerian tours, derangements, posets, tilings, and abaci. The book also delves into algebraic aspects of combinatorics, offering detailed treatments of formal power series, symmetric groups, group actions, symmetric polynomials, determinants, and the combinatorial calculus of tableaux. Each chapter includes summaries and extensive problem sets that review and reinforce the material.
Lucid, engaging, yet fully rigorous, this text describes a host of combinatorial techniques to help solve complicated enumeration problems. It covers the basic principles of enumeration, giving due attention to the role of bijective proofs in enumeration theory.

The following hyperlink points to a review of this book by a "researcher in infocomm security with specialty in math and cryptography".
A: A bijection is really just a one-to-one correspondence between two sets. There should be a lot of information online if you look carefully enough, but I personally have this book and it talks about one-to-one correspondences a great deal (and how to prove that two things are in a one-to-one correspondence).
A: A good problem set of bijective proofs by Richard Stanley would help someone in your position.
I know this question is old, but the link will be good for the next person learning how to write bijective proofs.
