Applied Combinatorics by Alan Tucker is a good one. It's short, not hard to follow, a lot of problems to work through, and it's split into two sections: graph theory in section 1, and combinatorics (generating …

In fact,I once tried to define combinatorics in one sentence on Math Overflow this way and was vilified for omitting infinite combinatorics. I personally don't consider this kind of mathematics to be …

Is there a comprehensive resource listing binomial identities? I am more interested in combinatorial proofs of such identities, but even a list without proofs will do.

Jan 11, 2016 · Combinatorics is a wide branch in Math, and a proof based on Combinatorial arguments can use many various tools, such as Bijection, Double Counting, Block Walking, et cetera, so a …

Jun 28, 2017 · This is the Binomial theorem: $$ (a+b)^n=\sum_ {k=0}^n {n\choose k}a^ {n-k}b^k.$$ I do not understand the symbol $ {n\choose k}.$ How do I actually compute this? What does this notation …

Aug 24, 2013 · If you want a slightly more detailed explanation and exercises I recommend the book Introduction to Combinatorics published by the United Kingdom Mathematics Trust (UKMT) available …

Can someone explain to me the proof of $${n+1\\choose k} = {n\\choose k} + {n\\choose k-1}$$?

Dec 6, 2021 · Can someone please explain what double counting is? I have no idea what it is, and Google search yields results that are too complicated for me to understand at this point in time. If …

I feel that generating functions are powerful because they allow you to use tools from calculus and analysis to solve problems in areas such as discrete mathematics and combinatorics, where such …

Jan 18, 2019 · I'm learning combinatorics and need a little help differentiating between a combinatorial proof and an algebraic proof. Here is an example I came across: Prove the following two formulas by