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 …

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 …

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.

May 20, 2020 · To reiterate... $2^n-1$ is a fine answer to its own question... the question of how many non-empty subsets a set has. $2^n$ is a fine answer to its own question... the question …

How many ways are there to distribute 5 balls into 7 boxes if each box must have at most one in it if: a) both the boxes and balls are labeled b) the balls are labeled but the boxes are not c) the

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 …

Jul 22, 2016 · I want to prepare for the maths olympiad and I was wondering if you can recommend me some books about combinatorics, number theory and geometry at a beginner …

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? …

Jan 19, 2020 · Is there an explicit formula for the sum $$0\\binom{n}{0}+1\\binom{n}{1}+\\dots+n\\binom{n}{n} = \\sum_{k=0}^nk\\binom{n}{k}$$?

The first basic thing to grasp is that manipulating generating functions is much easier than manipulating sequences, but the power of generating functions goes much deeper than this. …