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 …

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 …

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.

Oct 17, 2018 · Comically badly worded question - particularly amusing is the phrase 'each card displays one positive integer without repetition from this set' :) it's almost like the output of 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? …

Mar 18, 2020 · Imagine we want to put $7$ stars in $3$ bins. We can use a visual representation to show how we organise them: $$★ ★ ★ ★ | ★ | ★ ★$$ The bars split the different bins. So, …

I don't understand the meta-questions. The four cases are different because "distinguishable" and "indistinguishable" are different.

Explore related questions combinatorics binomial-coefficients See similar questions with these tags.

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 …