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 22, 2025 · Symbolic method, bijective proofs or double counting proofs? combinatorics proof-explanation combinatorial-proofs analytic-combinatorics Nov 20, 2023 at 21:24

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 …

Sep 23, 2020 · combinatorics graph-theory coloring ramsey-theory Share Cite edited Sep 23, 2020 at 14:04

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, according …

Jan 30, 2015 · What you have there is the best way to prove that identity that I know of. I'm sure there are other combinatorial interpertations of it, but that is the most natural one. Another way to prove …