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 …

3 days ago · For questions about the study of finite or countable discrete structures, especially how to count or enumerate elements in a set (perhaps of all possibilities) or any subset. It includes …

There is some common confusion between these two terms. The word "permutation" in general refers to one of three things depending on context. It can mean the order (arrangement) of a set as in …

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 …

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 bot fed …

Feb 24, 2026 · Problem: For which positive integers $n$ (where $n\geq3$) can the following condition be satisfied: The set $ [n]=\ {1,2,3,...,n\}$ can be divided into several ...

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

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.