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 …

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

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.

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? …

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 …

Mar 21, 2011 · For a set $S$ with $n$ elements, the notation for a combination $\\binom{n}{k}$, or $C(n, k)$, indicates the number of combinations of $k$ elements from $S$, but how ...

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

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 …

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. …