Of the books that have already been mentioned, I like Graham, Knuth, & Patashnik, Concrete Mathematics, isn’t precisely a book on combinatorics, but it offers an excellent treatment of …

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 · Using combinatorial proof is usually a much better approach though to remember many identities like the hockey-stick identity or Vandermonde Identity.

Do you know any good book that deals extensively with identities obtained using combinatorial and/or probabilistic arguments (e.g., by solving the same combinatorial or probability problem …

Aug 6, 2020 · Can anyone recommend me an olympiad style combinatorics book which is suitable for a high schooler ? I know only some basics like Pigeon hole principle and stars and bars . I …

Let me add one purely-combinatorial proof. : the justification for doing so is that I think we can tell this in a "committee-forming" way that is used for other identities (e.g. Pascal's rule), without …

Nov 26, 2018 · I'm currently working on a probability course, and I am constantly having trouble figuring out when to use permutations vs. combinations vs. factorials vs. exponents in order to …

Here's a combinatorial proof for $$\sum_ {k=1}^n k^2 = \binom {n+1} {2} + 2 \binom {n+1} {3},$$ which is just another way of expressing the sum. Both sides count the number of ordered …

Jan 30, 2015 · I'm sure there are other combinatorial interpertations of it, but that is the most natural one. Another way to prove this is to grind out the algebra, but why would you do that? …

Nov 12, 2022 · Combinatorial proof of Stirling Numbers of the second kind Ask Question Asked 2 years, 11 months ago Modified 2 years, 11 months ago