Jan 11, 2016 · The essence of a combinatorial proof is to provide a bijection between the elements of a known set and the elements of the set under consideration. A nice characterization is given by R.P. …

Sep 25, 2024 · Doing some exercise, where one has to proof some identity by using combinatorial arguments,I noticed that it would be useful to get combinatorial "interpretations" for …

Nov 13, 2023 · Addition: I've looked at two reputable books on combinatorics to see what they include. Here is a selection from their table of contents: J. H. van Lint, R.M. Wilson. "A Course in …

1 day ago · combinatorial proof of equivalence of two forms for Ramanujan's Q function (balls, trees and cyclic forests) combinatorics trees combinatorial-proofs balls-in-bins 5 hours ago

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 many …

Combinatorial game theory (abbreviated CGT) is the subfield of combinatorics (not traditional game theory) which deals with games of perfect information such as Nim and Go. It includes topics such as …

I was looking through practice questions and need some guidance/assistance in Fermat's combinatorial identity. I read through this on the stack exchange, but the question was modified in the latest edition …

I'm struggling to prove identity $(6.20)$ from Concrete Mathematics p. 265: $$ \\sum_{j= m}^n {j \\brace m} (m+1)^{n-j} = {n+1\\brace m+1} $$ It is a vertical recurrence, for the triangle of Stirling

Personally, I see "combinatorics" as the "art of counting", which implies that the underlying objects are at least countable (= discrete), but better finite. I find it natural that "graph theory" is filed under …

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 needing to …