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 …

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 …

Dec 23, 2025 · 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 …

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

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 …

Apr 26, 2024 · I'm practicing the strategy of double counting a set ("story proof") to prove combinatorial identities. I came across this identity refered as "Even-Odd Identity" on Art of …

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 …

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 …

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.

Dec 19, 2023 · Combinatorial classes are for unlabeled objects, while combinatorial species are for labeled objects. The two methods are not analogous. You say that "classes" are associated …