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. …

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 with …

Jan 2, 2026 · 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 …

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 …

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 …

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

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

Jun 9, 2025 · When I see an alternating sum in a potentially combinatorial identity, I often expect it to be an inclusion-exclusion some. But maybe it can be expressed as the fact that the number of circular …

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 …

combinatorial proof of equivalence of two forms for Ramanujan's Q function (balls, trees and cyclic forests) this question follows from my answers to two questions. balls given a bag containing n n …