5 days ago · 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

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 characterization is given by R.P. …

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 …

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.

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

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 Prob...

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 …

Combinatorial geometry is concerned with combinatorial properties and constructive methods of discrete geometric objects. Questions on this topic are on packing, covering, coloring, folding, symmetry, …

For questions about the study of finite or countable discrete structures, especially how to count or enumerate elements in a set (perhaps of all possibilities) or any subset. It includes questions on …