2016年1月11日 · The other answers also talk about other ways to prove using Combinatorial Arguments. Combinatorics is a wide branch in Math, and a proof based on Combinatorial …

Aspects of combinatorics include counting the structures of a given kind and size (enumerative combinatorics), deciding when certain criteria can be met, and constructing and analyzing …

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 …

2024年4月12日 · $\begingroup$ Might not work for your tastes, but Lovasz has a lovely book called "Combinatorial Problems and Exercises", that develops a lot of theory through problems …

2016年7月22日 · Combinatorial Proof regarding Falling Factorials and sums of Falling Factorials Hot Network Questions How, anatomically, can an alien species have pointed digits (without …

2014年10月9日 · The book Combinatorial Identities from John Riordan ($1968$) is a wonderful classic with thousands of binomial identities which are systematically organised. But it does …

Combinatorial proof of $\sum_{k=0}^{n} \binom{3n-k}{2n} = \binom{3n+1}{n}$ Hot Network Questions How (in)efficient would a rocket be that flew to orbital heights, hovered for a while, …

Give a combinatorial proof of the following identity: $$3^n=\sum_{i=0}^{n}\binom{n}{i}2^{n-i}$$ I can't see any counting argument that would yield $3^n$, and the right hand side is also pretty …

Combinatorial (and Algebraic Proof) of an Identity Involving Lah Numbers 2 Find a Closed form for the Combinatorial Sum $\sum_{k=0}^m\binom{n-k}{m-k} $ and Provide a Combinatorial Proof …

2021年1月14日 · $\begingroup$ Following the clue given by @QiaochuYuan, I found the answer presented as Identity 17 in Combinatorial sums and finite differences by Michael Z. Spivey …