Question

Combinatorial Proof of $\binom{\binom{n}{2}}{2} = 3 \binom{n}{3}+ 3 \binom{n}{4}$ for $n \geq 4$

score 676 · Answer 1 · 2010-12-25 18:31:45

676

Views

Combinatorial Proof of $\binom{\binom{n}{2}}{2} = 3 \binom{n}{3}+ 3 \binom{n}{4}$ for $n \geq 4$

Published on 25 Dec 2010 - 18:31

score 741 · Answer 2 · 2011-01-31 22:54:34

741

Views

On a combinatorial identity involving elementary symmetric polynomials

Published on 31 Jan 2011 - 22:54

score 12.5k · Answer 3 · 2011-02-06 22:26:27

12.5k

Views

The Hexagonal Property of Pascal's Triangle

Published on 06 Feb 2011 - 22:26

score 12.1k · Answer 4 · 2011-05-09 06:09:46

12.1k

Views

Identity for convolution of central binomial coefficients: $\sum\limits_{k=0}^n \binom{2k}{k}\binom{2(n-k)}{n-k}=2^{2n}$

Published on 09 May 2011 - 6:09

score 3.6k · Answer 5 · 2011-06-05 03:39:13

3.6k

Views

Evaluate $\sum\limits_{k=1}^n k^2$ and $\sum\limits_{k=1}^n k(k+1)$ combinatorially

Published on 05 Jun 2011 - 3:39

score 607 · Answer 6 · 2011-06-05 05:08:41

607

Views

Evaluate $\sum_{k=1}^n \binom{2k}{2}$ combinatorially

Published on 05 Jun 2011 - 5:08

score 1.8k · Answer 7 · 2011-06-11 11:45:30

1.8k

Views

Combinatorial proof that binomial coefficients are given by alternating sums of squares?

Published on 11 Jun 2011 - 11:45

score 5k · Answer 8 · 2011-07-29 13:42:46

5k

Views

Combinatorial proof: $e^x=\sum\limits_{k=0}^{\infty}\frac{x^k}{k!}$

Published on 29 Jul 2011 - 13:42

score 748 · Answer 9 · 2011-09-06 01:53:43

748

Views

A combinatorial proof for the identity $\sum_i \sum_j \min(i,j) = \sum_k k^2$

Published on 06 Sep 2011 - 1:53

score 8.6k · Answer 10 · 2011-09-23 11:21:39

8.6k

Views

Combinatorial proof of $\sum\limits_{k=0}^n {n \choose k}3^k=4^n$

Published on 23 Sep 2011 - 11:21

score 1.1k · Answer 11 · 2011-10-02 16:39:25

1.1k

Views

Combinatorial proof for $\sum_{k=0}^n 2^k \binom{n}{k} = 3^n$

Published on 02 Oct 2011 - 16:39

score 877 · Answer 12 · 2011-10-02 18:57:44

877

Views

Combinatorial proof for $\binom{n}{a}\binom{a}{k}\binom{n-a}{b-k} = \binom{n}{b}\binom{b}{k}\binom{n-b}{a-k}$?

Published on 02 Oct 2011 - 18:57

score 7.1k · Answer 13 · 2011-11-09 21:55:00

7.1k

Views

Combinatorial proof that $\sum \limits_{k=0}^n \binom{2k}{k} \binom{2n-2k}{n-k} (-1)^k = 2^n \binom{n}{n/2}$ when $n$ is even

Published on 09 Nov 2011 - 21:55

score 835 · Answer 14 · 2011-12-07 15:31:14

835

Views

Combinatorial Argument

Published on 07 Dec 2011 - 15:31

score 1.4k · Answer 15 · 2011-12-14 15:43:29

1.4k

Views

Combinatorial interpretation for Vandermonde's identity $\sum\limits_i\binom{m}{i}\binom{n}{j-i}=\binom{m+n}{j}$?

Published on 14 Dec 2011 - 15:43

List Question

Combinatorial Proof of $\binom{\binom{n}{2}}{2} = 3 \binom{n}{3}+ 3 \binom{n}{4}$ for $n \geq 4$

On a combinatorial identity involving elementary symmetric polynomials

The Hexagonal Property of Pascal's Triangle

Identity for convolution of central binomial coefficients: $\sum\limits_{k=0}^n \binom{2k}{k}\binom{2(n-k)}{n-k}=2^{2n}$

Evaluate $\sum\limits_{k=1}^n k^2$ and $\sum\limits_{k=1}^n k(k+1)$ combinatorially

Evaluate $\sum_{k=1}^n \binom{2k}{2}$ combinatorially

Combinatorial proof that binomial coefficients are given by alternating sums of squares?

Combinatorial proof: $e^x=\sum\limits_{k=0}^{\infty}\frac{x^k}{k!}$

A combinatorial proof for the identity $\sum_i \sum_j \min(i,j) = \sum_k k^2$

Combinatorial proof of $\sum\limits_{k=0}^n {n \choose k}3^k=4^n$

Combinatorial proof for $\sum_{k=0}^n 2^k \binom{n}{k} = 3^n$

Combinatorial proof for $\binom{n}{a}\binom{a}{k}\binom{n-a}{b-k} = \binom{n}{b}\binom{b}{k}\binom{n-b}{a-k}$?

Combinatorial proof that $\sum \limits_{k=0}^n \binom{2k}{k} \binom{2n-2k}{n-k} (-1)^k = 2^n \binom{n}{n/2}$ when $n$ is even

Combinatorial Argument

Combinatorial interpretation for Vandermonde's identity $\sum\limits_i\binom{m}{i}\binom{n}{j-i}=\binom{m+n}{j}$?

Trending Questions

Popular # Hahtags

Popular Questions