Search Results
| Search type | Search syntax |
|---|---|
| Tags | [tag] |
| Exact | "words here" |
| Author |
user:1234 user:me (yours) |
| Score |
score:3 (3+) score:0 (none) |
| Answers |
answers:3 (3+) answers:0 (none) isaccepted:yes hasaccepted:no inquestion:1234 |
| Views | views:250 |
| Code | code:"if (foo != bar)" |
| Sections |
title:apples body:"apples oranges" |
| URL | url:"*.example.com" |
| Saves | in:saves |
| Status |
closed:yes duplicate:no migrated:no wiki:no |
| Types |
is:question is:answer |
| Exclude |
-[tag] -apples |
| For more details on advanced search visit our help page | |
Results tagged with binomial-coefficients
Search options not deleted
user 88133
For questions that explicitly reference the binomial coefficients, Pascal's Triangle, and Binomial identities.
5
votes
Accepted
Combinatorial proof of identity
Santa Claus has $N+1$ reindeer whose noses are of varying redness. Every year, Santa needs $n+1$ reindeer to pull his sleigh. The reddest-nosed reindeer always leads the sleigh.
The way Santa chooses …
- 6,237
2
votes
Sum of products of binomials
Let $G$ be the (infinite) graph with vertex set $\mathbb{Z}^2$, and the following edges. When $x+y < 0$, the vertex $(x,y)$ has outgoing edges to $(x+1,y)$ and to $(x,y+1)$. When $x+y \geq 0$, the ver …
- 6,237
13
votes
Accepted
Sum of multinomals = sum of binomials: why?
For convenience set $m=n-2k$. Then
\begin{equation}
\begin{split}
\binom{n-2k+j}{j,k-2j,n-3k+2j} &= \binom{m+j}{j,k-2j,m-k+2j} \\
&= \binom{m+j}{m} \binom{m}{k-2j} \\
&= [t^j](1-t)^{-(m+1)} …
- 6,237