# Tagged Questions

**1**

vote

**1**answer

308 views

### Estimate on sum of squares of multinomial coefficients

I am interested in approximating the sum of the squares of the multinomial coefficients, i.e.
$a_\ell^p := \sum_{k_0+\ldots+k_p = \ell} (\frac{\ell!}{k_0! \ldots k_p!})^2$
or more general,
...

**3**

votes

**1**answer

168 views

### Is the Binomial Expectation of a Multivariate Convex Function Convex in the Vector p?

Let $\mathbf{p}=(p_1,\dots,p_m)$ be a vector in $[0,1]^m$ and let $\mathbf{X}=(X_1,\dots,X_m)$ be a vector of independently-distributed binomial random variables such that $X_i\sim ...

**2**

votes

**2**answers

309 views

### Sampling without replacement until hitting a subset

I randomly sample uniformly from $ \{1,..,N \}$ without replacement until drawing a number $ \leq k$. Denote the expected number of draws by $R(N,k)$. I want a good approximation for $\sum_{k=1}^N ...

**5**

votes

**1**answer

293 views

### Sparse approximate representation of a collection of vectors

Suppose I have a collection of $n$ vectors $C \subset \mathbb{F}_2^n$. They are of course spanned by the canonical set of $n$ basis vectors.
What I would like to find is a much smaller (~ $\log n$) ...

**11**

votes

**6**answers

3k views

### Solving NP problems in (usually) Polynomial time?

Just because a problem is NP-complete doesn't mean it can't be usually solved quickly.
The best example of this is probably the traveling salesman problem, for which extraordinarily large instances ...