# All Questions

**0**

votes

**0**answers

132 views

+50

### On even almost perfect numbers other than the powers of two, as compared to odd perfect numbers given in Eulerian form

This question has been cross-posted from MSE.
Let $\sigma(x)$ be the sum of the divisors of $x$. We say that $X$ is almost perfect if $\sigma(X) = 2X - 1$.
Antalan and Tagle (in a 2004 preprint ...

**18**

votes

**0**answers

953 views

+50

### Is formula valid for relating $\pi$ with ALL of its OEIS A002485(n)/A002486(n) convergents?

Could anyone try to prove that the below conjectured formula is valid for relating $\pi$ with ALL of its convergents - those, which are described in OEIS via A002485(n)/A002486(n) ?
$$(-1)^n\cdot(\pi ...

**5**

votes

**1**answer

219 views

+50

### When is a general sheaf (on the projective plane) globally generated?

Let $v$ be a chern character on $\mathbb P^2$ so that the moduli of sheaves of chern character $v$ is non-empty of the expected dimension. When is it true that the general sheaf in moduli is globally ...

**16**

votes

**0**answers

209 views

+50

### Is the Flajolet-Martin constant irrational? Is it transcendental?

Facebook has a new tool to estimate the average path length between you and any other person on Facebook. An interesting aspect of their method is the use of the Flajolet-Martin algorithm.
In the ...

**8**

votes

**1**answer

228 views

+50

### Obstructed automorphisms of schemes

Let $X$ be a smooth projective scheme over a field $\mathbf{k}$ of characteristic zero such that $\mathrm{H}^0(X, \mathrm{T}X)$ vanishes, and let $f$ be an automorphism of $X$. I would like to have an ...

**4**

votes

**0**answers

66 views

+50

### Complexity of approximating the size of the range of a matrix

Given an $m$ by $n$ matrix $M$ with $m \leq n$ and elements from $\{-1,1\}$, let us define:
$$S_M = |\{Mx : x \in \{-1,1\}^n\}.$$
It is NP-hard to compute $S_M$ exactly I believe by applying the ...