# Tagged Questions

**1**

vote

**1**answer

333 views

### Prove or disprove $ \int_{0}^{\infty} \int_{-x}^{0} f(x)f(y)dydx > \int_{0}^{\infty} \int_{-\infty}^{-x} f(x)f(y)dydx. $

Consider a symmetric, unimodal distribution $f(x)$ such that $\int_{0}^{\infty} f(x) > 1/2$. I want to prove or disprove the following:
$$
\int_{0}^{\infty} \int_{-x}^{0} f(x)f(y)dydx > ...

**2**

votes

**1**answer

143 views

### AM-GM interpolation in the limit

Given a sequence of positive numbers $X = (x_1, x_2, \dots)$, define the $k$th elementary symmetric mean of the first $n$ entries to be
$$ S(X, n, k) := \frac{\displaystyle\sum_{1 \leq i_1 < ...

**1**

vote

**0**answers

88 views

### An inequality for elementary symmetric means of a periodic sequence

Given a tuple of positive numbers tuple $X = (x_1, x_2, \dots,)$, define the $k$th elementary symmetric mean of the first $n$ entries to be
$$ S(X, n, k) := \frac{\displaystyle\sum_{i_1 < \cdots ...

**7**

votes

**5**answers

825 views

### Rearrangement-style inequality with lots of terms and little evidence

This is another of the problems I designed for contests but wasn't able to solve on my own for years. Maybe AoPS is a better place for it, but let me try it here.
[UPDATE: I have streamlined the ...

**7**

votes

**1**answer

386 views

### Characterizing intersection of zero sets of elementary symmetric polynomials on R^n

Stated simply, the question is:
Consider two elementary symmetric polynomials $\sigma_{k}$ and $\sigma_{k+1}$ on $\mathbb{R}^{n}$ with zero sets $U_{k}$ and $U_{k+1}$. Let $V_{i_{1}i_{2}\dotsb ...