## Sets with Small Intersection

Suppose that we want to construct subsets $S_1, \ldots, S_m \subseteq
\{1,\ldots,n\}$ with the following properties:
1. $|S_i| \geq k$ for all $i$
2. $|S_i \cap S_

Suppose that we want to construct subsets $S_1, \ldots, S_m \subseteq
\{1,\ldots,n\}$ with the following properties:
1. $|S_i| \geq k$ for all $i$
2. $|S_i \cap S_

Here is interesting linear algebra fact: let $A$ be an $n \times n$ matrix and
$u$ be a vector such that $u^{\top}A = \lambda u^{\top}$. Then for any matrix
$B$, $u^

Consider the following statements:
1. The shape with the largest volume enclosed by a given surface area is the
$n$-dimensional sphere.
2. A marginal or sum of log-concave distributions is log-concave.
3.

Here are two strange facts about matrices, which I can prove but not in a
satisfying way.
1. If $A$ and $B$ are symmetric matrices satisfying $0 \preceq A \preceq B$,
then $A^

Consider a probability distribution ${p(y)}$ on a space ${\mathcal{Y}}$. Suppose
we want to construct a set ${\mathcal{P}}$ of probability distributions on
${\mathcal{Y}}$ such that ${p(y)}$ is the maximum-entropy