3
votes
0answers
107 views
+150

How large do algebraic representations need to be for packing circles in squares?

(This question is inspired by Erich's Packing Center. I'm just asking about circles in squares to keep things simple, since I suspect any answer would apply just-as-well to the rest of the problems ...
8
votes
0answers
157 views
+50

Maximum occupancy balls in bins with limited independence

Throw $n$ balls into $n$ bins and let $X_n$ be the maximum occupancy. That is the maximum number of balls found in any bin. If you throw the balls uniformly and independently it is known that ...
8
votes
1answer
274 views
+50

Morgan Shalen compactification of $\mathbb C^2$

I'm reading the Otal's survey on the compactification of Morgan Shalen. (available here) He claims in an example (page 8) that the compactification of $\mathbb C^2$ is $S^4$, which sounds completely ...
8
votes
1answer
250 views
+50

Example of a ring $R$ such that $\dim(R[[X]])<\dim(R[X])$

Dimension refers to the Krull dimension of a commutative ring. In the paper "Prime ideals in power series rings" J. Arnold gives an example of such a ring: Let $k$ be a field and $K=k(t)$ a ...