16
votes
5answers
883 views
+50

What arrangement of unit cubes minimizes surface area?

For each of these two questions, one can assume that the arrangements are polycubes (for which a definition can be found in the excerpt-image below). Question A. How does one arrange $n$ unit cubes ...
9
votes
0answers
302 views
+50

When does $Pr[vr_i=ur_i\mid \forall j < i: vr_j=ur_j] =O( 1/\sqrt n)$?

In A conjecture about the entropy of matrix vector products I asked a conjecture relating to the entropy of a matrix-vector product. This conjecture is as yet unproven. domotorp then made another ...
4
votes
0answers
107 views
+50

If the generating function summation and zeta regularized sum of a divergent exist, do they always coincide?

One could assign a value to divergent series by means of several summation methods. One summation method we could consider is the generating function method. Let's sum, for example, the fibonacci ...
9
votes
1answer
280 views
+100

Coherence between different ranking methods of a graph's vertices

Given a (connected) graph $G$ it is natural to want to rank its vertices, with the more "central" vertices ranked higher. Two natural ways of doing it are: By the degrees. By the entries in a ...
5
votes
0answers
94 views
+50

Toda Flow Embeddings

What are strategies for generating the following types of pictures: Here's what's going on here. Take a toda flow in 3 variables. The equations of motion are: ...