Mathematical Conversations
That's a Big Hypercube
In a recent collaboration with a group of algebraic combinatorists at ICERM, we came across a rather surprising set of permutations, which (in a natural sense I'll explain in the talk) form an unexpectedly gigantic hypercube. This set of combinatorial objects also turns out to have been known to people who worked on low-discrepancy subsets of the plane, but it comes as a surprise that it has something to do with the permutation group! I won't give any proofs from the paper, but everything in it is completely elementary and could have been observed 50 years ago, but happened not to be.
Another interesting wrinkle is that this gigantic hypercube was discovered as a result of an unusually successful experiment using the Google DeepMind evolutionary coding agent AlphaEvolve, although we were looking for something else.