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A couple of months ago I discussed a method to reduce a dynamical problem (computing the maximal rotation number of a prescribed element $w$ in a free group given the rotation numbers of the generators) to a purely combinatorial one. Now Alden Walker and I have uploaded our paper, entitled “Ziggurats and rotation numbers”, to the arXiv.

The purpose of this blog post (aside from continuing the trend of posts titles containing the letter “Z”) is to discuss a very interesting conjecture that arose in the course of writing this paper. The conjecture does not need many prerequisites to appreciate or to attack, and it is my hope that some smart undergrad somewhere will crack it. The context is as follows.