Aperiodcast – 13/5/2012

In true Aperiodical fashion, we left 13 days before recording another Aperiodcast, so here’s what we think about the last almost-two-weeks on the site.

Anyway, some students from the University of California, San Diego have extended the result, giving a better algorithm for finding the minimum number of switches to put everyone’s head back in the right places, give optimal solutions for two particular situations, and give necessary and sufficient conditions for it being possible to represent the identity permutation as $m$ distinct transpositions in $S_n$.