2012/09/22 by Ron Evans, Lihua Huang · 3 voices
Mathematics · #math.CO #math.GR #msc:20B30
published as Math. Magazine 87 (2014) 252--262 · 17 pages
arxiv published 2012/09/22 · arxiv created 2014/11/27 · arxiv updated 2014/12/01
Let P be a permutation expressed as a product of nontrivial disjoint cycles. When writing P as a product of distinct transpositions none equal to a factor of P, what is the smallest number of transpositions that can be used? We answer this question and give applications to mind-switching problems that have arisen in connection with the popular sci-fi television series Futurama and Stargate SG-1.