A simple framework on sorting permutations
arXiv:1502.07971
Abstract
In this paper we present a simple framework to study various distance problems of permutations, including the transposition and block-interchange distance of permutations as well as the reversal distance of signed permutations. These problems are very important in the study of the evolution of genomes. We give a general formulation for lower bounds of the transposition and block-interchange distance from which the existing lower bounds obtained by Bafna and Pevzner, and Christie can be easily derived. As to the reversal distance of signed permutations, we translate it into a block-interchange distance problem of permutations so that we obtain a new lower bound. Furthermore, studying distance problems via our framework motivates several interesting combinatorial problems related to product of permutations, some of which are studied in this paper as well.
13 pages. This is the second part from division of the paper: arXiv:1411.5552v2 [math.CO], into two parts. The first part is: arXiv:1502.07674 [math.CO]. The original paper arXiv:1411.5552v2 [math.CO] will be removed soon. Comments are welcome. [v2]:Theorem 3 has been generalized to arbitrary permutations