Factorization of permutations

Abstract

We consider the problem of factoring permutations as a product of special types of transpositions, namely, those transpositions involving two positions with bounded distances. In particular, we investigate the minimum number, $δ$, such that every permutation can be factored into no more than $δ$ special transpositions. This study is related to sorting algorithms, Cayley graphs, and genomics.

16 pages, a substantially revised version