Bubble sort, Cayley graph, permutation, symmetric group, genomics
The problem of factoring a permutation as a product of special types of transpositions, namely, those transpositions involving two positions with bounded distances, is considered. In particular, the minimum number, δ, such that every permutation can be factored into no more than δ special transpositions is investigated. This study is related to sorting algorithms, Cayley graphs, and genomics.
Huang, Zejun; Li, Chi-Kwong; Li, Sharon H.; and Sze, Nung-Sing.
"Factorization of Permutations",
Electronic Journal of Linear Algebra,