Abstract Title
Sorting, Groups, and Reversals – A Game of Factoring
Abstract
Past research on the topic of sorting signed permutations by context-directed reversals (CDR) focused mainly on algorithmic properties of CDR sorting. Our work focuses on an algebraic study of signed permutations in an attempt to better understand sortability and reachability under CDR sorting operations. We formulated a convenient matrix representation of signed permutations that enables us to study signed permutations and CDR moves as elements of the Hyperoctahedral Group. This approach allows us to avoid certain technicalities as we attempt to understand available CDR moves while sorting with iterative applications of CDR. This research culminates in reducing CDR sorting games to a shortest-length-factoring problem in a Coxeter group and a method for factoring signed permutations into fixed points. We also introduced a method of attaining the shortest-length factoring via solutions of a special system of linear equations.
Sorting, Groups, and Reversals – A Game of Factoring
Past research on the topic of sorting signed permutations by context-directed reversals (CDR) focused mainly on algorithmic properties of CDR sorting. Our work focuses on an algebraic study of signed permutations in an attempt to better understand sortability and reachability under CDR sorting operations. We formulated a convenient matrix representation of signed permutations that enables us to study signed permutations and CDR moves as elements of the Hyperoctahedral Group. This approach allows us to avoid certain technicalities as we attempt to understand available CDR moves while sorting with iterative applications of CDR. This research culminates in reducing CDR sorting games to a shortest-length-factoring problem in a Coxeter group and a method for factoring signed permutations into fixed points. We also introduced a method of attaining the shortest-length factoring via solutions of a special system of linear equations.