Conjugating full cycles by adjacent transpositions: diameter and sorting time
Ron M. Adin, Eli Bagno, Yuval Roichman
TL;DR
This paper investigates the complexity of transforming cyclic permutations into a canonical form using adjacent transpositions, providing bounds on the number of steps and the diameter of the related permutation graph.
Contribution
It introduces new bounds on the sorting time and diameter for cyclic permutations via conjugation by adjacent transpositions.
Findings
Established upper and lower bounds on transformation steps
Determined the diameter of the Schreier graph for cyclic permutations
Provided insights into permutation sorting complexity
Abstract
We establish upper and lower bounds on the maximal number of steps needed to transform a cyclic permutation to the canonical cyclic permutation using conjugation by adjacent transpositions, and on the diameter of the underlying Schreier graph.
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Taxonomy
TopicsGenome Rearrangement Algorithms · Advanced Combinatorial Mathematics · graph theory and CDMA systems