A Lower Bound on the Transposition Diameter

Sorting permutations by transpositions is an important and difficult problem in genome rearrangements. The transposition diameter TD(n) is the maximum transposition distance among all pairs of permutations in Sn. It was previously conjectured [H. Eriksson et al., Discrete Math., 241 (2001), pp. 289–300] that TD(n) ≤ n+1 2 . This conjecture was disproved by Elias and Hartman [IEEE/ACM Trans. Comput. Biol. Bioinform., 3 (2006), pp. 369–379] by showing TD(n) ≥ n+1 2 + 1. In this paper we improved the lower bound to TD(n) ≥ 17 33 n+ 1 33 via computation.