Unitary Toric Classes, the Reality and Desire Diagram, and Sorting by Transpositions

H. Eriksson et al made a breakthrough to the problem of sorting by transpositions by proposing a quotient structure named toric graph, which allowed the reduction of the search space, establishing the transposition diameter ..., for the cases n =13 and n = 15. I. Elias and T. Hartman extended the lower bound ..., to all odd values of n, ... The value n = 15 is the largest for which ... is known. The goal of the present paper is to further study the toric graph, focusing on the case when n + 1 is prime, providing positive evidence that J. Meidanis, M. E. M. T. Walter, and Z. Dias's conjecture is still valid when n is even. The authors show that, when n+1 is prime, the properties of the reverse permutation are shared by permutations that fall into unitary toric classes. (ProQuest: ... denotes formulae/symbols omitted.)