@techreport{TR-IC-00-16,
number = {IC-00-16},
author = {J. Meidanis and M. E. M. T. Walter and Z. Dias},
title = {A Lower Bound on the Reversal and Transposition Diameter},
month = {October},
year = {2000},
institution = {Institute of Computing, University of Campinas},
note = {In English, 13 pages.
\par\selectlanguage{english}\textbf{Abstract}
One possible model to study genome evolution is to represent
genomes as permutations of genes and compute distances based on
the minimum number of certain operations (rearrangements) needed
to transform one permutation into another. Under this model, the
shorter the distance, the closer the genomes are. Two operations
that have been extensively studied are the reversal and the
transposition. A reversal is an operation that reverses the
order of the genes on a certain portion of the permutation. A
transposition is an operation that ``cuts'' a certain portion of
the permutation and ``pastes'' it elsewhere in the same
permutation. In this paper we show that the reversal and
transposition distance of the signed permutation $\pi_n=(-1, -2,
\dots, -(n-1), -n)$ with respect to the identity is $\lfloor {n
/ 2} \rfloor + 2$ for all $n \geq 3$. We conjecture that this
value is the diameter of the permutation group under these
operations.
}
}