@techreport{TR-IC-18-07,
   number = {IC-18-07},
   author = {João Paulo Pereira Zanetti and João Meidanis},
   title  =  {Counting  sorting scenarios and intermediate genomes for
                   the rank distance},
   month = {April},
   year = {2018},
   institution = {Institute of Computing, University of Campinas},
   note = {In English, 23 pages.
    \par\selectlanguage{english}\textbf{Abstract}
       An important problem in genome comparison is the genome sorting
       problem,  that  is  to find a sequence of basic operations that
       transforms  one  genome  into  another  and  corresponds to the
       distance  between  them.  These  sequences  are  called optimal
       sorting  scenarios. However, there is usually a large number of
       such  scenarios,  and  a  naive  algorithm is very likely to be
       biased  towards  a  specific  type  of  scenario, impairing its
       usefulness in real-world applications. One way to go beyond the
       traditional  sorting  algorithms  is  to  explore  all possible
       solutions, looking at all the optimal sorting scenarios instead
       of  just  an  arbitrary  one.  Another  approach  in  the  same 
       direction  is to analyze all the intermediate genomes, that is,
       all  genomes  that  are part of an optimal sorting scenario. In
       this  paper, we show how to count the number of optimal sorting
       scenarios  and  the  number of intermediate genomes between any
       two given genomes, under the rank distance.
  }
}