%0 Journal Article %T Whole mirror duplication-random loss model and pattern avoiding permutations %+ Laboratoire Electronique, Informatique et Image [UMR6306] (Le2i) %A Baril, Jean-Luc %A Vernay, Rémi %< avec comité de lecture %@ 0020-0190 %J Information Processing Letters %I Elsevier %V 110 %N 11 %P 474-480 %8 2010-05-16 %D 2010 %R 10.1016/j.ipl.2010.04.016 %K Algorithms %K Combinatorial problems %K Pattern avoiding permutation %K Whole duplication-random loss model %K Genome %K Generating algorithm %K Binary reflected Gray code %Z Mathematics [math]/Combinatorics [math.CO] %Z Computer Science [cs]/Bioinformatics [q-bio.QM] %Z Computer Science [cs]/Computational Complexity [cs.CC]Journal articles %X In this paper we study the problem of the whole mirror duplication-random loss model in terms of pattern avoiding permutations. We prove that the class of permutations obtained with this model after a given number p of duplications of the identity is the class of permutations avoiding the alternating permutations of length p2+1. We also compute the number of duplications necessary and sufficient to obtain any permutation of length n. We provide two efficient algorithms to reconstitute a possible scenario of whole mirror duplications from identity to any permutation of length n. One of them uses the well-known binary reflected Gray code (Gray, 1953). Other relative models are also considered. %G English %L hal-00785281 %U https://u-bourgogne.hal.science/hal-00785281 %~ UNIV-BOURGOGNE %~ CNRS %~ ENSAM %~ INSMI %~ LE2I %~ AGREENIUM %~ LIB_UB %~ LIB-COMBINRES %~ ARTS-ET-METIERS-SCIENCES-ET-TECHNOLOGIES %~ HESAM %~ HESAM-ENSAM %~ INSTITUT-AGRO