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Whole mirror duplication-random loss model and pattern avoiding permutations

Abstract : 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.
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https://hal-univ-bourgogne.archives-ouvertes.fr/hal-00785281
Contributor : Jean-Luc Baril <>
Submitted on : Tuesday, February 5, 2013 - 6:00:54 PM
Last modification on : Friday, July 17, 2020 - 2:54:05 PM

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Jean-Luc Baril, Rémi Vernay. Whole mirror duplication-random loss model and pattern avoiding permutations. Information Processing Letters, Elsevier, 2010, 110 (11), pp.474-480. ⟨10.1016/j.ipl.2010.04.016⟩. ⟨hal-00785281⟩

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