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Article Dans Une Revue Information Processing Letters Année : 2010

Whole mirror duplication-random loss model and pattern avoiding permutations

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Résumé

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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hal-00785281 , version 1 (05-02-2013)

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