New algorithms for the duplication-loss model
RECOMB '00 Proceedings of the fourth annual international conference on Computational molecular biology
Efficient generation of the binary reflected gray code and its applications
Communications of the ACM
Sorting by Transpositions Based on the First Increasing Substring Concept
BIBE '04 Proceedings of the 4th IEEE Symposium on Bioinformatics and Bioengineering
On the tandem duplication-random loss model of genome rearrangement
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
New Bounds and Tractable Instances for the Transposition Distance
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Perfect Sorting by Reversals Is Not Always Difficult
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Introduction to partially ordered patterns
Discrete Applied Mathematics
Counting permutations by their alternating runs
Journal of Combinatorial Theory Series A
A variant of the tandem duplication — random loss model of genome rearrangement
Theoretical Computer Science
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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 2^p+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) [10]. Other relative models are also considered.