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)
Enumeration schemes for restricted permutations
Combinatorics, Probability and Computing
A variant of the tandem duplication — random loss model of genome rearrangement
Theoretical Computer Science
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In this paper, we are interested in the combinatorial analysis of the whole genome duplication-random loss model of genome rearrangement initiated in Chaudhuri et al. (2006) [9] and Bouvel and Rossin (2009) [8]. In this model, genomes composed of n genes are modeled by permutations of the set of integers {1,2,...,n}, that can evolve through duplication-loss steps. It was previously shown that the class of permutations obtained in this model after a given number p of steps is a class of pattern-avoiding permutations of finite basis. The excluded patterns were described as the minimal permutations with d=2^p descents, minimal being intended in the sense of the pattern-involvement relation on permutations. Here, we give a local and simpler characterization of the set B"d of minimal permutations with d descents. We also provide a more detailed analysis-characterization, bijection and enumeration-of two particular subsets of B"d, namely the patterns in B"d of size d+2 and 2d.