Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Posets and Permutations in the Duplication-Loss Model: Minimal
  Permutations with d Descents   In this paper, we are interested in the combinatorial analysis of the whole
genome duplication - random loss model of genome rearrangement initiated in a
paper of Chaudhuri, Chen, Mihaescu, and Rao in SODA 2006 and continued by
Bouvel and Rossin in 2007. In this model, genomes composed of n genes are
modeled by permutations of the set of integers [1..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.

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The categories of this paper are: q-bio
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The categories of this paper are: math-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: q-fin
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The categories of this paper are: quant-ph
12
The categories of this paper are: nucl-th
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The categories of this paper are: chem-ph
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The categories of this paper are: adap-org
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The categories of this paper are: hep-ex
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The categories of this paper are: cond-mat
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The categories of this paper are: astro-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: econ
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The categories of this paper are: comp-gas
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The categories of this paper are: physics
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The categories of this paper are: ao-sci