MO640 - Exercises - Algebraic theory, Feijao and Meidanis 2013

Exercises marked with (*) require further reading/search beyond the suggested texts.

  1. Write in algebraic form as a product of disjoint permutation cycles the reversal involving blocks B and C of the linear chromosome below.

    chromosome with A, -B, C, D

  2. Write in algebraic form as a product of disjoint permutation cycles the excision of the segment involving blocks A, B, and C of the linear chromosome below, forming a circular intermediate.

    linear chromosome

  3. Find the algebraic distance between the two genomes below.

    genomes pi and sigma

  4. Find a sorting rearrangement with weight 1 or less taking π to σ of the previous exercise, according to the algebraic concept of distance.

  5. Iterate the previous exercise as many times as needed to find an optimal series of light algebraic sorting operations leading from π to σ. 'Light' operation here means an operation with weight 1 or less.


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© 2015 Joao Meidanis