[20150507] Question #3

Assigned to: Juan Felipe Hernández Albarracín

Statement

Find the algebraic distance between the two genomes below.

Answer

Algebraic representation of the chromosomes:

π_chr = (a b -d f -c e -e c -f d -b -a)
σ_chr = (d f -f -d)(a -c -b e -e b c -a)(z -z)

The algebraic distance of two genomes π and σ is:

d(π,σ) = ||σπ^-1|| / 2

So π_chr^-1 must be calculated:

π_chr^-1 = (-a -b d -f c -e e -c f -d b a)

σ_chrπ_chr^-1 = (-a e -b f d -d c b -c -f)(z -z)(a)(-e)

The norm of a genome π is defined by:

||π|| = |E| - |orb(π)|

Where E is the set of all the symbols present in the permutations and orb(π) is the set of orbits in π. Since there are 14 symbols in total and 4 orbits in σ_chrπ_chr^-1:

d(π,σ) = (14 - 4) / 2 = 5