MO640 - Exercises - Algebraic theory, Feijao and Meidanis 2013

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

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

Answer:

From the image

π = ( Xh Yt ) ( Yh Ah ) ( At Bt ) ( Bh Ch ) ( Ct Zt )

Excision of the segment involving blocks A, B and C forming a circular intermediate yields:

( Xh Yt ) ( Yh Zt ) ( At Bt ) ( Bh Ch ) ( Ct Ah )

Therefore,

ρπ = ( Xh Yt ) ( Yh Zt ) ( At Bt ) ( Bh Ch ) ( Ct Ah )
ρ ( Xh Yt ) ( Yh Ah ) ( At Bt ) ( Bh Ch ) ( Ct Zt ) = ( Xh Yt ) ( Yh Zt ) ( At Bt ) ( Bh Ch ) ( Ct Ah )
ρ = (Yh Ct) (Ah Zt)

MO640 Home

© 2015 Joao Meidanis