Efficient Disjoint Cycle Calculation | Past Exam Paper Help

[Charles007]

Express as the product of disjoint cycles:
a. (1,2,3)(4,5)(1,6,7,8,9)(1,5)
b. (1,2)(1,2,3)(1,2)


I know how to do in 2 row permutations, with right to - left. can anyone tell me , how to express it without transfer it into 2 row permutations.

2 disjoint product. eg. (123)(234) calculate from right to left. how ?

I know transfer it into 2 row permutations, (1-2,2-3,3-1,4-4)* (1-1,2-3,3-4,4-2)



Thank you. I am doing my past exam paper, university doesn't give us answer.

 

[tiny-tim]

Welcome to PF!

Hi Charles007! Welcome to PF!

2 disjoint product. eg. (123)(234) calculate from right to left. how ?

The right one sends 2 to 3, then left one sends 3 to 1, so both together send 2 to 1.

Then do the same, starting with 3, and again starting with 4, and again starting with 1.

(I've done them in the order 2,3,4,1, but any order would do)