Exercise
Every element in Sn can be written as the product of transpositions. Which of the following bounds on the number of transpositions needed is sharpest?
n - 1
n
n2/4
n!
Correct. Every cycle of length m can be written as the product
of m - 1 transpositions, hence the total number of transpositions needed cannot exceed n - 1.
Try to give an example for your guess.
Try to give an example for your guess.
Try to give an example for your guess.