Suppose that $r=(13456)$ and $s=(132)$. Then both are even permutations and are geenrators of $A_6$ which is the alternating group of order 360.
I was curious to know, if we choose any arbitrary even permutation say $\alpha$ from $A_6$, how can we express it as a string of $r,s$ ? In other words, how to find the integers $m_1, m_2, m_3, \cdots$ such that $$\alpha=r^{m_1}s^{m_2}r^{m_3}s^{m_4}\cdots $$ would hold ?
I tried to find some method but totally in blank. I have no idea how to get them. Say $\alpha=(14526)$. Can someone help me to get the result ? In case if this problem has been solved before here, please share me the link. I have previously tried a similar problem in this website here and got idea that odd permutation cannot be expressed. So I am trying to express even permutation now.
Please help me
Thanking you