# orbit

• Nov 9th 2009, 12:52 AM
Sampras
orbit
Suppose $\displaystyle f,g \in X$ and have the same pattern. Prove that $\displaystyle W(f) = W(g)$.

Now an orbit of and element $\displaystyle f$ in $\displaystyle X$ is all the "possible stuff" that a permutation $\displaystyle \pi$ can map $\displaystyle f$ to. So does $\displaystyle f,g \in X$ imply that they are in the same orbit?
• Nov 9th 2009, 03:28 AM
Drexel28
Quote:

Originally Posted by Sampras
Suppose $\displaystyle f,g \in X$ and have the same pattern. Prove that $\displaystyle W(f) = W(g)$.

Now an orbit of and element $\displaystyle f$ in $\displaystyle X$ is all the "possible stuff" that a permutation $\displaystyle \pi$ can map $\displaystyle f$ to. So does $\displaystyle f,g \in X$ imply that they are in the same orbit?

I'm sorry. Maybe some other member will swoop in and help you. But if not, I just have two questions. What does 'pattern' mean in this context? and what is $\displaystyle W(y)$ represent. Also, what is $\displaystyle X$? Just some group under consideration? If so, then $\displaystyle f,g\in X$ does not mean that $\displaystyle f\in\mathcal{O}(g)$ or vice versa (which is really the same thing).
• Nov 9th 2009, 04:08 AM
tonio
Quote:

Originally Posted by Sampras
Suppose $\displaystyle f,g \in X$ and have the same pattern. Prove that $\displaystyle W(f) = W(g)$.

Now an orbit of and element $\displaystyle f$ in $\displaystyle X$ is all the "possible stuff" that a permutation $\displaystyle \pi$ can map $\displaystyle f$ to. So does $\displaystyle f,g \in X$ imply that they are in the same orbit?

If you don't properly define your "stuff" people won't properly understand it: what are f,g? What is a "pattern" for them? What is W(f)? What is X?
What action of what group (presumably $\displaystyle S_n$) on what set are we talkin about here?

Tonio