Great to know this, thank you for that insight!

Very interesting, thank you for sharing! I'd imagine that you could reach every cluster in that way when working with type $A_n$ guys. Do you know if it's true?

Thank you both for your comments, you have been very helpful.

Hi @JanGrabowski, thank you for your comment. Seems like I am failing in explaining myself properly. Say we have an initial seed arising from a triangulation (of a marked surface). I can flip a diagonal $a$ to get a diagonal $c$, say, then flip some diagonal $b$. Then I could flip $c$, but I don't want to allow for that as $c$ wasn't in the initial cluster. On the other hand, flipping $a$ then $b$ is fine. Does that make more sense?

Hi @SamHopkins, thanks for the comment. I am asking if we can get every cluster variable by mutating at variables from the initial seed only. So say if $ex=\{x_1,\dots,x_k\}$ then, for instance, we can do $\mu_{x_k}\circ \cdots \circ \mu_{x_1}$ or just $\mu_{x_1} \circ \mu_{x_2}$, etc . Yeah, that's too much to ask, as you pointed out. Maybe it is true for finite type guys.

I see. Thank you, Jan.

Yes, when we don't invert the coefficients, this is true. I am still not sure if it holds if we do invert them (the coefficients).

My apologies for a late reply and thank you for such a great answer! I must say that the I feel like I have never paid enough attention to a (choice of) coefficient ring and I also feel like I should really try to understand its role better. Your answer will definitely be a great reference for that! Thanks again!

@JanGrabowski I see, thank you!

I would be interesting in both @JohnMachacek